Comprehensive Profile of White Matter Changes Following Traumatic Brain Injury in a Densely Sampled Participant

Notes

Figure 1-mixed model a,b,c,d - a, c=>mixed models

Figure 2- cog and emotion

Figure 3-dbsi-mixed model + individual tract

Figure 4 Mixed Model effects for all participants Not as dense evaluation

Figure 5- one year follow-up

Right Cingulum Bundle is significant for all dBSI metrics. Consider.

Data Snapshot

DaysSinceTBI	WeeksSinceTBI_label	WeeksSinceTBI	Tract	FA	AD	RD	MD	fiber_ratio_map	fiber1_ratio_map	fiber2_ratio_map	fiber3_ratio_map	cell_ratio_map	water_ratio_map	perfusion_ratio_map	hind_ratio_map	Dep_BDI	Anx_BAI	GNG_MeanTrimmedCorrectGoRT	GNG_GoTrialAccuracy	GNG_MeanTrimmedNoGoRT	GNG_NoGoTrialAccuracy	dprimeScore	NUMSYM_MeanTrimmedCorrectRT	NUMSYM_Accuracy	ANTISACC_MeanTrimmedCorrectRT	ANTISACC_Accuracy	MotionType	HeadMotion	WeeksSinceTBI_norm	HeadMotion_norm	WeeksSinceTBI_norm2	WeeksSinceTBI_z	WeeksSinceTBI_z2	HeadMotion_z	dprimeScore_z	NUMSYM_RT_z	ANTISACC_RT_z	Anx_BAI_z	Dep_BDI_z
1	Week1	1	forceps major	0.5825151	0.000833279	0.000286841	0.000468987	0.8912177	0.7120187	0.09056854	0.08863013	0.01885955	0.05280789	0.01808319	0.01871481	38	24	297.6661	0.985	243.3222	0.48	2.033184	1324.360	0.9310345	906.5447	0.8928571	Absolute	1.15	0.00000000	0.33834586	0.00000000	-1.668473	2.783804	0.7318824	-1.371796965	2.134727	2.069394	1.990912	1.6710475
1	Week1	1	forceps major	0.5825151	0.000833279	0.000286841	0.000468987	0.8912177	0.7120187	0.09056854	0.08863013	0.01885955	0.05280789	0.01808319	0.01871481	38	24	297.6661	0.985	243.3222	0.48	2.033184	1324.360	0.9310345	906.5447	0.8928571	Relative	0.61	0.00000000	0.13533835	0.00000000	-1.668473	2.783804	-0.4437524	-1.371796965	2.134727	2.069394	1.990912	1.6710475
1	Week1	1	forceps major	0.5825151	0.000833279	0.000286841	0.000468987	0.8912177	0.7120187	0.09056854	0.08863013	0.01885955	0.05280789	0.01808319	0.01871481	38	24	297.6661	0.985	243.3222	0.48	2.033184	1324.360	0.9310345	906.5447	0.8928571	Combined	0.88	0.00000000	0.23684211	0.00000000	-1.668473	2.783804	0.1440650	-1.371796965	2.134727	2.069394	1.990912	1.6710475
7	Week2	2	forceps major	0.5885705	0.000835230	0.000282993	0.000467072	0.8925706	0.7293279	0.08434395	0.07889841	0.01708641	0.05133848	0.02133046	0.01735954	23	14	267.6253	1.000	263.1091	0.52	2.649414	1419.198	0.9482759	819.2654	0.9285714	Absolute	0.72	0.03846154	0.17669173	0.00147929	-1.540129	2.371998	-0.2042712	0.003094785	2.554826	1.118071	0.463792	-0.1433606
7	Week2	2	forceps major	0.5885705	0.000835230	0.000282993	0.000467072	0.8925706	0.7293279	0.08434395	0.07889841	0.01708641	0.05133848	0.02133046	0.01735954	23	14	267.6253	1.000	263.1091	0.52	2.649414	1419.198	0.9482759	819.2654	0.9285714	Relative	0.37	0.03846154	0.04511278	0.00147929	-1.540129	2.371998	-0.9662567	0.003094785	2.554826	1.118071	0.463792	-0.1433606
7	Week2	2	forceps major	0.5885705	0.000835230	0.000282993	0.000467072	0.8925706	0.7293279	0.08434395	0.07889841	0.01708641	0.05133848	0.02133046	0.01735954	23	14	267.6253	1.000	263.1091	0.52	2.649414	1419.198	0.9482759	819.2654	0.9285714	Combined	0.54	0.03846154	0.10902256	0.00147929	-1.540129	2.371998	-0.5961495	0.003094785	2.554826	1.118071	0.463792	-0.1433606

Head Motion

Relative head motion shows the least variance and will therefore be used for all further analyses. Wherever the variable HeadMotion is used/mentioned, it implies relative head motion.

DTI Trajectory

Theoretical framework for quadratic model fit

Recovery from TBI may involve rapid, early plastic changes (including synaptogenesis and cortical map reorganization). However, these changes are short-lived, transitioning into more gradual, activity-dependent adaptations. This pattern of recovery reflects a curvilinear trajectory where rapid changes taper off, and improvements occur more slowly or in spurts, depending on rehabilitation and environmental influences (Nudo, 2013, Zotey, 2023). Therefore, both linear and quadratic mixed effects models will be tested to assess the trajectory of diffusion metrics over time and across tracts.

References

Nudo, R. J. (2013). Recovery after brain injury: mechanisms and principles. Frontiers in human neuroscience, 7, 887.
Zotey, V., Andhale, A., Shegekar, T., & Juganavar, A. (2023). Adaptive neuroplasticity in brain injury recovery: Strategies and insights. Cureus, 15(9).

Model Fit Decision Process

Biopsychosocial Model Fit

FA Trajectory

What is FA

FA is Fractional Anisotropy.
Fractional Anisotropy (FA) is a measure of white matter integrity. FA is used to quantify the degree of direction of water diffusion in white matter. Water tends to diffuse more easily along the axonal fibers of white matter tracts than across them.
FA values range from 0 to 1, where:
- 0 indicates isotropic diffusion, meaning water diffuses equally in all directions (e.g., in cerebrospinal fluid or gray matter).
- 1 indicates completely anisotropic diffusion, meaning water diffuses only along one direction, which is characteristic of healthy, coherent white matter tracts.
FA is an important biomarker for assessing white matter integrity following TBI. A decrease in FA has commonly been interpreted as a loss of white matter (WM) integrity. Hypotheses for this loss of WM integrity include axonal injury, demyelination, and/or disruption of microstructural organization.

Objective assessment of quadratic model fit

WeeksSinceTBI_z | Tract: This tells the model to allow each tract to have its own slope for WeeksSinceTBI. Both the intercept and the slope can vary between tracts.

Linear Model

mixed.model_linear <- lmer(FA ~ WeeksSinceTBI_z + HeadMotion_z + (WeeksSinceTBI_z | Tract), data = data)

Quadratic Model

mixed.model_quadratic <- lmer(FA ~ WeeksSinceTBI_z + I(WeeksSinceTBI_z^2) + HeadMotion_z + (WeeksSinceTBI_z | Tract), data = data)

Which model is better?

Model Comparison Metric	Linear Model	Quadratic Model	Interpretation
AIC (BIC)	-3737.9 (-3708.6)	-3791.2 (-3757.7)	Quadratic model is better (AIC_Q < AIC_L)
Log Likelihood	1876.0	1903.6	Quadratic model is better (AIC_Q < AIC_L)
Anova		p-value=1.048e-13***	Anova model comparison => quadratic model significantly different from linear model

Is a random slope model necessary?

We find that a quadratic model better explains FA trajectory. In this model, we determine whether rate of FA change differs by tract. The significant p-value ssociated with the model with the random slope suggests that rate of FA change significantly differs by tract.

Model Comparison Metric	No Slope Quadratic Model	With Slope Quadratic Model
AIC (BIC)	-3737.9 (-3708.6)	-3791.2 (-3757.7)
Log Likelihood	1876.0	1903.6
Anova		p-value=1.048e-13***

Confidence Intervals Generated by Bootstrapping (n=1000)

Description	2.5 %	97.5 %	Significance
Variance of the Random Intercept by Tract	0.0299542	0.0602082	Significant variability in the intercept across tracts
Variance of the random slope for WeeksSinceTBI linear	-0.8350131	-0.0282876	No significant variability in linear slope across tracts
Variance of the random slope for WeeksSinceTBI_z^2 quadratic	0.0009287	0.0023405	Significant variability in quadratic slope across tracts
Residual or unexplained variance	0.0037738	0.0043187	Unexplained variance is significant
Predicted FA value at baseline (when WeeksSinceTBI_z and HeadMotion_z are 0)	0.4806064	0.5210649	Predicted FA value at baseline is significant
Linear effect of WeeksSinceTBI on FA	-0.0030722	-0.0014126	There is a significant descrease in FA as WeeksSinceTBI increases
Quadratic effect of WeeksSinceTBI on FA	0.0011863	0.0020131	There is a significant U-Shaped Relationship between FA and WeeksSinceTBI
Linear effect of Head Motion	-0.0063866	-0.0042053	Lower FA is significantly associated with higher head motion

## Error in `mutate()`:
## ℹ In argument: `Baseline_Predicted = predicted[WeeksSinceTBI == 1]`.
## ℹ In group 1: `Tract = forceps major`.
## Caused by error:
## ! object 'predicted' not found

## Error: object 'normalized_predicted_data' not found

This plot illustrates the predicted FA across different values of time since TBI, accounting for both linear and quadratic effects and adjusting for random effects of Tract (i.e., holding random effects constant, focusing on the relationship between weeks since TBI with FA, in isolation).

RD Trajectory

What is RD

RD is Radial Diffusivity.
Radial diffusivity (RD) represents the degree of water diffusion perpendicular to the main direction of white matter fibers (i.e., across axons and their surrounding myelin sheaths).
It is used to index changes in the myelin sheath around axons. Increases in RD are often interpreted as indicating myelin damage or demyelination, where the insulating layer around the axons is compromised.

Objective assessment of quadratic model fit

WeeksSinceTBI_z | Tract: This tells the model to allow each tract to have its own slope for WeeksSinceTBI. Both the intercept and the slope can vary between tracts.

Linear Model

mixed.model_linear <- lmer(RD ~ WeeksSinceTBI_z + HeadMotion_z + (WeeksSinceTBI_z | Tract), data = data)

Quadratic Model

mixed.model_quadratic <- lmer(RD ~ WeeksSinceTBI_z + I(WeeksSinceTBI_z^2) + HeadMotion_z + (WeeksSinceTBI_z | Tract), data = data)

Which model is better?

Model Comparison Metric	Linear Model	Quadratic Model	Interpretation
AIC (BIC) -	10726 (-10697) -	10788 (-10754)	Quadratic model is better (AIC_Q < AIC_L)
Log Likelihood	5370.3	5401.9	Quadratic model is better (AIC_Q < AIC_L)
Anova		p-value=1.875e-15 ***	Anova model comparison => quadratic model significantly different from linear model

Is a random slope model necessary?

We find that a quadratic model better explains RD trajectory. In this model, we determine whether rate of RD change differs by tract. The significant p-value ssociated with the model with the random slope suggests that rate of RD change significantly differs by tract.

Model Comparison Metric	No Slope Quadratic Model	With Slope Quadratic Model
AIC (BIC)	-10756 (-10731)	-10788 (-10754)
Log Likelihood	5384.3	5401.9
Anova		p-value=2.304e-08 ***

Confidence Intervals Generated by Bootstrapping (n=1000)

Description	2.5 %	97.5 %	Significance
Variance of the Random Intercept by Tract	0.0000248	0.0000487	Significant variability in the intercept across tracts
Variance of the random slope for WeeksSinceTBI linear	-0.6099353	0.4831035	No significant variability in linear slope across tracts
Variance of the random slope for WeeksSinceTBI_z^2 quadratic	0.0000006	0.0000017	Significant variability in quadratic slope across tracts
Residual or unexplained variance	0.0000028	0.0000032	Unexplained variance is significant
Predicted RD value at baseline (when WeeksSinceTBI_z and HeadMotion_z are 0)	0.0003127	0.0003485	Predicted RD value at baseline is significant
Linear effect of WeeksSinceTBI on RD	0.0000015	0.0000027	There is a significant descrease in RD as WeeksSinceTBI increases
Quadratic effect of WeeksSinceTBI on RD	-0.0000016	-0.0000010	There is a significant U-Shaped Relationship between RD and WeeksSinceTBI
Linear effect of Head Motion	0.0000020	0.0000037	Lower RD is significantly associated with higher head motion

## Error in `mutate()`:
## ℹ In argument: `Baseline_Predicted = predicted[WeeksSinceTBI == 1]`.
## ℹ In group 1: `Tract = forceps major`.
## Caused by error:
## ! object 'predicted' not found

## Error: object 'normalized_predicted_data' not found

This plot illustrates the predicted RD across different values of time since TBI, accounting for both linear and quadratic effects and adjusting for random effects of Tract (i.e., holding random effects constant, focusing on the relationship between weeks since TBI with RD, in isolation).

AD Trajectory

What is AD

AD is Axial Diffusivity.
Axial diffusivity (AD) represents the diffusion of water molecules along the primary axis of a white matter tract (i.e.,the principal direction of diffusion).
Changes in axial integrity may be indicative of axonal damage following TBI.

Objective assessment of quadratic model fit

Linear Model

mixed.model_linear <- lmer(AD ~ WeeksSinceTBI_z + HeadMotion_z + (WeeksSinceTBI_z | Tract), data = data)

Quadratic Model

mixed.model_quadratic <- lmer(AD ~ WeeksSinceTBI_z + I(WeeksSinceTBI_z^2) + HeadMotion_z + (WeeksSinceTBI_z | Tract), data = data)

Which model is better?

Model Comparison Metric	Linear Model	Quadratic Model	Interpretation
AIC (BIC) -	10264 (-10235)	-10264 (-10230)	Linear model is sufficient
Log Likelihood	5139.2	5139.8	Linear model is sufficient
Anova		p-value=0.2879	Quadratic is not significantly adding anything to linear model; stick with linear model

Is a random slope model necessary?

We find that a linear model is sufficient to describe the AD trajectory. In this model, we determine whether rate of AD change differs by tract. A parsimonious linear mixed effects model with only random intercept across tracts was deemed a better fit. Thus,a random slope model was not considered necessary to assess the trajectory of AD over time across tracts.

Model Comparison Metric	No Slope Linear Model	With Slope Linear Model
AIC (BIC)	-10249 (-10228)	10264 (-10235)
Log Likelihood	5129.4	5139.2
Anova		p-value=5.51e-05 ***

Confidence Intervals Generated by Bootstrapping (n=1000)

Even though the AIC, BIC, and likelihood test shows the linear model fits better with random slopes, convergence/boundary fit issues were encountered when trying to build confidence intervals using bootstrapping. The boundary (singular) fit error suggests that the model may be overfitting or estimating parameters poorly. When overfitting occurs, the improvement in fit may not generalize well to new data. Thus, simplifying the model increases parsimony and ensures robustness. To this end, only a random intercept model will be considered.

Description	2.5 %	97.5 %	Significance
Variance of the Random Intercept by Tract	0.0000441	0.0000852	Significant variability in the intercept across tracts
Residual or unexplained variance	0.0000051	0.0000058	Unexplained variance is significant
Predicted AD value at baseline (when WeeksSinceTBI_z and HeadMotion_z are 0)	0.0007426	0.0008015	Predicted AD value at baseline is significant
Linear effect of WeeksSinceTBI on AD	0.0000012	0.0000021	There is a significant descrease in AD as WeeksSinceTBI increases
Linear effect of Head Motion	-0.0000036	-0.0000006	Lower AD is significantly associated with higher head motion

On the X-axis, “Weeks Since TBI (z)” represents z-scored values of weeeks since the injury, which center around 0 (the mean in the data) and spread out to ±1 or more standard deviations from the mean.
Essentially, the plot illustrates the predicted AD across different values of time since TBI, accounting for both linear and quadratic effects and adjusting for random effects of Tract (i.e., holding random effects constant, focusing on the relationship between weeks since TBI with AD, in isolation).

MD Trajectory

What is MD

MD is Mean Diffusivity.
Mean diffusivity (MD) represents the average diffusion of water molecules within a voxel. It reflects the overall magnitude of water diffusion in all directions, without favoring any particular direction (unlike FA, AD, and MD).
As a non-directional measure of tissue integrity, it’s interpretation is as follows:
- Low MD: Indicates restricted diffusion, which can be due to dense cellular structures, such as in healthy white matter. However, in pathological conditions like edema or cell swelling, it can increase due to the buildup of water content.
- High MD: Suggests increased water diffusion, which may reflect tissue degeneration, loss of cellular barriers (such as in atrophy or demyelination), or the presence of free extracellular water.

Objective assessment of quadratic model fit

WeeksSinceTBI_z | Tract: This tells the model to allow each tract to have its own slope for WeeksSinceTBI. Both the intercept and the slope can vary between tracts.

Linear Model

mixed.model_linear <- lmer(MD ~ WeeksSinceTBI_z + HeadMotion_z + (WeeksSinceTBI_z | Tract), data = data)

Quadratic Model

mixed.model_quadratic <- lmer(MD ~ WeeksSinceTBI_z + I(WeeksSinceTBI_z^2) + HeadMotion_z + (WeeksSinceTBI_z | Tract), data = data)

Which model is better?

Model Comparison Metric	Linear Model	Quadratic Model	Interpretation
AIC (BIC) -	10735 (-10706) -	10767 (-10733)	Quadratic model is better (AIC_Q < AIC_L)
Log Likelihood	5374.5	5391.3	Quadratic model is better (AIC_Q < AIC_L)
Anova		p-value=6.639e-09 ***	Anova model comparison => quadratic model significantly different from linear model

Is a random slope model necessary?

We find that a quadratic model better explains MD trajectory. In this model, we determine whether rate of MD change differs by tract. A parsimonious quadratic mixed effects model with only random intercept across tracts was deemed a better fit. Thus,a random slope model was not considered necessary to assess the trajectory of MD over time across tracts.

Model Comparison Metric	No Slope Quadratic Model	With Slope Quadratic Model
AIC (BIC)	-10748 (-10722)	-10767 (-10733)
Log Likelihood	5379.8	5391.3
Anova		p-value=9.928e-06 ***

Confidence Intervals Generated by Bootstrapping (n=1000)

Even though the AIC, BIC, and likelihood test shows the linear model fits better with random slopes, convergence/boundary fit issues were encountered when trying to build confidence intervals using bootstrapping. The boundary (singular) fit error suggests that the model may be overfitting or estimating parameters poorly. When overfitting occurs, the improvement in fit may not generalize well to new data. Thus, simplifying the model increases parsimony and ensures robustness. To this end, only a random intercept model will be considered.

Description	2.5 %	97.5 %	Significance
Variance of the Random Intercept by Tract	2.64e-05	0.0000516	Significant variability in the intercept across tracts
Residual or unexplained variance	3.00e-06	0.0000034	Unexplained variance is significant
Predicted MD value at baseline (when WeeksSinceTBI_z and HeadMotion_z are 0)	4.60e-04	0.0004976	Predicted MD value at baseline is significant
Linear effect of WeeksSinceTBI on MD	1.70e-06	0.0000022	There is a significant descrease in MD as WeeksSinceTBI increases
Quadratic effect of WeeksSinceTBI on MD	-1.30e-06	-0.0000006	There is a significant U-Shaped Relationship between MD and WeeksSinceTBI
Linear effect of Head Motion	1.00e-07	0.0000020	Lower MD is significantly associated with higher head motion

On the X-axis, “Weeks Since TBI (z)” represents z-scored values of weeeks since the injury, which center around 0 (the mean in the data) and spread out to ±1 or more standard deviations from the mean.
Essentially, the plot illustrates the predicted MD across different values of time since TBI, accounting for both linear and quadratic effects and adjusting for random effects of Tract (i.e., holding random effects constant, focusing on the relationship between weeks since TBI with MD, in isolation).

DTI: Summary models

DiffusionMetric	BestModelFit
FA	Random Slope Quadratic Mixed Effects Model
RD	Random Slope Quadratic Mixed Effects Model
AD	Random Intercept Linear Mixed Effects Model
MD	Random Intercept Quadratic Mixed Effects Model

DTI: Descriptive Table

Note that for the descriptive table further below, the trajectory of AD is better described by a linear model, so quadratic-fitted models should not be considered.

DiffusionMetric	BestModelFit
FA	Random Slope Quadratic Mixed Effects Model
RD	Random Slope Quadratic Mixed Effects Model
AD	Random Intercept Linear Mixed Effects Model
MD	Random Intercept Quadratic Mixed Effects Model

All metrics by Tract

Descriptive Statistics of Diffusion Metric Trajectories
Tract	Metric	MinValue	MaxValue	R_Sqrd_AIC_Linear	R_Sqrd_AIC_Quadratic	BetaTime_Linear	BetaTime_Quadratic	BetaTimeSqrd_Quadratic	Vertex_Within_Range	Vertex_Value	ParabolaDirection
forceps major	FA	0.5683, Week: 20	0.5886, Week: 2	0.524, AIC: -225.963	0.806, AIC: -248.143	-4.1e-04***	-1.68e-03***	4.57e-05***	Yes	18.437	/\
forceps major	AD	8e-04, Week: 5	8e-04, Week: 27	0.505, AIC: -584.972	0.536, AIC: -584.727	4.5e-07***	9.89e-07*	-1.93e-08	Yes	25.592	\/
forceps major	RD	3e-04, Week: 2	3e-04, Week: 20	0.561, AIC: -601.285	0.813, AIC: -622.281	4.43e-07***	1.65e-06***	-4.31e-08***	Yes	19.099	\/
forceps major	MD	5e-04, Week: 5	5e-04, Week: 20	0.582, AIC: -601.992	0.746, AIC: -613.423	4.45e-07***	1.43e-06***	-3.52e-08***	Yes	20.288	\/
forceps minor	FA	0.4999, Week: 18	0.5233, Week: 3	0.444, AIC: -216.252	0.54, AIC: -219.406	-3.08e-04**	-1.14e-03**	2.96e-05*	Yes	19.143	/\
forceps minor	AD	8e-04, Week: 4	8e-04, Week: 21	0.084, AIC: -566.346	0.084, AIC: -564.352	2.2e-07	2.65e-07	-1.61e-09	No	82.386	\/
forceps minor	RD	3e-04, Week: 3	3e-04, Week: 18	0.34, AIC: -592.095	0.413, AIC: -593.272	2.77e-07**	9.05e-07*	-2.25e-08	Yes	20.121	\/
forceps minor	MD	5e-04, Week: 4	5e-04, Week: 21	0.228, AIC: -586.703	0.262, AIC: -585.9	2.58e-07*	6.92e-07	-1.55e-08	Yes	22.274	\/
left atr	FA	0.456, Week: 7	0.4798, Week: 3	0.099, AIC: -205.938	0.141, AIC: -205.252	-1.78e-04	-7.02e-04	1.88e-05	Yes	18.705	/\
left atr	AD	7e-04, Week: 2	7e-04, Week: 20	0.149, AIC: -584.324	0.19, AIC: -583.671	1.82e-07	6.62e-07	-1.72e-08	Yes	19.263	\/
left atr	RD	3e-04, Week: 6	3e-04, Week: 7	0.15, AIC: -591.803	0.201, AIC: -591.456	1.97e-07	6.58e-07	-1.65e-08	Yes	19.900	\/
left atr	MD	5e-04, Week: 5	5e-04, Week: 20	0.176, AIC: -596.801	0.236, AIC: -596.858	1.92e-07*	6.6e-07	-1.68e-08	Yes	19.682	\/
right atr	FA	0.454, Week: 18	0.4822, Week: 3	0.555, AIC: -209.724	0.703, AIC: -218.634	-4.56e-04***	-1.75e-03***	4.63e-05**	Yes	18.881	/\
right atr	AD	7e-04, Week: 10	7e-04, Week: 1	0.027, AIC: -575.631	0.028, AIC: -573.651	1.06e-07	3.63e-08	2.49e-09	No	-7.279	/\
right atr	RD	3e-04, Week: 3	3e-04, Week: 18	0.523, AIC: -595.932	0.634, AIC: -601.025	3.5e-07***	1.19e-06**	-3.02e-08*	Yes	19.745	\/
right atr	MD	5e-04, Week: 4	5e-04, Week: 18	0.367, AIC: -595.901	0.427, AIC: -596.575	2.69e-07**	8.08e-07*	-1.93e-08	Yes	20.908	\/
left cab	FA	0.4504, Week: 7	0.4669, Week: 16	0.219, AIC: -215.344	0.224, AIC: -213.521	7.24e-05	2.36e-04	-5.85e-06	Yes	20.146	\/
left cab	AD	8e-04, Week: 5	9e-04, Week: 18	0.154, AIC: -563.93	0.251, AIC: -565.218	3.33e-07*	1.41e-06*	-3.85e-08	Yes	18.282	\/
left cab	RD	4e-04, Week: 2	4e-04, Week: 7	0.349, AIC: -617.944	0.405, AIC: -618.378	7.29e-08	4.16e-07	-1.23e-08	Yes	16.927	\/
left cab	MD	5e-04, Week: 12	5e-04, Week: 18	0.237, AIC: -605.202	0.357, AIC: -607.833	1.6e-07*	7.46e-07*	-2.1e-08*	Yes	17.754	\/
right cab	FA	0.454, Week: 25	0.472, Week: 2	0.462, AIC: -228.683	0.526, AIC: -230.141	-1.95e-04*	3.52e-04	-1.96e-05	Yes	8.989	\/
right cab	AD	8e-04, Week: 4	9e-04, Week: 20	0.171, AIC: -563.503	0.252, AIC: -564.31	2.79e-07	1.28e-06	-3.6e-08	Yes	17.831	\/
right cab	RD	4e-04, Week: 4	4e-04, Week: 13	0.367, AIC: -605.862	0.372, AIC: -604.069	2.33e-07**	3.61e-07	-4.57e-09	No	39.512	\/
right cab	MD	5e-04, Week: 4	6e-04, Week: 20	0.237, AIC: -594.135	0.278, AIC: -593.623	2.49e-07*	6.69e-07	-1.5e-08	Yes	22.218	\/
left cing	FA	0.5776, Week: 13	0.604, Week: 6	0.096, AIC: -193.793	0.182, AIC: -194.498	-2.41e-04	-1.17e-03	3.33e-05	Yes	17.578	/\
left cing	AD	8e-04, Week: 5	9e-04, Week: 1	0.02, AIC: -563.09	0.064, AIC: -562.318	1.14e-07	-5.66e-07	2.44e-08	Yes	11.624	/\
left cing	RD	3e-04, Week: 6	3e-04, Week: 13	0.162, AIC: -589.509	0.232, AIC: -589.85	2.14e-07*	7.83e-07	-2.04e-08	Yes	19.189	\/
left cing	MD	5e-04, Week: 6	5e-04, Week: 20	0.149, AIC: -596.006	0.155, AIC: -594.212	1.8e-07	3.33e-07	-5.48e-09	No	30.393	\/
right cing	FA	0.5816, Week: 22	0.623, Week: 3	0.649, AIC: -195.286	0.715, AIC: -198.944	-9.3e-04***	-2.2e-03***	4.56e-05*	Yes	24.156	/\
right cing	AD	8e-04, Week: 7	9e-04, Week: 1	0.059, AIC: -546.397	0.183, AIC: -548.201	-2.68e-07	-1.86e-06*	5.7e-08	Yes	16.306	/\
right cing	RD	3e-04, Week: 3	3e-04, Week: 22	0.739, AIC: -603.261	0.789, AIC: -606.891	6.08e-07***	1.27e-06***	-2.38e-08*	Yes	26.714	\/
right cing	MD	5e-04, Week: 4	5e-04, Week: 18	0.407, AIC: -599.602	0.409, AIC: -597.679	3.16e-07***	2.28e-07	3.14e-09	No	-36.328	/\
left cst	FA	0.5041, Week: 5	0.5263, Week: 3	0.24, AIC: -203.548	0.304, AIC: -203.903	-1.87e-04	-9.13e-04	2.6e-05	Yes	17.558	/\
left cst	AD	7e-04, Week: 5	7e-04, Week: 20	0.234, AIC: -588.489	0.239, AIC: -586.634	2.37e-07*	8.93e-08	5.28e-09	No	-8.450	/\
left cst	RD	3e-04, Week: 6	3e-04, Week: 13	0.303, AIC: -604.538	0.352, AIC: -604.492	2.02e-07*	5.98e-07	-1.42e-08	Yes	21.097	\/
left cst	MD	4e-04, Week: 6	4e-04, Week: 13	0.334, AIC: -614.318	0.354, AIC: -613.126	2.14e-07**	4.28e-07	-7.68e-09	No	27.871	\/
right cst	FA	0.5066, Week: 5	0.5274, Week: 3	0.533, AIC: -225.867	0.581, AIC: -226.779	-2.03e-04*	-7.34e-04*	1.9e-05	Yes	19.280	/\
right cst	AD	7e-04, Week: 4	7e-04, Week: 1	0.06, AIC: -584.769	0.092, AIC: -583.719	7.49e-08	-3.26e-07	1.44e-08	Yes	11.351	/\
right cst	RD	3e-04, Week: 2	3e-04, Week: 5	0.575, AIC: -632.073	0.586, AIC: -630.787	1.43e-07**	2.88e-07	-5.2e-09	No	27.721	\/
right cst	MD	4e-04, Week: 4	4e-04, Week: 20	0.28, AIC: -624.128	0.281, AIC: -622.162	1.2e-07*	8.34e-08	1.32e-09	No	-31.483	/\
left ilf	FA	0.5, Week: 7	0.5207, Week: 3	0.128, AIC: -214.907	0.331, AIC: -220.089	-3.17e-06	-9.87e-04*	3.52e-05*	Yes	14.001	/\
left ilf	AD	8e-04, Week: 5	9e-04, Week: 18	0.456, AIC: -576.552	0.519, AIC: -577.864	5.28e-07***	1.38e-06*	-3.06e-08	Yes	22.585	\/
left ilf	RD	3e-04, Week: 3	4e-04, Week: 7	0.167, AIC: -598.155	0.473, AIC: -608.52	1.7e-07	1.19e-06***	-3.66e-08**	Yes	16.277	\/
left ilf	MD	5e-04, Week: 2	5e-04, Week: 18	0.33, AIC: -598.518	0.553, AIC: -607.447	2.89e-07**	1.25e-06***	-3.46e-08**	Yes	18.137	\/
right ilf	FA	0.4814, Week: 18	0.5058, Week: 3	0.605, AIC: -219.569	0.687, AIC: -223.878	-5.44e-04***	-1.4e-03***	3.05e-05*	Yes	22.868	/\
right ilf	AD	8e-04, Week: 4	8e-04, Week: 20	0.584, AIC: -575	0.633, AIC: -576.412	7.35e-07***	1.63e-06**	-3.19e-08	Yes	25.472	\/
right ilf	RD	3e-04, Week: 4	4e-04, Week: 20	0.674, AIC: -592.609	0.763, AIC: -599.287	6.59e-07***	1.64e-06***	-3.5e-08**	Yes	23.357	\/
right ilf	MD	5e-04, Week: 4	5e-04, Week: 20	0.67, AIC: -590.386	0.749, AIC: -595.734	6.84e-07***	1.63e-06***	-3.4e-08*	Yes	24.019	\/
left slfp	FA	0.4782, Week: 18	0.4941, Week: 2	0.284, AIC: -231.984	0.456, AIC: -237.402	-1.11e-04	-8.38e-04**	2.6e-05*	Yes	16.096	/\
left slfp	AD	7e-04, Week: 7	7e-04, Week: 18	0.118, AIC: -598.702	0.12, AIC: -596.759	1.43e-07	6.6e-08	2.75e-09	No	-12.003	/\
left slfp	RD	3e-04, Week: 2	3e-04, Week: 18	0.253, AIC: -620.808	0.35, AIC: -622.568	1.18e-07*	5.17e-07*	-1.43e-08	Yes	18.083	\/
left slfp	MD	4e-04, Week: 7	4e-04, Week: 18	0.191, AIC: -618.858	0.227, AIC: -618.07	1.26e-07*	3.67e-07	-8.62e-09	Yes	21.282	\/
right slfp	FA	0.4839, Week: 13	0.503, Week: 3	0.442, AIC: -218.726	0.7, AIC: -233.458	-3.37e-04**	-1.63e-03***	4.62e-05***	Yes	17.609	/\
right slfp	AD	7e-04, Week: 19	7e-04, Week: 1	0.118, AIC: -602.321	0.144, AIC: -601.124	-1.21e-07	-3.88e-07	9.56e-09	Yes	20.275	/\
right slfp	RD	3e-04, Week: 3	3e-04, Week: 13	0.313, AIC: -618.357	0.593, AIC: -630.479	1.52e-07*	8.91e-07***	-2.65e-08***	Yes	16.819	\/
right slfp	MD	4e-04, Week: 2	4e-04, Week: 10	0.1, AIC: -626.163	0.246, AIC: -628.945	6.08e-08	4.65e-07*	-1.45e-08*	Yes	16.058	\/
left slft	FA	0.5232, Week: 13	0.5349, Week: 2	0.258, AIC: -234.144	0.413, AIC: -238.457	-1.42e-04	-7.93e-04**	2.33e-05*	Yes	17.005	/\
left slft	AD	7e-04, Week: 5	8e-04, Week: 19	0.188, AIC: -599.955	0.206, AIC: -598.564	1.2e-07	3.63e-07	-8.71e-09	Yes	20.821	\/
left slft	RD	3e-04, Week: 2	3e-04, Week: 18	0.215, AIC: -620.227	0.373, AIC: -624.292	1.35e-07*	6.37e-07**	-1.8e-08*	Yes	17.708	\/
left slft	MD	4e-04, Week: 5	5e-04, Week: 18	0.182, AIC: -619.994	0.294, AIC: -621.965	1.3e-07*	5.45e-07*	-1.49e-08	Yes	18.316	\/
right slft	FA	0.5001, Week: 18	0.5221, Week: 2	0.587, AIC: -217.462	0.779, AIC: -232.296	-5.48e-04***	-1.87e-03***	4.74e-05***	Yes	19.746	/\
right slft	AD	7e-04, Week: 7	7e-04, Week: 1	0.054, AIC: -605.155	0.112, AIC: -604.865	2.73e-08	-3.39e-07	1.31e-08	Yes	12.914	/\
right slft	RD	3e-04, Week: 2	3e-04, Week: 20	0.58, AIC: -614.011	0.73, AIC: -623.922	3.58e-07***	1.11e-06***	-2.69e-08**	Yes	20.623	\/
right slft	MD	4e-04, Week: 4	4e-04, Week: 20	0.484, AIC: -624.26	0.553, AIC: -626.093	2.48e-07***	6.26e-07**	-1.35e-08	Yes	23.115	\/
left unc	FA	0.4494, Week: 7	0.4727, Week: 3	0.105, AIC: -209.047	0.197, AIC: -209.968	-3.57e-05	-7.62e-04	2.6e-05	Yes	14.642	/\
left unc	AD	8e-04, Week: 2	8e-04, Week: 17	0.281, AIC: -575.687	0.312, AIC: -574.844	3.91e-07**	9.14e-07	-1.87e-08	Yes	24.399	\/
left unc	RD	4e-04, Week: 3	4e-04, Week: 7	0.186, AIC: -593.985	0.316, AIC: -596.706	1.77e-07	9.06e-07*	-2.61e-08*	Yes	17.350	\/
left unc	MD	5e-04, Week: 2	5e-04, Week: 17	0.251, AIC: -594.642	0.352, AIC: -596.555	2.49e-07*	9.09e-07*	-2.36e-08	Yes	19.211	\/
right unc	FA	0.4481, Week: 18	0.4706, Week: 12	0.46, AIC: -208.207	0.46, AIC: -206.209	-4.41e-04***	-4.19e-04	-7.77e-07	No	-270.041	\/
right unc	AD	8e-04, Week: 4	8e-04, Week: 20	0.168, AIC: -567.987	0.177, AIC: -566.281	2.97e-07	6.04e-07	-1.1e-08	No	27.491	\/
right unc	RD	4e-04, Week: 4	4e-04, Week: 18	0.423, AIC: -585.384	0.423, AIC: -583.393	4.24e-07***	4.63e-07	-1.4e-09	No	165.397	\/
right unc	MD	5e-04, Week: 4	5e-04, Week: 20	0.35, AIC: -585.446	0.352, AIC: -583.544	3.82e-07**	5.1e-07	-4.59e-09	No	55.504	\/

FA,RD by tract

Descriptive Statistics of Diffusion Metric Trajectories
Tract	Metric	MinValue	MaxValue	R_Sqrd_AIC_Linear	R_Sqrd_AIC_Quadratic	BetaTime_Linear	BetaTime_Quadratic	BetaTimeSqrd_Quadratic	Vertex_Within_Range	Vertex_Value	ParabolaDirection
forceps major	FA	0.5683, Week: 20	0.5886, Week: 2	0.524, AIC: -225.963	0.806, AIC: -248.143	-4.1e-04***	-1.68e-03***	4.57e-05***	Yes	18.437	/\
forceps major	RD	3e-04, Week: 2	3e-04, Week: 20	0.561, AIC: -601.285	0.813, AIC: -622.281	4.43e-07***	1.65e-06***	-4.31e-08***	Yes	19.099	\/
forceps minor	FA	0.4999, Week: 18	0.5233, Week: 3	0.444, AIC: -216.252	0.54, AIC: -219.406	-3.08e-04**	-1.14e-03**	2.96e-05*	Yes	19.143	/\
forceps minor	RD	3e-04, Week: 3	3e-04, Week: 18	0.34, AIC: -592.095	0.413, AIC: -593.272	2.77e-07**	9.05e-07*	-2.25e-08	Yes	20.121	\/
left atr	FA	0.456, Week: 7	0.4798, Week: 3	0.099, AIC: -205.938	0.141, AIC: -205.252	-1.78e-04	-7.02e-04	1.88e-05	Yes	18.705	/\
left atr	RD	3e-04, Week: 6	3e-04, Week: 7	0.15, AIC: -591.803	0.201, AIC: -591.456	1.97e-07	6.58e-07	-1.65e-08	Yes	19.900	\/
right atr	FA	0.454, Week: 18	0.4822, Week: 3	0.555, AIC: -209.724	0.703, AIC: -218.634	-4.56e-04***	-1.75e-03***	4.63e-05**	Yes	18.881	/\
right atr	RD	3e-04, Week: 3	3e-04, Week: 18	0.523, AIC: -595.932	0.634, AIC: -601.025	3.5e-07***	1.19e-06**	-3.02e-08*	Yes	19.745	\/
left cab	FA	0.4504, Week: 7	0.4669, Week: 16	0.219, AIC: -215.344	0.224, AIC: -213.521	7.24e-05	2.36e-04	-5.85e-06	Yes	20.146	\/
left cab	RD	4e-04, Week: 2	4e-04, Week: 7	0.349, AIC: -617.944	0.405, AIC: -618.378	7.29e-08	4.16e-07	-1.23e-08	Yes	16.927	\/
right cab	FA	0.454, Week: 25	0.472, Week: 2	0.462, AIC: -228.683	0.526, AIC: -230.141	-1.95e-04*	3.52e-04	-1.96e-05	Yes	8.989	\/
right cab	RD	4e-04, Week: 4	4e-04, Week: 13	0.367, AIC: -605.862	0.372, AIC: -604.069	2.33e-07**	3.61e-07	-4.57e-09	No	39.512	\/
left cing	FA	0.5776, Week: 13	0.604, Week: 6	0.096, AIC: -193.793	0.182, AIC: -194.498	-2.41e-04	-1.17e-03	3.33e-05	Yes	17.578	/\
left cing	RD	3e-04, Week: 6	3e-04, Week: 13	0.162, AIC: -589.509	0.232, AIC: -589.85	2.14e-07*	7.83e-07	-2.04e-08	Yes	19.189	\/
right cing	FA	0.5816, Week: 22	0.623, Week: 3	0.649, AIC: -195.286	0.715, AIC: -198.944	-9.3e-04***	-2.2e-03***	4.56e-05*	Yes	24.156	/\
right cing	RD	3e-04, Week: 3	3e-04, Week: 22	0.739, AIC: -603.261	0.789, AIC: -606.891	6.08e-07***	1.27e-06***	-2.38e-08*	Yes	26.714	\/
left cst	FA	0.5041, Week: 5	0.5263, Week: 3	0.24, AIC: -203.548	0.304, AIC: -203.903	-1.87e-04	-9.13e-04	2.6e-05	Yes	17.558	/\
left cst	RD	3e-04, Week: 6	3e-04, Week: 13	0.303, AIC: -604.538	0.352, AIC: -604.492	2.02e-07*	5.98e-07	-1.42e-08	Yes	21.097	\/
right cst	FA	0.5066, Week: 5	0.5274, Week: 3	0.533, AIC: -225.867	0.581, AIC: -226.779	-2.03e-04*	-7.34e-04*	1.9e-05	Yes	19.280	/\
right cst	RD	3e-04, Week: 2	3e-04, Week: 5	0.575, AIC: -632.073	0.586, AIC: -630.787	1.43e-07**	2.88e-07	-5.2e-09	No	27.721	\/
left ilf	FA	0.5, Week: 7	0.5207, Week: 3	0.128, AIC: -214.907	0.331, AIC: -220.089	-3.17e-06	-9.87e-04*	3.52e-05*	Yes	14.001	/\
left ilf	RD	3e-04, Week: 3	4e-04, Week: 7	0.167, AIC: -598.155	0.473, AIC: -608.52	1.7e-07	1.19e-06***	-3.66e-08**	Yes	16.277	\/
right ilf	FA	0.4814, Week: 18	0.5058, Week: 3	0.605, AIC: -219.569	0.687, AIC: -223.878	-5.44e-04***	-1.4e-03***	3.05e-05*	Yes	22.868	/\
right ilf	RD	3e-04, Week: 4	4e-04, Week: 20	0.674, AIC: -592.609	0.763, AIC: -599.287	6.59e-07***	1.64e-06***	-3.5e-08**	Yes	23.357	\/
left slfp	FA	0.4782, Week: 18	0.4941, Week: 2	0.284, AIC: -231.984	0.456, AIC: -237.402	-1.11e-04	-8.38e-04**	2.6e-05*	Yes	16.096	/\
left slfp	RD	3e-04, Week: 2	3e-04, Week: 18	0.253, AIC: -620.808	0.35, AIC: -622.568	1.18e-07*	5.17e-07*	-1.43e-08	Yes	18.083	\/
right slfp	FA	0.4839, Week: 13	0.503, Week: 3	0.442, AIC: -218.726	0.7, AIC: -233.458	-3.37e-04**	-1.63e-03***	4.62e-05***	Yes	17.609	/\
right slfp	RD	3e-04, Week: 3	3e-04, Week: 13	0.313, AIC: -618.357	0.593, AIC: -630.479	1.52e-07*	8.91e-07***	-2.65e-08***	Yes	16.819	\/
left slft	FA	0.5232, Week: 13	0.5349, Week: 2	0.258, AIC: -234.144	0.413, AIC: -238.457	-1.42e-04	-7.93e-04**	2.33e-05*	Yes	17.005	/\
left slft	RD	3e-04, Week: 2	3e-04, Week: 18	0.215, AIC: -620.227	0.373, AIC: -624.292	1.35e-07*	6.37e-07**	-1.8e-08*	Yes	17.708	\/
right slft	FA	0.5001, Week: 18	0.5221, Week: 2	0.587, AIC: -217.462	0.779, AIC: -232.296	-5.48e-04***	-1.87e-03***	4.74e-05***	Yes	19.746	/\
right slft	RD	3e-04, Week: 2	3e-04, Week: 20	0.58, AIC: -614.011	0.73, AIC: -623.922	3.58e-07***	1.11e-06***	-2.69e-08**	Yes	20.623	\/
left unc	FA	0.4494, Week: 7	0.4727, Week: 3	0.105, AIC: -209.047	0.197, AIC: -209.968	-3.57e-05	-7.62e-04	2.6e-05	Yes	14.642	/\
left unc	RD	4e-04, Week: 3	4e-04, Week: 7	0.186, AIC: -593.985	0.316, AIC: -596.706	1.77e-07	9.06e-07*	-2.61e-08*	Yes	17.350	\/
right unc	FA	0.4481, Week: 18	0.4706, Week: 12	0.46, AIC: -208.207	0.46, AIC: -206.209	-4.41e-04***	-4.19e-04	-7.77e-07	No	-270.041	\/
right unc	RD	4e-04, Week: 4	4e-04, Week: 18	0.423, AIC: -585.384	0.423, AIC: -583.393	4.24e-07***	4.63e-07	-1.4e-09	No	165.397	\/

DTI: Select Tract Plots

Commissural Tracts

Forceps Major

FA

ModelFit.Quadratic_vs_Linear	Metrics
Increase in Adjusted R²	0.2958511
ANOVA Comparison	0.0000070

RD

ModelFit.Quadratic_vs_Linear	Metrics
Increase in Adjusted R²	0.2637996
ANOVA Comparison	0.0000118

Projection Tracts

Right Anterior Thalamic Radiation

FA

ModelFit.Quadratic_vs_Linear	Metrics
Increase in Adjusted R²	0.1463576
ANOVA Comparison	0.0025547

RD

ModelFit.Quadratic_vs_Linear	Metrics
Increase in Adjusted R²	0.1020108
ANOVA Comparison	0.0150094

Association Tracts

Right Superior Longitudinal Fasiculus

FA

ModelFit.Quadratic_vs_Linear	Metrics
Increase in Adjusted R²	0.2651275
ANOVA Comparison	0.0001865

RD

ModelFit.Quadratic_vs_Linear	Metrics
Increase in Adjusted R²	0.2838504
ANOVA Comparison	0.0005980

dBSI Trajectory

Intro to DBSI

Model Fit Decision Process

Biopsychosocial Model Fit

Fiber Ratio Trajectory

What is Fiber Ratio

Fiber Ratio (FR) refers to the proportion of the imaging voxel occupied by fiber-like structures, such as axons or myelinated fibers, compared to other components (like free water or cellular elements).
A high fiber ratio indicates that a larger portion of the voxel is occupied by aligned fibers, which often corresponds to healthier, intact white matter. In areas with a high fiber ratio, diffusion tends to be more anisotropic (directionally dependent), with water moving more freely along the fiber direction (axial diffusivity) than perpendicular to it (radial diffusivity).
A low fiber ratio suggests less fiber density within the voxel, possibly due to degeneration, damage, or a mixture of other cellular or free water components. This may result in more isotropic diffusion, where water moves more equally in all directions, indicating lower structural integrity of the fibers.

Objective assessment of quadratic model fit

WeeksSinceTBI_z | Tract: This tells the model to allow each tract to have its own slope for WeeksSinceTBI. Both the intercept and the slope can vary between tracts.

Linear Model

mixed.model_linear <- lmer(fiber_ratio_map ~ WeeksSinceTBI_z + HeadMotion_z + (WeeksSinceTBI_z | Tract), data = data)

Quadratic Model

mixed.model_quadratic <- lmer(fiber_ratio_map ~ WeeksSinceTBI_z + I(WeeksSinceTBI_z^2) + HeadMotion_z + (WeeksSinceTBI_z | Tract), data = data)

Which model is better?

Model Comparison Metric	Linear Model	Quadratic Model	Interpretation
AIC (BIC) -	11622 (-11585)	-11684 (-11642)	Quadratic model is better (AIC_Q < AIC_L)
Log Likelihood	5818.0	5849.9	Quadratic model is better
Anova		p-value=1.322e-15 ***	Anova model comparison => quadratic model significantly different from linear model

Is a random slope model necessary?

We find that a quadratic model better explains fiber ratio trajectory. In this model, we determine whether rate of fiber ratio change differs by tract. The significant p-value associated with the model with the random slope suggests that rate of fiber ratio change significantly differs by tract.

Model Comparison Metric	No Slope Quadratic Model	With Slope Quadratic Model
AIC (BIC)	11655 (-11624)	-11684 (-11642)
Log Likelihood	5833.6	5849.9
Anova		p-value=8.52e-08 ***

Confidence Intervals Generated by Bootstrapping (n=1000)

Description	2.5 %	97.5 %	Significance
Variance of the Random Intercept by Tract	0.0042364	0.0086566	Significant variability in the intercept across tracts
Variance of the random slope for WeeksSinceTBI linear	-1.0000000	1.0000000	No significant variability in linear slope across tracts
Variance of the random slope for WeeksSinceTBI_z^2 quadratic	0.0000248	0.0010832	Significant variability in quadratic slope across tracts
Residual or unexplained variance	0.0040622	0.0046289	Unexplained variance is significant
Predicted fiber ratio at baseline (when WeeksSinceTBI_z and HeadMotion_z are 0)	0.9024536	0.9091571	Predicted fiber ratio value at baseline is significant
Linear effect of WeeksSinceTBI on fiber ratio	0.0002721	0.0011822	There is a significant descrease in fiber ratio as WeeksSinceTBI increases
Quadratic effect of WeeksSinceTBI on fiber ratio	-0.0014515	-0.0005463	There is a significant U-Shaped Relationship between fiber ratio and WeeksSinceTBI
Linear effect of Head Motion	-0.0015370	0.0008138	Lower fiber ratio is significantly associated with higher head motion

This plot illustrates the predicted RD across different values of time since TBI, accounting for both linear and quadratic effects and adjusting for random effects of Tract (i.e., holding random effects constant, focusing on the relationship between weeks since TBI with RD, in isolation).
On the X-axis, “Weeks Since TBI (z)” represents z-scored values of weeeks since the injury, which center around 0 (the mean in the data) and spread out to ±1 or more standard deviations from the mean.
The plot illustrates the predicted fiber ratio across different values of time since TBI, accounting for both linear and quadratic effects and adjusting for random effects of Tract (i.e., holding random effects constant, focusing on the relationship between weeks since TBI with fiber ratio, in isolation).

Cellularity Ratio Trajectory

What is Cellularity Ratio

It quantifies the proportion of a voxel occupied by cell bodies or cellular material, such as neurons, glial cells, or inflammatory cells.
This ratio provides information about the density of cells within the tissue, often associated with cellular responses, like inflammation or tumor growth, where cellular infiltration increases.
High cellularity can indicate pathological conditions, such as inflammation, tumors, or scarring. In such cases, high cellularity can crowd the extracellular space and impede water movement in all directions, which affects diffusion measures.

Objective assessment of quadratic model fit

WeeksSinceTBI_z | Tract: This tells the model to allow each tract to have its own slope for WeeksSinceTBI. Both the intercept and the slope can vary between tracts.

Linear Model

mixed.model_linear <- lmer(cell_ratio_map ~ WeeksSinceTBI_z + HeadMotion_z + (WeeksSinceTBI_z | Tract), data = data)

Quadratic Model

mixed.model_quadratic <- lmer(cell_ratio_map ~ WeeksSinceTBI_z + I(WeeksSinceTBI_z^2) + HeadMotion_z + (WeeksSinceTBI_z | Tract), data = data)

Which model is better?

Model Comparison Metric	Linear Model	Quadratic Model	Interpretation
AIC (BIC)	-15386 (-15349)	-15453 (-15410)	Quadratic model is better (AIC_Q < AIC_L)
Log Likelihood	7700.0	7734.3	Quadratic model is better
Anova		p-value< 2.2e-16 ***	Anova model comparison => quadratic model significantly different from linear model

Is a random slope model necessary?

We find that a quadratic model better explains cellularity ratio trajectory. In this model, we determine whether rate of cellularity ratio change differs by tract. The significant p-value associated with the model with the random slope suggests that rate of cellularity ratio change significantly differs by tract.

Model Comparison Metric	No Slope Quadratic Model	With Slope Quadratic Model
AIC (BIC)	-15421 (-15390)	-15453 (-15410)
Log Likelihood	7716.6	7734.3
Anova		p-value=1.949e-08 ***

Confidence Intervals Generated by Bootstrapping (n=1000)

Description	2.5 %	97.5 %	Significance
Variance of the Random Intercept by Tract	0.0033987	0.0067217	Significant variability in the intercept across tracts
Variance of the random slope for WeeksSinceTBI linear	-1.0000000	1.0000000	No significant variability in linear slope across tracts
Variance of the random slope for WeeksSinceTBI_z^2 quadratic	0.0000105	0.0002891	Significant variability in quadratic slope across tracts
Residual or unexplained variance	0.0010952	0.0012467	Unexplained variance is significant
Predicted cellularity ratio at baseline (when WeeksSinceTBI_z and HeadMotion_z are 0)	0.0130562	0.0176185	Predicted cellularity ratio value at baseline is significant
Linear effect of WeeksSinceTBI on cellularity ratio	-0.0006857	-0.0004192	The relationship between cellularity ratio and WeeksSinceTBI is not significant
Quadratic effect of WeeksSinceTBI on cellularity ratio	0.0001906	0.0004222	There is a significant U-Shaped Relationship between cellularity ratio and WeeksSinceTBI
Linear effect of Head Motion	0.0000446	0.0007145	Lower cellularity ratio is significantly associated with higher head motion

On the X-axis, “Weeks Since TBI (z)” represents z-scored values of weeeks since the injury, which center around 0 (the mean in the data) and spread out to ±1 or more standard deviations from the mean.
The plot illustrates the predicted cellularity ratio across different values of time since TBI, accounting for both linear and quadratic effects and adjusting for random effects of Tract (i.e., holding random effects constant, focusing on the relationship between weeks since TBI with cellularity ratio, in isolation).

Perfusion Ratio Trajectory

What is Perfusion Ratio

It refers to the proportion of a voxel’s signal that is attributed to perfusion — or blood flow — within the tissue. It differentiate between water diffusion due to cellular and extracellular structures and water movement that is primarily related to blood flow. Thus, the perfusion ratio isolates the component of diffusion that is specifically due to microvascular blood flow, rather than movement restricted by cellular structures or white matter tracts.
A higher perfusion ratio could indicate inflammatory responses or vascular changes in the affected tissue.
A low perfusion ratio might indicate areas of the brain that have reduced blood supply, possibly due to vascular damage or long-term changes in blood flow.

Objective assessment of quadratic model fit

WeeksSinceTBI_z | Tract: This tells the model to allow each tract to have its own slope for WeeksSinceTBI. Both the intercept and the slope can vary between tracts.

Linear Model

mixed.model_linear <- lmer(perfusion_ratio_map ~ WeeksSinceTBI_z + HeadMotion_z + (WeeksSinceTBI_z | Tract), data = data)

Quadratic Model

mixed.model_quadratic <- lmer(perfusion_ratio_map ~ WeeksSinceTBI_z + I(WeeksSinceTBI_z^2) + HeadMotion_z + (WeeksSinceTBI_z | Tract), data = data)

Which model is better?

Model Comparison Metric	Linear Model	Quadratic Model	Interpretation
AIC (BIC)	-13926 (-13889()	-13925 -13883	Linear model is better (AIC_L < AIC_Q)
Log Likelihood	6969.9	6970.6
Anova		p-value=0.2282	Quadratic model is not significant.

Is a random slope model necessary?

We find that a linear model better explains perfusion ratio trajectory. Testing against a random slope model, we did not find a significant effect of slope (p=0.07).

Model Comparison Metric	No Slope Linear Model	With Slope Linear Model
AIC (BIC)	-13924 (-13898)	-13926 (-13889)
Log Likelihood	6967.2	6969.9
Anova		p-value=0.06853 .

Confidence Intervals Generated by Bootstrapping (n=1000)

Description	2.5 %	97.5 %	Significance
Variance of the Random Intercept by Tract	0.0012776	0.0026151	Significant variability in the intercept across tracts
Residual or unexplained variance	0.0018808	0.0021455	Unexplained variance is significant
Predicted perfusion ratio at baseline (when WeeksSinceTBI_z and HeadMotion_z are 0)	0.0176581	0.0196948	Predicted perfusion ratio value at baseline is significant
Linear effect of WeeksSinceTBI on perfusion ratio	-0.0007550	-0.0003874	As WeeksSinceTBI increases, perfusion ratio significantly increases
Linear effect of Head Motion	-0.0003905	0.0007362	Perfusion ratio is not associated with head motion

On the X-axis, “Weeks Since TBI (z)” represents z-scored values of weeeks since the injury, which center around 0 (the mean in the data) and spread out to ±1 or more standard deviations from the mean.
The plot illustrates the predicted perfusion ratio across different values of time since TBI, accounting for linear effects only and adjusting for random intercept effects of Tract.

(Free) Water Ratio Trajectory

What is (Free) Water Ratio

This measures the proportion of water molecules that are moving freely without barriers, often representing extracellular fluid or edema. An increase in the free water ratio can suggest fluid accumulation, like in swelling.

Objective assessment of quadratic model fit

WeeksSinceTBI_z | Tract: This tells the model to allow each tract to have its own slope for WeeksSinceTBI. Both the intercept and the slope can vary between tracts.

Linear Model

mixed.model_linear <- lmer(water_ratio_map ~ WeeksSinceTBI_z + HeadMotion_z + (WeeksSinceTBI_z | Tract), data = data)

Quadratic Model

mixed.model_quadratic <- lmer(water_ratio_map ~ WeeksSinceTBI_z + I(WeeksSinceTBI_z^2) + HeadMotion_z + (WeeksSinceTBI_z | Tract), data = data)

Which model is better?

Model Comparison Metric	Linear Model	Quadratic Model	Interpretation
AIC (BIC)	-12600 (-12563)	-12700 (-12658)	Quadratic model is better (AIC_Q < AIC_L)
Log Likelihood	6306.9	6358.1	Quadratic model is better
Anova		p-value< 2.2e-16 ***	Anova model comparison => quadratic model significantly different from linear model

Is a random slope model necessary?

We find that a quadratic model better explains water ratio trajectory. In this model, we determine whether rate of water ratio change differs by tract. The significant p-value associated with the model with the random slope suggests that rate of water ratio change significantly differs by tract.

Model Comparison Metric	No Slope Quadratic Model	With Slope Quadratic Model
AIC (BIC)	-12577 (-12546)	-12700 (-12658)
Log Likelihood	6294.7	6358.1
Anova		p-value < 2.2e-16 ***

Confidence Intervals Generated by Bootstrapping (n=1000)

Description	2.5 %	97.5 %	Significance
Variance of the Random Intercept by Tract	0.0042016	0.0081483	Significant variability in the intercept across tracts
Variance of the random slope for WeeksSinceTBI linear	-0.6012991	0.6069875	No significant variability in linear slope across tracts
Variance of the random slope for WeeksSinceTBI_z^2 quadratic	0.0004913	0.0013390	Significant variability in quadratic slope across tracts
Residual or unexplained variance	0.0028299	0.0032275	Unexplained variance is significant
Predicted water ratio at baseline (when WeeksSinceTBI_z and HeadMotion_z are 0)	0.0345099	0.0405137	Predicted water ratio value at baseline is significant
Linear effect of WeeksSinceTBI on water ratio	-0.0008096	0.0001956	The relationship between water ratio and WeeksSinceTBI is not significant
Quadratic effect of WeeksSinceTBI on water ratio	0.0005445	0.0011610	There is a significant U-Shaped Relationship between water ratio and WeeksSinceTBI
Linear effect of Head Motion	-0.0011293	0.0005622	Lower water ratio is significantly associated with higher head motion

On the X-axis, “Weeks Since TBI (z)” represents z-scored values of weeeks since the injury, which center around 0 (the mean in the data) and spread out to ±1 or more standard deviations from the mean.
The plot illustrates the predicted water ratio across different values of time since TBI, accounting for both linear and quadratic effects and adjusting for random effects of Tract (i.e., holding random effects constant, focusing on the relationship between weeks since TBI with water ratio, in isolation).

Hindered Ratio Trajectory

What is Hindered Ratio

This represents the degree of diffusion that is limited or hindered, often due to surrounding tissue or barriers like cell walls. High hindered diffusion can occur in areas with swelling (edema) or fluid buildup around damaged tissue, where water can move but faces restrictions.

Objective assessment of quadratic model fit

WeeksSinceTBI_z | Tract: This tells the model to allow each tract to have its own slope for WeeksSinceTBI. Both the intercept and the slope can vary between tracts.

Linear Model

mixed.model_linear <- lmer(hind_ratio_map ~ WeeksSinceTBI_z + HeadMotion_z + (WeeksSinceTBI_z | Tract), data = data)

Quadratic Model

mixed.model_quadratic <- lmer(hind_ratio_map ~ WeeksSinceTBI_z + I(WeeksSinceTBI_z^2) + HeadMotion_z + (WeeksSinceTBI_z | Tract), data = data)

Which model is better?

Model Comparison Metric	Linear Model	Quadratic Model	Interpretation
AIC (BIC)	-12739 (-12702)	-12738 (-12696)	Linear model is better (AIC_L < AIC_Q)
Log Likelihood	6376.4	6377.1	Quadratic model is marginally better
Anova		p-value=0.2506	Quadratic model is not significant

Is a random slope model necessary?

We find that a linear model better explains hindered ratio trajectory. Testing against a random slope model, we find that although there is a significant effect of slope (p=0.0004513 ***), the mixed linear model with the random slope does not converge on at least 5 of the 1000 simulations, when boostrapping is performed on this model.Therefore, we elect to go with a linear random intercept mixed model.

Model Comparison Metric	No Slope Linear Model	With Slope Linear Model
AIC (BIC)	-12727 (-12701)	-12739 (-12702)
Log Likelihood	6368.7	6376.4
Anova		p-value 0.0004513 *** (however, bootstrapping leads to singularity fit issues, so this random slope model will not be considered)

Confidence Intervals Generated by Bootstrapping (n=1000)

Description	2.5 %	97.5 %	Significance
Variance of the Random Intercept by Tract	0.0058276	0.0118613	Significant variability in the intercept across tracts
Residual or unexplained variance	0.0028074	0.0031794	Unexplained variance is significant
Predicted hindered ratio at baseline (when WeeksSinceTBI_z and HeadMotion_z are 0)	0.0170595	0.0253127	Predicted hindered ratio value at baseline is significant
Linear effect of WeeksSinceTBI on hindered ratio	0.0004411	0.0009715	As WeeksSinceTBI increases, there is a significant increase in hindered ratio
Linear effect of Head Motion	-0.0006021	0.0009952	The relationship between hindered ratio and head motion is not significant

- On the X-axis, “Weeks Since TBI (z)” represents z-scored values of weeeks since the injury, which center around 0 (the mean in the data) and spread out to ±1 or more standard deviations from the mean.

The plot illustrates the predicted hindered ratio across different standardized values of time since TBI, adjusting for random intercept effects of Tract.

dBSI: Summary models

dBSIMetric	description_high	description_low	BestModelFit
Fiber Ratio	Suggests that a larger portion of the voxel is occupied by aligned fibers, i.e., healthier, intact white matter.	Suggests less fiber density within the voxel, possibly due to degeneration, damage, or a mixture of other cellular or free water components.	Random Slope Quadratic Mixed Effects Model
Cellularity Ratio	Suggests possible pathological conditions, such as inflammation, tumors, or scarring, due to ceullular infiltration.	Suggests a lower density of cells within the voxel, possibly indicating healthy, non-pathological tissue, a lack of inflammatory or tumor infiltration, or, in some cases, tissue degeneration or atrophy.	Random Slope Quadratic Mixed Effects Model
Perfusion Ratio	Suggest inflammatory responses or vascular changes in the affected tissue that result in increased blood flow, relative to movement restricted by cellular structures or white matter tracts.	Suggests areas of the brain that have reduced blood supply, possibly due to vascular damage or long-term changes in blood flow.	Random Intercept Linear Mixed Effects Model
Free Water Ratio	Suggests an increase in unrestricted water movement due to excess extracellular fluid such as due to swelling or edema, which allows water to diffuse freely without encountering many barriers.	Suggests that most water molecules within the voxel are constrained by cellular structures or tissue barriers, indicating a dense cellular environment with limited extracellular space. This can reflect healthy, intact tissue with minimal edema or, in pathological conditions, densely packed cells such as in tumors or areas of high cellular infiltration, which restrict free water movement.	Random Slope Quadratic Mixed Effects Model
Hindered Ratio	Suggests an increase in partially restricted water movement due to tissue structures or cellular barriers that remain present in swollen areas.	Suggests minimal restriction on water diffusion within the voxel, often due to a lack of surrounding barriers like cell walls or extracellular matrix components. This can suggest a less dense or open environment, such as in healthy tissue with ample extracellular space, or, in some cases, tissue atrophy or cell loss, where structural barriers are reduced, allowing for more free and unrestricted water movement.	Random Intercept Linear Mixed Effects Model

dBSI: Descriptive Table

dBSIMetric	description_high	description_low	BestModelFit
Fiber Ratio	Suggests that a larger portion of the voxel is occupied by aligned fibers, i.e., healthier, intact white matter.	Suggests less fiber density within the voxel, possibly due to degeneration, damage, or a mixture of other cellular or free water components.	Random Slope Quadratic Mixed Effects Model
Cellularity Ratio	Suggests possible pathological conditions, such as inflammation, tumors, or scarring, due to ceullular infiltration.	Suggests a lower density of cells within the voxel, possibly indicating healthy, non-pathological tissue, a lack of inflammatory or tumor infiltration, or, in some cases, tissue degeneration or atrophy.	Random Slope Quadratic Mixed Effects Model
Perfusion Ratio	Suggest inflammatory responses or vascular changes in the affected tissue that result in increased blood flow, relative to movement restricted by cellular structures or white matter tracts.	Suggests areas of the brain that have reduced blood supply, possibly due to vascular damage or long-term changes in blood flow.	Random Intercept Linear Mixed Effects Model
Free Water Ratio	Suggests an increase in unrestricted water movement due to excess extracellular fluid such as due to swelling or edema, which allows water to diffuse freely without encountering many barriers.	Suggests that most water molecules within the voxel are constrained by cellular structures or tissue barriers, indicating a dense cellular environment with limited extracellular space. This can reflect healthy, intact tissue with minimal edema or, in pathological conditions, densely packed cells such as in tumors or areas of high cellular infiltration, which restrict free water movement.	Random Slope Quadratic Mixed Effects Model
Hindered Ratio	Suggests an increase in partially restricted water movement due to tissue structures or cellular barriers that remain present in swollen areas.	Suggests minimal restriction on water diffusion within the voxel, often due to a lack of surrounding barriers like cell walls or extracellular matrix components. This can suggest a less dense or open environment, such as in healthy tissue with ample extracellular space, or, in some cases, tissue atrophy or cell loss, where structural barriers are reduced, allowing for more free and unrestricted water movement.	Random Intercept Linear Mixed Effects Model

All metrics by Tract

Descriptive Statistics of Diffusion Metric Trajectories
Tract	Metric	MinValue	MaxValue	R_Sqrd_AIC_Linear	R_Sqrd_AIC_Quadratic	BetaTime_Linear	BetaTime_Quadratic	BetaTimeSqrd_Quadratic	Vertex_Within_Range	Vertex_Value	ParabolaDirection
forceps major	fiber_ratio_map	0.8912, Week: 1	0.9048, Week: 15	0.339, AIC: -237.517	0.395, AIC: -237.901	2.36e-04**	6.26e-04*	-1.39e-05	Yes	22.428	\/
forceps major	cell_ratio_map	0.0133, Week: 17	0.0189, Week: 1	0.459, AIC: -289.9	0.696, AIC: -303.418	-9.54e-05**	-4.31e-04***	1.2e-05***	Yes	17.923	/\
forceps major	perfusion_ratio_map	0.0158, Week: 24	0.0227, Week: 7	0.237, AIC: -270.467	0.24, AIC: -268.552	-9.86e-05*	-5.77e-05	-1.47e-06	No	-19.683	\/
forceps major	water_ratio_map	0.0416, Week: 27	0.0528, Week: 1	0.23, AIC: -240.583	0.31, AIC: -241.539	-1.68e-04*	-5.76e-04*	1.46e-05	Yes	19.721	/\
forceps major	hind_ratio_map	0.0162, Week: 9	0.0272, Week: 11	0.135, AIC: -234.151	0.177, AIC: -233.48	1.26e-04	4.38e-04	-1.12e-05	Yes	19.585	\/
forceps minor	fiber_ratio_map	0.8851, Week: 20	0.9095, Week: 14	0.022, AIC: -195.565	0.159, AIC: -197.639	1.01e-04	1.19e-03	-3.9e-05	Yes	15.255	\/
forceps minor	cell_ratio_map	0.0116, Week: 24	0.0178, Week: 5	0.327, AIC: -274.635	0.373, AIC: -274.551	-1.01e-04**	-2.77e-04	6.31e-06	Yes	21.963	/\
forceps minor	perfusion_ratio_map	0.0135, Week: 15	0.0229, Week: 9	0.052, AIC: -245.115	0.106, AIC: -244.714	-6.7e-05	2.12e-04	-9.99e-06	Yes	10.605	\/
forceps minor	water_ratio_map	0.0419, Week: 14	0.0554, Week: 27	0.021, AIC: -217.51	0.259, AIC: -223.031	-6.29e-05	-1.02e-03**	3.43e-05*	Yes	14.874	/\
forceps minor	hind_ratio_map	0.0139, Week: 9	0.0297, Week: 20	0.07, AIC: -218.12	0.084, AIC: -216.55	1.29e-04	-1.12e-04	8.64e-06	Yes	6.466	/\
left atr	fiber_ratio_map	0.8965, Week: 20	0.9228, Week: 14	0.025, AIC: -195.116	0.195, AIC: -198.295	-9.99e-05	1.13e-03	-4.39e-05*	Yes	12.819	\/
left atr	cell_ratio_map	0.0156, Week: 27	0.0215, Week: 2	0.324, AIC: -276.631	0.381, AIC: -277.012	-9.55e-05**	-2.84e-04*	6.75e-06	Yes	21.026	/\
left atr	perfusion_ratio_map	0.0126, Week: 1	0.022, Week: 10	0.11, AIC: -243.877	0.114, AIC: -241.992	-9.39e-05	-1.64e-05	-2.78e-06	No	-2.951	\/
left atr	water_ratio_map	0.0259, Week: 14	0.0443, Week: 20	0.109, AIC: -217.82	0.244, AIC: -220.251	1.66e-04	-5.84e-04	2.69e-05	Yes	10.864	/\
left atr	hind_ratio_map	0.0146, Week: 9	0.0285, Week: 20	0.073, AIC: -217.592	0.108, AIC: -216.604	1.24e-04	-2.47e-04	1.33e-05	Yes	9.280	/\
right atr	fiber_ratio_map	0.8922, Week: 13	0.9149, Week: 12	0.052, AIC: -194.504	0.087, AIC: -193.505	1.29e-04	6.95e-04	-2.03e-05	Yes	17.136	\/
right atr	cell_ratio_map	0.0145, Week: 15	0.0194, Week: 10	0.058, AIC: -277.628	0.177, AIC: -279.285	-3.77e-05	-2.64e-04	8.12e-06	Yes	16.275	/\
right atr	perfusion_ratio_map	0.0128, Week: 27	0.0221, Week: 9	0.113, AIC: -262.933	0.183, AIC: -263.176	-4.84e-05	1.88e-04	-8.46e-06	Yes	11.097	\/
right atr	water_ratio_map	0.0342, Week: 12	0.0507, Week: 9	0.137, AIC: -209.983	0.163, AIC: -208.83	-1.92e-04	-5.84e-04	1.4e-05	Yes	20.789	/\
right atr	hind_ratio_map	0.0155, Week: 9	0.0271, Week: 20	0.121, AIC: -225.563	0.132, AIC: -223.897	1.49e-04	-3.68e-05	6.64e-06	Yes	2.769	/\
left cab	fiber_ratio_map	0.8924, Week: 3	0.9067, Week: 5	0.128, AIC: -224.078	0.205, AIC: -224.576	8.94e-05	6e-04	-1.83e-05	Yes	16.399	\/
left cab	cell_ratio_map	0.0069, Week: 19	0.0102, Week: 3	0.318, AIC: -310.076	0.457, AIC: -314.21	-3.75e-05*	-1.95e-04**	5.64e-06*	Yes	17.279	/\
left cab	perfusion_ratio_map	0.0165, Week: 23	0.0238, Week: 2	0.197, AIC: -263.771	0.216, AIC: -262.437	-9.55e-05*	-2.24e-04	4.61e-06	Yes	24.319	/\
left cab	water_ratio_map	0.032, Week: 22	0.0419, Week: 1	0.273, AIC: -243.616	0.319, AIC: -243.376	-1.14e-04	-4.14e-04	1.08e-05	Yes	19.230	/\
left cab	hind_ratio_map	0.0267, Week: 5	0.041, Week: 7	0.153, AIC: -225.964	0.155, AIC: -224.03	1.54e-04	2.36e-04	-2.93e-06	No	40.253	\/
right cab	fiber_ratio_map	0.8963, Week: 7	0.9107, Week: 9	0.037, AIC: -222.688	0.066, AIC: -221.488	-1.68e-05	2.84e-04	-1.08e-05	Yes	13.177	\/
right cab	cell_ratio_map	0.0064, Week: 20	0.0099, Week: 4	0.226, AIC: -308.547	0.29, AIC: -308.852	-4.77e-05*	-1.51e-04	3.68e-06	Yes	20.435	/\
right cab	perfusion_ratio_map	0.0151, Week: 5	0.025, Week: 1	0.021, AIC: -241.878	0.162, AIC: -244.077	-4.13e-05	-5.1e-04*	1.68e-05	Yes	15.184	/\
right cab	water_ratio_map	0.0302, Week: 15	0.0388, Week: 8	0.342, AIC: -255.642	0.377, AIC: -255.142	-8.81e-05	-3.11e-04	7.97e-06	Yes	19.480	/\
right cab	hind_ratio_map	0.0254, Week: 4	0.0408, Week: 23	0.17, AIC: -223.253	0.24, AIC: -223.629	1.9e-04*	6.96e-04	-1.81e-05	Yes	19.190	\/
left cing	fiber_ratio_map	0.9056, Week: 3	0.9303, Week: 15	0.131, AIC: -206.781	0.435, AIC: -216.39	2.12e-04	1.61e-03***	-5.01e-05**	Yes	16.071	\/
left cing	cell_ratio_map	0.0102, Week: 21	0.0164, Week: 6	0.356, AIC: -280.67	0.38, AIC: -279.702	-1.1e-04**	-2.26e-04	4.18e-06	No	27.081	/\
left cing	perfusion_ratio_map	0.0189, Week: 14	0.0257, Week: 6	0.318, AIC: -262.744	0.327, AIC: -261.095	-1.38e-04**	-2.33e-04	3.42e-06	No	34.158	/\
left cing	water_ratio_map	0.025, Week: 15	0.0383, Week: 3	0.052, AIC: -235.756	0.327, AIC: -243.016	6.76e-06	-7.39e-04**	2.67e-05**	Yes	13.829	/\
left cing	hind_ratio_map	0.0123, Week: 16	0.0214, Week: 24	0.03, AIC: -239.776	0.144, AIC: -241.166	2.9e-05	-4.12e-04	1.58e-05	Yes	13.037	/\
right cing	fiber_ratio_map	0.9057, Week: 2	0.9213, Week: 17	0.39, AIC: -223.154	0.574, AIC: -230.845	3.12e-04**	1.27e-03***	-3.44e-05**	Yes	18.498	\/
right cing	cell_ratio_map	0.011, Week: 21	0.016, Week: 3	0.407, AIC: -285.41	0.437, AIC: -284.823	-1.04e-04**	-2.28e-04	4.46e-06	Yes	25.598	/\
right cing	perfusion_ratio_map	0.0171, Week: 22	0.0264, Week: 9	0.236, AIC: -263.706	0.276, AIC: -263.16	-9.47e-05*	-2.83e-04	6.76e-06	Yes	20.958	/\
right cing	water_ratio_map	0.0304, Week: 9	0.0461, Week: 2	0.552, AIC: -244.993	0.646, AIC: -249.295	-2.64e-04***	-7.96e-04**	1.91e-05*	Yes	20.885	/\
right cing	hind_ratio_map	0.009, Week: 9	0.0188, Week: 22	0.264, AIC: -252.415	0.273, AIC: -250.749	1.49e-04**	3.67e-05	4.03e-06	No	-4.556	/\
left cst	fiber_ratio_map	0.8919, Week: 20	0.9115, Week: 4	0.04, AIC: -204.975	0.059, AIC: -203.516	-1.09e-04	2.35e-04	-1.24e-05	Yes	9.525	\/
left cst	cell_ratio_map	0.0201, Week: 15	0.0277, Week: 6	0.252, AIC: -264.378	0.286, AIC: -263.633	-1.07e-04*	-2.81e-04	6.22e-06	Yes	22.583	/\
left cst	perfusion_ratio_map	0.0172, Week: 14	0.0248, Week: 2	0.18, AIC: -262.016	0.207, AIC: -260.899	-9.67e-05*	5.58e-05	-5.47e-06	Yes	5.107	\/
left cst	water_ratio_map	0.033, Week: 4	0.0499, Week: 20	0.249, AIC: -226.346	0.309, AIC: -226.575	2.34e-04**	-2.29e-04	1.66e-05	Yes	6.907	/\
left cst	hind_ratio_map	0.0061, Week: 9	0.0124, Week: 18	0.19, AIC: -270.221	0.219, AIC: -269.219	7.83e-05*	2.17e-04	-4.99e-06	Yes	21.806	\/
right cst	fiber_ratio_map	0.9007, Week: 13	0.9141, Week: 4	0.147, AIC: -223.765	0.148, AIC: -221.799	-3.92e-05	2.21e-05	-2.2e-06	Yes	5.039	\/
right cst	cell_ratio_map	0.0192, Week: 20	0.0242, Week: 13	0.143, AIC: -280.554	0.15, AIC: -278.781	-5.92e-05	-1.14e-04	1.98e-06	No	28.902	/\
right cst	perfusion_ratio_map	0.0161, Week: 27	0.0262, Week: 9	0.111, AIC: -245.091	0.16, AIC: -244.612	-9.77e-05	1.75e-04	-9.76e-06	Yes	8.950	\/
right cst	water_ratio_map	0.0304, Week: 4	0.0441, Week: 27	0.149, AIC: -228.283	0.17, AIC: -226.955	1.04e-04	-1.45e-04	8.92e-06	Yes	8.106	/\
right cst	hind_ratio_map	0.0059, Week: 3	0.0128, Week: 27	0.173, AIC: -264.079	0.177, AIC: -262.198	9.25e-05*	3.82e-05	1.94e-06	No	-9.828	/\
left ilf	fiber_ratio_map	0.8892, Week: 18	0.9041, Week: 23	0.088, AIC: -224.42	0.089, AIC: -222.432	9.94e-05	1.35e-04	-1.28e-06	No	52.788	\/
left ilf	cell_ratio_map	0.0087, Week: 17	0.0133, Week: 3	0.264, AIC: -288.178	0.307, AIC: -287.827	-7.72e-05**	-2.05e-04	4.57e-06	Yes	22.398	/\
left ilf	perfusion_ratio_map	0.0163, Week: 11	0.0254, Week: 19	0.038, AIC: -249.273	0.053, AIC: -247.693	-2.62e-05	1.08e-04	-4.79e-06	Yes	11.219	\/
left ilf	water_ratio_map	0.0343, Week: 19	0.046, Week: 2	0.132, AIC: -231.34	0.193, AIC: -231.321	-1.41e-04	-5.4e-04	1.43e-05	Yes	18.878	/\
left ilf	hind_ratio_map	0.0261, Week: 3	0.0397, Week: 18	0.195, AIC: -232.462	0.242, AIC: -232.1	1.44e-04	5.01e-04	-1.28e-05	Yes	19.594	\/
right ilf	fiber_ratio_map	0.8869, Week: 1	0.9049, Week: 25	0.367, AIC: -228.106	0.368, AIC: -226.143	2.86e-04**	2.27e-04	2.1e-06	No	-54.058	/\
right ilf	cell_ratio_map	0.0085, Week: 21	0.0125, Week: 1	0.434, AIC: -302.923	0.536, AIC: -306.294	-7.37e-05**	-2.43e-04**	6.07e-06*	Yes	20.029	/\
right ilf	perfusion_ratio_map	0.0114, Week: 27	0.0198, Week: 19	0.082, AIC: -252.115	0.098, AIC: -250.585	-5e-05	8.42e-05	-4.81e-06	Yes	8.756	\/
right ilf	water_ratio_map	0.037, Week: 11	0.0487, Week: 2	0.296, AIC: -242.306	0.382, AIC: -243.824	-1.96e-04**	-6.24e-04*	1.53e-05	Yes	20.339	/\
right ilf	hind_ratio_map	0.0242, Week: 4	0.0424, Week: 11	0.005, AIC: -211.129	0.062, AIC: -210.701	3.63e-05	5.55e-04	-1.86e-05	Yes	14.933	\/
left slfp	fiber_ratio_map	0.8911, Week: 20	0.9144, Week: 15	0.057, AIC: -198.872	0.06, AIC: -196.948	1.24e-04	2.69e-04	-5.2e-06	Yes	25.900	\/
left slfp	cell_ratio_map	0.0169, Week: 21	0.0251, Week: 3	0.166, AIC: -263.201	0.172, AIC: -261.383	-9.04e-05*	-1.59e-04	2.44e-06	No	32.456	/\
left slfp	perfusion_ratio_map	0.0123, Week: 14	0.0205, Week: 16	0.215, AIC: -257.925	0.226, AIC: -256.302	-1.13e-04*	-2.21e-04	3.87e-06	No	28.518	/\
left slfp	water_ratio_map	0.0337, Week: 7	0.0511, Week: 20	0.112, AIC: -217.732	0.14, AIC: -216.594	1.68e-04	-1.74e-04	1.23e-05	Yes	7.110	/\
left slfp	hind_ratio_map	0.0111, Week: 5	0.0216, Week: 14	0.309, AIC: -250.011	0.394, AIC: -251.575	-8.26e-05	2.91e-04	-1.34e-05	Yes	10.868	\/
right slfp	fiber_ratio_map	0.8959, Week: 24	0.9081, Week: 12	0.08, AIC: -238.948	0.087, AIC: -237.166	-7.64e-05	4.06e-05	-4.19e-06	Yes	4.843	\/
right slfp	cell_ratio_map	0.0227, Week: 15	0.0265, Week: 5	0.082, AIC: -289.952	0.174, AIC: -290.809	5.37e-06	-1.55e-04	5.76e-06	Yes	13.489	/\
right slfp	perfusion_ratio_map	0.0144, Week: 25	0.0227, Week: 9	0.062, AIC: -247.425	0.063, AIC: -245.46	-6.2e-05	-1.02e-04	1.43e-06	No	35.602	/\
right slfp	water_ratio_map	0.0354, Week: 9	0.0473, Week: 14	0.081, AIC: -241.226	0.088, AIC: -239.43	5.79e-06	1.14e-04	-3.89e-06	Yes	14.700	\/
right slfp	hind_ratio_map	0.0089, Week: 3	0.0154, Week: 27	0.265, AIC: -261.638	0.268, AIC: -259.726	1.22e-04**	7.35e-05	1.75e-06	No	-20.991	/\
left slft	fiber_ratio_map	0.9037, Week: 2	0.9184, Week: 15	0.081, AIC: -215.606	0.117, AIC: -214.682	1.46e-04	5.43e-04	-1.42e-05	Yes	19.101	\/
left slft	cell_ratio_map	0.0135, Week: 21	0.0193, Week: 3	0.316, AIC: -283.37	0.332, AIC: -282.008	-9.62e-05**	-1.84e-04	3.14e-06	No	29.287	/\
left slft	perfusion_ratio_map	0.0135, Week: 14	0.0216, Week: 2	0.071, AIC: -258.601	0.088, AIC: -257.095	-6.18e-05	-1.84e-04	4.37e-06	Yes	21.018	/\
left slft	water_ratio_map	0.0367, Week: 19	0.0474, Week: 20	0.089, AIC: -233.252	0.159, AIC: -233.389	7.62e-05	-3.23e-04	1.43e-05	Yes	11.293	/\
left slft	hind_ratio_map	0.0121, Week: 5	0.0182, Week: 14	0.182, AIC: -264.978	0.24, AIC: -264.984	-6.37e-05	1.52e-04	-7.72e-06	Yes	9.833	\/
right slft	fiber_ratio_map	0.9005, Week: 14	0.9112, Week: 12	0.024, AIC: -240.765	0.024, AIC: -238.765	4.51e-05	3.91e-05	2.17e-07	No	-90.097	/\
right slft	cell_ratio_map	0.018, Week: 20	0.0216, Week: 5	0.119, AIC: -299.502	0.189, AIC: -299.734	-2.62e-05	-1.46e-04	4.29e-06	Yes	17.014	/\
right slft	perfusion_ratio_map	0.0135, Week: 27	0.0218, Week: 9	0.096, AIC: -250.499	0.097, AIC: -248.522	-8.25e-05	-5.18e-05	-1.1e-06	No	-23.534	\/
right slft	water_ratio_map	0.0392, Week: 11	0.0502, Week: 13	0.034, AIC: -238.697	0.034, AIC: -236.704	-5.09e-05	-3.08e-05	-7.2e-07	No	-21.390	\/
right slft	hind_ratio_map	0.009, Week: 9	0.0165, Week: 27	0.215, AIC: -259.718	0.218, AIC: -257.802	1.11e-04*	1.6e-04	-1.77e-06	No	45.407	\/
left unc	fiber_ratio_map	0.9016, Week: 7	0.9237, Week: 14	0.136, AIC: -204.103	0.139, AIC: -202.169	1.84e-05	1.41e-04	-4.39e-06	Yes	16.058	\/
left unc	cell_ratio_map	0.0098, Week: 17	0.0152, Week: 5	0.393, AIC: -279.568	0.396, AIC: -277.713	-1.16e-04***	-1.61e-04	1.61e-06	No	49.928	/\
left unc	perfusion_ratio_map	0.0115, Week: 14	0.0224, Week: 9	0.041, AIC: -241.048	0.057, AIC: -239.502	-6.37e-05	9.82e-05	-5.8e-06	Yes	8.465	\/
left unc	water_ratio_map	0.0194, Week: 14	0.033, Week: 20	0.033, AIC: -227.71	0.108, AIC: -227.873	1.02e-05	-4.35e-04	1.6e-05	Yes	13.637	/\
left unc	hind_ratio_map	0.0255, Week: 16	0.0403, Week: 18	0.188, AIC: -224.124	0.201, AIC: -222.537	1.5e-04	3.62e-04	-7.57e-06	Yes	23.890	\/
right unc	fiber_ratio_map	0.9025, Week: 1	0.9249, Week: 15	0.131, AIC: -198.884	0.171, AIC: -198.172	2.06e-04	7.97e-04	-2.12e-05	Yes	18.822	\/
right unc	cell_ratio_map	0.0085, Week: 14	0.0144, Week: 10	0.086, AIC: -274.629	0.113, AIC: -273.455	-3.27e-05	-1.5e-04	4.19e-06	Yes	17.865	/\
right unc	perfusion_ratio_map	0.0136, Week: 24	0.0201, Week: 9	0.172, AIC: -260.365	0.214, AIC: -259.771	9.69e-06	2.07e-04	-7.08e-06	Yes	14.640	\/
right unc	water_ratio_map	0.0219, Week: 21	0.0319, Week: 7	0.263, AIC: -238.851	0.286, AIC: -237.701	-1.83e-04*	-4.13e-04	8.24e-06	Yes	25.058	/\
right unc	hind_ratio_map	0.023, Week: 4	0.0404, Week: 1	0.004, AIC: -214.479	0.047, AIC: -213.662	1.53e-06	-4.23e-04	1.52e-05	Yes	13.905	/\

dBSI: Select Tract Plots

Commissural Tracts

Forceps Major

Fiber Ratio

Fiber Ratio
Model	Estimate_WeeksSinceTBI	P_value
Linear	0.0002363	0.0018308
Quadratic_LinearComponent	0.0006255	0.0326348
Quadratic_SquaredComponent	-0.0000139	0.1585541

ModelFit.Quadratic_vs_Linear	Metrics
Increase in Adjusted R²	0.0320241
ANOVA Comparison	0.1585541

Linear Fit

(not significantly different from quadratic fit)

Quadratic Fit

Cellularity Ratio

Cellularity Ratio
Model	Estimate_WeeksSinceTBI	P_value
Linear	-0.0000954	0.0010404
Quadratic_LinearComponent	-0.0004309	0.0000239
Quadratic_SquaredComponent	0.0000120	0.0003201

ModelFit.Quadratic_vs_Linear	Metrics
Increase in Adjusted R²	0.2416477
ANOVA Comparison	0.0003201

Linear Fit

Quadratic Fit ***

Perfusion Ratio

Perfusion Ratio
Model	Estimate_WeeksSinceTBI	P_value
Linear	-9.86e-05	0.0127597
Quadratic_LinearComponent	-5.77e-05	0.7147195
Quadratic_SquaredComponent	-1.50e-06	0.7893735

ModelFit.Quadratic_vs_Linear	Metrics
Increase in Adjusted R²	-0.0332024
ANOVA Comparison	0.7893735

Linear Fit

(not significantly different from quadratic fit)

Quadratic Fit

Vertex is outside time range, so not included

Free Water Ratio

Water Ratio
Model	Estimate_WeeksSinceTBI	P_value
Linear	-0.0001683	0.0143482
Quadratic_LinearComponent	-0.0005756	0.0352015
Quadratic_SquaredComponent	0.0000146	0.1164571

ModelFit.Quadratic_vs_Linear	Metrics
Increase in Adjusted R²	0.0540001
ANOVA Comparison	0.1164571

Linear Fit

(not significantly different from quadratic fit)

Quadratic Fit

Hindered Ratio

Hindered Ratio
Model	Estimate_WeeksSinceTBI	P_value
Linear	0.0001260	0.0920882
Quadratic_LinearComponent	0.0004383	0.1556728
Quadratic_SquaredComponent	-0.0000112	0.2924852

ModelFit.Quadratic_vs_Linear	Metrics
Increase in Adjusted R²	0.0062305
ANOVA Comparison	0.2924852

Linear Fit

(not significantly different from quadratic fit)

Quadratic Fit

Projection Tracts

Right Anterior Thalamic Radiation

Fiber Ratio

Fiber Ratio
Model	Estimate_WeeksSinceTBI	P_value
Linear	0.0001291	0.3969169
Quadratic_LinearComponent	0.0006954	0.2781244
Quadratic_SquaredComponent	-0.0000203	0.3611119

ModelFit.Quadratic_vs_Linear	Metrics
Increase in Adjusted R²	-0.0056671
ANOVA Comparison	0.3611119

Linear Fit

(not significantly different from quadratic fit)

Quadratic Fit

Cellularity Ratio

Cellularity Ratio
Model	Estimate_WeeksSinceTBI	P_value
Linear	-0.0000377	0.2520125
Quadratic_LinearComponent	-0.0002644	0.0500802
Quadratic_SquaredComponent	0.0000081	0.0807969

ModelFit.Quadratic_vs_Linear	Metrics
Increase in Adjusted R²	0.0905433
ANOVA Comparison	0.0807969

Linear Fit

Quadratic Fit *

Perfusion Ratio

Perfusion Ratio
Model	Estimate_WeeksSinceTBI	P_value
Linear	-0.0000484	0.2624520
Quadratic_LinearComponent	0.0001877	0.2871544
Quadratic_SquaredComponent	-0.0000085	0.1714949

ModelFit.Quadratic_vs_Linear	Metrics
Increase in Adjusted R²	0.0381677
ANOVA Comparison	0.1714949

Linear Fit

(not significantly different from quadratic fit)

Quadratic Fit

Free Water Ratio

Water Ratio
Model	Estimate_WeeksSinceTBI	P_value
Linear	-0.0001918	0.1006141
Quadratic_LinearComponent	-0.0005836	0.2281331
Quadratic_SquaredComponent	0.0000140	0.4007390

ModelFit.Quadratic_vs_Linear	Metrics
Increase in Adjusted R²	-0.0105203
ANOVA Comparison	0.4007390

Linear Fit

(not significantly different from quadratic fit)

Quadratic Fit

Hindered Ratio

Hindered Ratio
Model	Estimate_WeeksSinceTBI	P_value
Linear	0.0001485	0.0903880
Quadratic_LinearComponent	-0.0000368	0.9187762
Quadratic_SquaredComponent	0.0000066	0.5976135

ModelFit.Quadratic_vs_Linear	Metrics
Increase in Adjusted R²	-0.0291645
ANOVA Comparison	0.5976135

Linear Fit

(not significantly different from quadratic fit)

Quadratic Fit

Association Tracts

Right Superior Longitudinal Fasciculus

Fiber Ratio

Fiber Ratio
Model	Estimate_WeeksSinceTBI	P_value
Linear	-7.64e-05	0.2565797
Quadratic_LinearComponent	4.06e-05	0.8855729
Quadratic_SquaredComponent	-4.20e-06	0.6698430

ModelFit.Quadratic_vs_Linear	Metrics
Increase in Adjusted R²	-0.0349658
ANOVA Comparison	0.6698430

Linear Fit

(not significantly different from quadratic fit)

Quadratic Fit

Cellularity Ratio

Cellularity Ratio
Model	Estimate_WeeksSinceTBI	P_value
Linear	0.0000054	0.8353624
Quadratic_LinearComponent	-0.0001553	0.1462677
Quadratic_SquaredComponent	0.0000058	0.1227189

ModelFit.Quadratic_vs_Linear	Metrics
Increase in Adjusted R²	0.0609743
ANOVA Comparison	0.1227189

Linear Fit

Quadratic Fit *

Perfusion Ratio

Perfusion Ratio
Model	Estimate_WeeksSinceTBI	P_value
Linear	-0.0000620	0.2807554
Quadratic_LinearComponent	-0.0001019	0.6739911
Quadratic_SquaredComponent	0.0000014	0.8649065

ModelFit.Quadratic_vs_Linear	Metrics
Increase in Adjusted R²	-0.0428164
ANOVA Comparison	0.8649065

Linear Fit

(not significantly different from quadratic fit)

Quadratic Fit

Free Water Ratio

Water Ratio
Model	Estimate_WeeksSinceTBI	P_value
Linear	0.0000058	0.9275141
Quadratic_LinearComponent	0.0001144	0.6728312
Quadratic_SquaredComponent	-0.0000039	0.6796354

ModelFit.Quadratic_vs_Linear	Metrics
Increase in Adjusted R²	-0.0354359
ANOVA Comparison	0.6796354

Linear Fit

(not significantly different from quadratic fit)

Quadratic Fit

Hindered Ratio

Hindered Ratio
Model	Estimate_WeeksSinceTBI	P_value
Linear	0.0001223	0.0091592
Quadratic_LinearComponent	0.0000735	0.6927400
Quadratic_SquaredComponent	0.0000018	0.7865176

ModelFit.Quadratic_vs_Linear	Metrics
Increase in Adjusted R²	-0.0318972
ANOVA Comparison	0.7865176

Linear Fit **

Quadratic Fit

Cognitive Measures

Trajectory

Model Fit Decision Process

Biopsychosocial Model Fit

dPrime (Go-No-Go)

Model Fit

Is a mixed [multilevel] model necessary?

The random effect of tract does not contribute to the model fit [boundary fit is singular], so it has been removed. Therefore, instead of pursuing mixed linear models (that model the random effect of tract), we pursue multiple linear regression models, with linear and quadratic effects of dPrime with weeks since injury.

Linear Model

model_linear <- lm(dprimeScore ~ WeeksSinceTBI_z, data = data)

Quadratic Model

model_quadratic <- lm (dprimeScore ~ WeeksSinceTBI_z + I(WeeksSinceTBI_z^2), data = data)

Which model is better?

Model Comparison Metric	Linear Model	Quadratic Model	Interpretation
AIC (BIC)	1353.179 (1365.738)	1349.409 (1366.154)	Quadratic model is slightly better (AIC_Q < AIC_L)
Anova		p-value=0.01669 *	Anova model comparison => quadratic model significantly different from linear model

Better?

We find that a quadratic model better explains dPrimeScore trajectory, but could there be a better fitting model?

Both linear and quadratic models do not sufficiently capture the variance in the data (R^2 values < 0.1).

We turn to General Additive Models to see if a cubic spline fits the model better.

General Additive Model

EDF = 8 (EDF > 1 implies a non-linear relationship)
R-sq.(adj) = 0.683
Deviance explained = 68.9%

Plot

GAM

Official Figure

(for manuscript)

Linear

Quadratic

NumSym

Reaction Time

Model Fit

Is a mixed [multilevel] model necessary?

The random effect of tract does not contribute to the model fit [boundary fit is singular], so it has been removed. Therefore, instead of pursuing mixed linear models (that model the random effect of tract), we pursue multiple linear regression models, with linear and quadratic effects of NUMSYM_RT_z with weeks since injury.

Linear Model

model_linear <- lm(NUMSYM_RT_z ~ WeeksSinceTBI_z, data = data)

Quadratic Model

model_quadratic <- lm (NUMSYM_RT_z ~ WeeksSinceTBI_z + I(WeeksSinceTBI_z^2), data = data)

Which model is better?

Model Comparison Metric	Linear Model	Quadratic Model	Interpretation
AIC (BIC)	684.8372 (697.39581)	-96.0380 (-79.29316)	Quadratic model is significantly better (AIC_Q <<< AIC_L)
Anova		p-value=< 2.2e-16 ***	Anova model comparison => quadratic model significantly different from linear model
R-squared	0.76	0.95

Better?

We find that a quadratic model explains nearly all of the NUMSYM_RT_z trajectory (R^2=0.95), and therefore, the quadratic linear regression model is considered the best fitting model.

Quadratic Plot

With density plot:

Official Figure

(for manuscript)

Linear: Effect of Weeks Since Injury on RT

Effect of FA on RT

######: Quadratic

Accuracy

Model Fit

Is a mixed [multilevel] model necessary?

The random effect of tract does not contribute to the model fit [boundary fit is singular], so it has been removed. Therefore, instead of pursuing mixed linear models (that model the random effect of tract), we pursue multiple linear regression models, with linear and quadratic effects of NumSym_Accuracy with weeks since injury.
Since the accuracy scores on the NumSum task have limited variance and are bounded within a narrow range (0-1), z-scoring was not considered necessary. Z-scoring won’t provide much additional interpretive benefit since z-scores typically serve to normalize variability or make values comparable across different scales. Here, working directly with the bounded values (0–1) will likely keep the models below more interpretable and retain the natural scale of mean trial accuracy.

Linear Model

model_linear <- lm(NUMSYM_Accuracy ~ WeeksSinceTBI_z, data = data)

Quadratic Model

model_quadratic <- lm (NUMSYM_Accuracy ~ WeeksSinceTBI_z + I(WeeksSinceTBI_z^2), data = data)

Which model is better?

Model Comparison Metric	Linear Model	Quadratic Model	Interpretation
AIC (BIC)	-2337.768 (-2324.210)	-2357.603 (-2340.858)	Quadratic model is slightly better (AIC_Q < AIC_L)
Anova		p-value=1.923e-06 ***	Anova model comparison => quadratic model significantly different from linear model

Better?

We find that a quadratic model better explains NumSym_Accuracy trajectory, but could there be a better fitting model?

Both linear and quadratic models do not sufficiently capture the variance in the data (R^2 values < 0.2).

We turn to General Additive Models to see if a cubic spline fits the model better.

General Additive Model

EDF = 9 (EDF > 1 implies a non-linear relationship)
R-sq.(adj) = 0.475
Deviance explained = 48.4%

GAM Plot

Official Figure

(for manuscript)

Linear

Quadratic

AntiSacc

Reaction Time

Model Fit

Is a mixed [multilevel] model necessary?

The random effect of tract does not contribute to the model fit [boundary fit is singular], so it has been removed. Therefore, instead of pursuing mixed linear models (that model the random effect of tract), we pursue multiple linear regression models, with linear and quadratic effects of ANTISACC_RT_z with weeks since injury.

Linear Model

model_linear <- lm(ANTISACC_RT_z ~ WeeksSinceTBI_z, data = data)

Quadratic Model

model_quadratic <- lm (ANTISACC_RT_z ~ WeeksSinceTBI_z + I(WeeksSinceTBI_z^2), data = data)

Which model is better?

Model Comparison Metric	Linear Model	Quadratic Model	Interpretation
AIC (BIC)	1221.700 (1234.259) 1	182.446 (1199.191)	Quadratic model is significantly better (AIC_Q <<< AIC_L)
Anova		p-value=<1.556e-10 ***	Anova model comparison => quadratic model significantly different from linear model
R-squared	0.28	0.34

Better?

We find that a quadratic model explains some of the ANTISACC_RT_z trajectory (R^2=0.34).

Plot with linear and quadratic fits:

Plot with CI for better linear regression model with quadratic terms:

With density plot

We turn to General Additive Models to see if a cubic spline fits the model better.

GAM

EDF = 8 (EDF > 1 implies a non-linear relationship)
R-sq.(adj) = 0.45
Deviance explained = 46.3%

R² Difference: R^2 increases from 0.34 for the quadratic model to 0.45 for the GAM model, indicating an improvement in overall model fit. However, an increase of 0.11 may not justify the added complexity introduced by the GAM model.
ANOVA Results: The ANOVA test suggests that the difference between the two models is statistically significant (p< 2.2e-16 ***). This implies that the GAM model captures additional variability in the data that the quadratic model does not.
Visual Assessment of Plots:

Quadratic Model: The quadratic fit provides a smooth and simpler curve, capturing the main trend—a downward curve—but does not adapt as well to smaller fluctuations in the data.
GAM Model: The cubic spline fit with the GAM model shows more flexibility, accommodating slight oscillations around the main downward trend. This flexibility, however, may introduce a level of complexity that might not be necessary if the primary goal is to model the overall downward trend.

GAM Plot

Official Figure

(for manuscript)

Linear

Quadratic

Accuracy

Model Fit

Is a mixed [multilevel] model necessary?

The random effect of tract does not contribute to the model fit [boundary fit is singular], so it has been removed. Therefore, instead of pursuing mixed linear models (that model the random effect of tract), we pursue multiple linear regression models, with linear and quadratic effects of ANTISACC_Accuracy with weeks since injury.
Since the accuracy scores on the NumSum task have limited variance and are bounded within a narrow range (0-1), z-scoring was not considered necessary. Z-scoring won’t provide much additional interpretive benefit since z-scores typically serve to normalize variability or make values comparable across different scales. Here, working directly with the bounded values (0–1) will likely keep the models below more interpretable and retain the natural scale of mean trial accuracy.

Linear Model

model_linear <- lm(ANTISACC_Accuracy ~ WeeksSinceTBI_z, data = data)

Quadratic Model

model_quadratic <- lm(ANTISACC_Accuracy ~ WeeksSinceTBI_z + I(WeeksSinceTBI_z^2), data = data)

Which model is better?

Model Comparison Metric	Linear Model	Quadratic Model	Interpretation
AIC (BIC)	-1969.247 (-1956.688)	-2016.668 (-1999.923)	Quadratic model is better (AIC_Q << AIC_L)
Anova		p-value=2.476e-12 ***	Anova model comparison => quadratic model significantly different from linear model
R-squared	0.18.	0.25

Better?

We find that a quadratic model better explains ANTISACC_Accuracy trajectory, but could there be a better fitting model?

Both linear and quadratic models do not appear to sufficiently capture the variance in the data.

We turn to General Additive Models to see if a cubic spline fits the model better.

GAM

EDF = 9 (EDF > 1 implies a non-linear relationship)
R-sq.(adj) = 0.6
Deviance explained = 56.9%

GAM Plot

Official Figure

(for manuscript)

Linear

Quadratic

Mediation

WeeksSinceInjury_DTIMetric(Mediator)_Cognition {.tabset}

Go-No-Go

No mediation effect was found in dPrime Scores across metrics and tracts.

Number-Symbol

Reaction Time: Linear

Linear Plot: RT by Week

Quadratic model is significant via ANOVA

Quadratic Plot: RT by Week

Quadratic model is significant via ANOVA

Linear Plot: FA by RT

Quadratic model is NOT significant via ANOVA

Quadratic Plot: FA by RT

Quadratic model is NOT significant via ANOVA

Antisaccade

Reaction Time

Accuracy

No mediation effect was found in accuracy scores across metrics and tracts.

Emotion Measures

Trajectory

Model Fit Decision Process

Biopsychosocial Model Fit

Anxiety

Model Fit

Is a mixed [multilevel] model necessary?

The random slope and intercept effect of tract does not contribute to the model fit [boundary fit is singular], so it has been removed. Therefore, instead of pursuing mixed linear models (that model the random effect of tract), we pursue multiple linear regression models, with linear and quadratic effects of Anx_BAI with weeks since injury.

Linear Model

model_linear <- lm(Anx_BAI_z ~ WeeksSinceTBI_z, data = data)

Quadratic Model

model_quadratic <- lm (Anx_BAI_z ~ WeeksSinceTBI_z + I(WeeksSinceTBI_z^2), data = data)

Which model is better?

Model Comparison Metric	Linear Model	Quadratic Model	Interpretation
AIC (BIC)	3588.629 (3604.484)	2814.585 (2835.724)	Quadratic model is slightly better (AIC_Q < AIC_L)
Anova		p-value< 2.2e-16 ***	Anova model comparison => quadratic model significantly different from linear model
R^2	0.32	0.60	Quadratic curve fits the FA-by-time relationship fairly well.

Better?

We find that a quadratic model better explains Anxiety trajectory.

Plot

Linear

Quadratic

Depression

Model Fit

Is a mixed [multilevel] model necessary?

The random slope and intercept effect of tract does not contribute to the model fit [boundary fit is singular], so it has been removed. Therefore, instead of pursuing mixed linear models (that model the random effect of tract), we pursue multiple linear regression models, with linear and quadratic effects of Anx_BAI with weeks since injury.

Linear Model

model_linear <- lm(Dep_BDI_z ~ WeeksSinceTBI_z, data = data)

Quadratic Model

model_quadratic <- lm (Dep_BDI_z ~ WeeksSinceTBI_z + I(WeeksSinceTBI_z^2), data = data)

Which model is better?

Model Comparison Metric	Linear Model	Quadratic Model	Interpretation
AIC (BIC)	4114.316 (4130.171)	3502.208 (3523.347)	Quadratic model is slightly better (AIC_Q < AIC_L)
Anova		p-value< 2.2e-16 ***	Anova model comparison => quadratic model significantly different from linear model
R^2	0.02	0.3555	Quadratic curve fits the FA-by-time relationship fairly well.

Better?

We find that a quadratic model better explains dPrimeScore trajectory, but could there be a better fitting model?

We additionally explore General Additive Models to see if a cubic spline fits the model better.

General Additive Model

EDF = 9 (EDF > 1 implies a non-linear relationship)
R-sq.(adj) = 0.707
Deviance explained = 70.9%

Plot

Quadratic Fit

Cubic Fit

Mediation

WeeksSinceInjury_DTIMetric(Mediator)_Anxiety {.tabset}

Linear

Tract	Metric	MinValue	MaxValue	R_Sqrd_AIC_Linear	R_Sqrd_AIC_Quadratic	BetaTime_Linear	BetaTime_Quadratic	BetaTimeSqrd_Quadratic	Vertex_Within_Range	Vertex_Value	ParabolaDirection
forceps major	fiber_ratio_map	0.8912, Week: 1	0.9048, Week: 15	0.339, AIC: -237.517	0.395, AIC: -237.901	2.36e-04**	6.26e-04*	-1.39e-05	Yes	22.428	concave-down
forceps major	cell_ratio_map	0.0133, Week: 17	0.0189, Week: 1	0.459, AIC: -289.9	0.696, AIC: -303.418	-9.54e-05**	-4.31e-04***	1.2e-05***	Yes	17.923	concave-up
forceps major	perfusion_ratio_map	0.0158, Week: 24	0.0227, Week: 7	0.237, AIC: -270.467	0.24, AIC: -268.552	-9.86e-05*	-5.77e-05	-1.47e-06	No	-19.683	concave-down
forceps major	water_ratio_map	0.0416, Week: 27	0.0528, Week: 1	0.23, AIC: -240.583	0.31, AIC: -241.539	-1.68e-04*	-5.76e-04*	1.46e-05	Yes	19.721	concave-up
forceps major	hind_ratio_map	0.0162, Week: 9	0.0272, Week: 11	0.135, AIC: -234.151	0.177, AIC: -233.48	1.26e-04	4.38e-04	-1.12e-05	Yes	19.585	concave-down
forceps minor	fiber_ratio_map	0.8851, Week: 20	0.9095, Week: 14	0.022, AIC: -195.565	0.159, AIC: -197.639	1.01e-04	1.19e-03	-3.9e-05	Yes	15.255	concave-down
forceps minor	cell_ratio_map	0.0116, Week: 24	0.0178, Week: 5	0.327, AIC: -274.635	0.373, AIC: -274.551	-1.01e-04**	-2.77e-04	6.31e-06	Yes	21.963	concave-up
forceps minor	perfusion_ratio_map	0.0135, Week: 15	0.0229, Week: 9	0.052, AIC: -245.115	0.106, AIC: -244.714	-6.7e-05	2.12e-04	-9.99e-06	Yes	10.605	concave-down
forceps minor	water_ratio_map	0.0419, Week: 14	0.0554, Week: 27	0.021, AIC: -217.51	0.259, AIC: -223.031	-6.29e-05	-1.02e-03**	3.43e-05*	Yes	14.874	concave-up
forceps minor	hind_ratio_map	0.0139, Week: 9	0.0297, Week: 20	0.07, AIC: -218.12	0.084, AIC: -216.55	1.29e-04	-1.12e-04	8.64e-06	Yes	6.466	concave-up
left atr	fiber_ratio_map	0.8965, Week: 20	0.9228, Week: 14	0.025, AIC: -195.116	0.195, AIC: -198.295	-9.99e-05	1.13e-03	-4.39e-05*	Yes	12.819	concave-down
left atr	cell_ratio_map	0.0156, Week: 27	0.0215, Week: 2	0.324, AIC: -276.631	0.381, AIC: -277.012	-9.55e-05**	-2.84e-04*	6.75e-06	Yes	21.026	concave-up
left atr	perfusion_ratio_map	0.0126, Week: 1	0.022, Week: 10	0.11, AIC: -243.877	0.114, AIC: -241.992	-9.39e-05	-1.64e-05	-2.78e-06	No	-2.951	concave-down
left atr	water_ratio_map	0.0259, Week: 14	0.0443, Week: 20	0.109, AIC: -217.82	0.244, AIC: -220.251	1.66e-04	-5.84e-04	2.69e-05	Yes	10.864	concave-up
left atr	hind_ratio_map	0.0146, Week: 9	0.0285, Week: 20	0.073, AIC: -217.592	0.108, AIC: -216.604	1.24e-04	-2.47e-04	1.33e-05	Yes	9.280	concave-up
right atr	fiber_ratio_map	0.8922, Week: 13	0.9149, Week: 12	0.052, AIC: -194.504	0.087, AIC: -193.505	1.29e-04	6.95e-04	-2.03e-05	Yes	17.136	concave-down
right atr	cell_ratio_map	0.0145, Week: 15	0.0194, Week: 10	0.058, AIC: -277.628	0.177, AIC: -279.285	-3.77e-05	-2.64e-04	8.12e-06	Yes	16.275	concave-up
right atr	perfusion_ratio_map	0.0128, Week: 27	0.0221, Week: 9	0.113, AIC: -262.933	0.183, AIC: -263.176	-4.84e-05	1.88e-04	-8.46e-06	Yes	11.097	concave-down
right atr	water_ratio_map	0.0342, Week: 12	0.0507, Week: 9	0.137, AIC: -209.983	0.163, AIC: -208.83	-1.92e-04	-5.84e-04	1.4e-05	Yes	20.789	concave-up
right atr	hind_ratio_map	0.0155, Week: 9	0.0271, Week: 20	0.121, AIC: -225.563	0.132, AIC: -223.897	1.49e-04	-3.68e-05	6.64e-06	Yes	2.769	concave-up
left cab	fiber_ratio_map	0.8924, Week: 3	0.9067, Week: 5	0.128, AIC: -224.078	0.205, AIC: -224.576	8.94e-05	6e-04	-1.83e-05	Yes	16.399	concave-down
left cab	cell_ratio_map	0.0069, Week: 19	0.0102, Week: 3	0.318, AIC: -310.076	0.457, AIC: -314.21	-3.75e-05*	-1.95e-04**	5.64e-06*	Yes	17.279	concave-up
left cab	perfusion_ratio_map	0.0165, Week: 23	0.0238, Week: 2	0.197, AIC: -263.771	0.216, AIC: -262.437	-9.55e-05*	-2.24e-04	4.61e-06	Yes	24.319	concave-up
left cab	water_ratio_map	0.032, Week: 22	0.0419, Week: 1	0.273, AIC: -243.616	0.319, AIC: -243.376	-1.14e-04	-4.14e-04	1.08e-05	Yes	19.230	concave-up
left cab	hind_ratio_map	0.0267, Week: 5	0.041, Week: 7	0.153, AIC: -225.964	0.155, AIC: -224.03	1.54e-04	2.36e-04	-2.93e-06	No	40.253	concave-down
right cab	fiber_ratio_map	0.8963, Week: 7	0.9107, Week: 9	0.037, AIC: -222.688	0.066, AIC: -221.488	-1.68e-05	2.84e-04	-1.08e-05	Yes	13.177	concave-down
right cab	cell_ratio_map	0.0064, Week: 20	0.0099, Week: 4	0.226, AIC: -308.547	0.29, AIC: -308.852	-4.77e-05*	-1.51e-04	3.68e-06	Yes	20.435	concave-up
right cab	perfusion_ratio_map	0.0151, Week: 5	0.025, Week: 1	0.021, AIC: -241.878	0.162, AIC: -244.077	-4.13e-05	-5.1e-04*	1.68e-05	Yes	15.184	concave-up
right cab	water_ratio_map	0.0302, Week: 15	0.0388, Week: 8	0.342, AIC: -255.642	0.377, AIC: -255.142	-8.81e-05	-3.11e-04	7.97e-06	Yes	19.480	concave-up
right cab	hind_ratio_map	0.0254, Week: 4	0.0408, Week: 23	0.17, AIC: -223.253	0.24, AIC: -223.629	1.9e-04*	6.96e-04	-1.81e-05	Yes	19.190	concave-down
left cing	fiber_ratio_map	0.9056, Week: 3	0.9303, Week: 15	0.131, AIC: -206.781	0.435, AIC: -216.39	2.12e-04	1.61e-03***	-5.01e-05**	Yes	16.071	concave-down
left cing	cell_ratio_map	0.0102, Week: 21	0.0164, Week: 6	0.356, AIC: -280.67	0.38, AIC: -279.702	-1.1e-04**	-2.26e-04	4.18e-06	No	27.081	concave-up
left cing	perfusion_ratio_map	0.0189, Week: 14	0.0257, Week: 6	0.318, AIC: -262.744	0.327, AIC: -261.095	-1.38e-04**	-2.33e-04	3.42e-06	No	34.158	concave-up
left cing	water_ratio_map	0.025, Week: 15	0.0383, Week: 3	0.052, AIC: -235.756	0.327, AIC: -243.016	6.76e-06	-7.39e-04**	2.67e-05**	Yes	13.829	concave-up
left cing	hind_ratio_map	0.0123, Week: 16	0.0214, Week: 24	0.03, AIC: -239.776	0.144, AIC: -241.166	2.9e-05	-4.12e-04	1.58e-05	Yes	13.037	concave-up
right cing	fiber_ratio_map	0.9057, Week: 2	0.9213, Week: 17	0.39, AIC: -223.154	0.574, AIC: -230.845	3.12e-04**	1.27e-03***	-3.44e-05**	Yes	18.498	concave-down
right cing	cell_ratio_map	0.011, Week: 21	0.016, Week: 3	0.407, AIC: -285.41	0.437, AIC: -284.823	-1.04e-04**	-2.28e-04	4.46e-06	Yes	25.598	concave-up
right cing	perfusion_ratio_map	0.0171, Week: 22	0.0264, Week: 9	0.236, AIC: -263.706	0.276, AIC: -263.16	-9.47e-05*	-2.83e-04	6.76e-06	Yes	20.958	concave-up
right cing	water_ratio_map	0.0304, Week: 9	0.0461, Week: 2	0.552, AIC: -244.993	0.646, AIC: -249.295	-2.64e-04***	-7.96e-04**	1.91e-05*	Yes	20.885	concave-up
right cing	hind_ratio_map	0.009, Week: 9	0.0188, Week: 22	0.264, AIC: -252.415	0.273, AIC: -250.749	1.49e-04**	3.67e-05	4.03e-06	No	-4.556	concave-up
left cst	fiber_ratio_map	0.8919, Week: 20	0.9115, Week: 4	0.04, AIC: -204.975	0.059, AIC: -203.516	-1.09e-04	2.35e-04	-1.24e-05	Yes	9.525	concave-down
left cst	cell_ratio_map	0.0201, Week: 15	0.0277, Week: 6	0.252, AIC: -264.378	0.286, AIC: -263.633	-1.07e-04*	-2.81e-04	6.22e-06	Yes	22.583	concave-up
left cst	perfusion_ratio_map	0.0172, Week: 14	0.0248, Week: 2	0.18, AIC: -262.016	0.207, AIC: -260.899	-9.67e-05*	5.58e-05	-5.47e-06	Yes	5.107	concave-down
left cst	water_ratio_map	0.033, Week: 4	0.0499, Week: 20	0.249, AIC: -226.346	0.309, AIC: -226.575	2.34e-04**	-2.29e-04	1.66e-05	Yes	6.907	concave-up
left cst	hind_ratio_map	0.0061, Week: 9	0.0124, Week: 18	0.19, AIC: -270.221	0.219, AIC: -269.219	7.83e-05*	2.17e-04	-4.99e-06	Yes	21.806	concave-down
right cst	fiber_ratio_map	0.9007, Week: 13	0.9141, Week: 4	0.147, AIC: -223.765	0.148, AIC: -221.799	-3.92e-05	2.21e-05	-2.2e-06	Yes	5.039	concave-down
right cst	cell_ratio_map	0.0192, Week: 20	0.0242, Week: 13	0.143, AIC: -280.554	0.15, AIC: -278.781	-5.92e-05	-1.14e-04	1.98e-06	No	28.902	concave-up
right cst	perfusion_ratio_map	0.0161, Week: 27	0.0262, Week: 9	0.111, AIC: -245.091	0.16, AIC: -244.612	-9.77e-05	1.75e-04	-9.76e-06	Yes	8.950	concave-down
right cst	water_ratio_map	0.0304, Week: 4	0.0441, Week: 27	0.149, AIC: -228.283	0.17, AIC: -226.955	1.04e-04	-1.45e-04	8.92e-06	Yes	8.106	concave-up
right cst	hind_ratio_map	0.0059, Week: 3	0.0128, Week: 27	0.173, AIC: -264.079	0.177, AIC: -262.198	9.25e-05*	3.82e-05	1.94e-06	No	-9.828	concave-up
left ilf	fiber_ratio_map	0.8892, Week: 18	0.9041, Week: 23	0.088, AIC: -224.42	0.089, AIC: -222.432	9.94e-05	1.35e-04	-1.28e-06	No	52.788	concave-down
left ilf	cell_ratio_map	0.0087, Week: 17	0.0133, Week: 3	0.264, AIC: -288.178	0.307, AIC: -287.827	-7.72e-05**	-2.05e-04	4.57e-06	Yes	22.398	concave-up
left ilf	perfusion_ratio_map	0.0163, Week: 11	0.0254, Week: 19	0.038, AIC: -249.273	0.053, AIC: -247.693	-2.62e-05	1.08e-04	-4.79e-06	Yes	11.219	concave-down
left ilf	water_ratio_map	0.0343, Week: 19	0.046, Week: 2	0.132, AIC: -231.34	0.193, AIC: -231.321	-1.41e-04	-5.4e-04	1.43e-05	Yes	18.878	concave-up
left ilf	hind_ratio_map	0.0261, Week: 3	0.0397, Week: 18	0.195, AIC: -232.462	0.242, AIC: -232.1	1.44e-04	5.01e-04	-1.28e-05	Yes	19.594	concave-down
right ilf	fiber_ratio_map	0.8869, Week: 1	0.9049, Week: 25	0.367, AIC: -228.106	0.368, AIC: -226.143	2.86e-04**	2.27e-04	2.1e-06	No	-54.058	concave-up
right ilf	cell_ratio_map	0.0085, Week: 21	0.0125, Week: 1	0.434, AIC: -302.923	0.536, AIC: -306.294	-7.37e-05**	-2.43e-04**	6.07e-06*	Yes	20.029	concave-up
right ilf	perfusion_ratio_map	0.0114, Week: 27	0.0198, Week: 19	0.082, AIC: -252.115	0.098, AIC: -250.585	-5e-05	8.42e-05	-4.81e-06	Yes	8.756	concave-down
right ilf	water_ratio_map	0.037, Week: 11	0.0487, Week: 2	0.296, AIC: -242.306	0.382, AIC: -243.824	-1.96e-04**	-6.24e-04*	1.53e-05	Yes	20.339	concave-up
right ilf	hind_ratio_map	0.0242, Week: 4	0.0424, Week: 11	0.005, AIC: -211.129	0.062, AIC: -210.701	3.63e-05	5.55e-04	-1.86e-05	Yes	14.933	concave-down
left slfp	fiber_ratio_map	0.8911, Week: 20	0.9144, Week: 15	0.057, AIC: -198.872	0.06, AIC: -196.948	1.24e-04	2.69e-04	-5.2e-06	Yes	25.900	concave-down
left slfp	cell_ratio_map	0.0169, Week: 21	0.0251, Week: 3	0.166, AIC: -263.201	0.172, AIC: -261.383	-9.04e-05*	-1.59e-04	2.44e-06	No	32.456	concave-up
left slfp	perfusion_ratio_map	0.0123, Week: 14	0.0205, Week: 16	0.215, AIC: -257.925	0.226, AIC: -256.302	-1.13e-04*	-2.21e-04	3.87e-06	No	28.518	concave-up
left slfp	water_ratio_map	0.0337, Week: 7	0.0511, Week: 20	0.112, AIC: -217.732	0.14, AIC: -216.594	1.68e-04	-1.74e-04	1.23e-05	Yes	7.110	concave-up
left slfp	hind_ratio_map	0.0111, Week: 5	0.0216, Week: 14	0.309, AIC: -250.011	0.394, AIC: -251.575	-8.26e-05	2.91e-04	-1.34e-05	Yes	10.868	concave-down
right slfp	fiber_ratio_map	0.8959, Week: 24	0.9081, Week: 12	0.08, AIC: -238.948	0.087, AIC: -237.166	-7.64e-05	4.06e-05	-4.19e-06	Yes	4.843	concave-down
right slfp	cell_ratio_map	0.0227, Week: 15	0.0265, Week: 5	0.082, AIC: -289.952	0.174, AIC: -290.809	5.37e-06	-1.55e-04	5.76e-06	Yes	13.489	concave-up
right slfp	perfusion_ratio_map	0.0144, Week: 25	0.0227, Week: 9	0.062, AIC: -247.425	0.063, AIC: -245.46	-6.2e-05	-1.02e-04	1.43e-06	No	35.602	concave-up
right slfp	water_ratio_map	0.0354, Week: 9	0.0473, Week: 14	0.081, AIC: -241.226	0.088, AIC: -239.43	5.79e-06	1.14e-04	-3.89e-06	Yes	14.700	concave-down
right slfp	hind_ratio_map	0.0089, Week: 3	0.0154, Week: 27	0.265, AIC: -261.638	0.268, AIC: -259.726	1.22e-04**	7.35e-05	1.75e-06	No	-20.991	concave-up
left slft	fiber_ratio_map	0.9037, Week: 2	0.9184, Week: 15	0.081, AIC: -215.606	0.117, AIC: -214.682	1.46e-04	5.43e-04	-1.42e-05	Yes	19.101	concave-down
left slft	cell_ratio_map	0.0135, Week: 21	0.0193, Week: 3	0.316, AIC: -283.37	0.332, AIC: -282.008	-9.62e-05**	-1.84e-04	3.14e-06	No	29.287	concave-up
left slft	perfusion_ratio_map	0.0135, Week: 14	0.0216, Week: 2	0.071, AIC: -258.601	0.088, AIC: -257.095	-6.18e-05	-1.84e-04	4.37e-06	Yes	21.018	concave-up
left slft	water_ratio_map	0.0367, Week: 19	0.0474, Week: 20	0.089, AIC: -233.252	0.159, AIC: -233.389	7.62e-05	-3.23e-04	1.43e-05	Yes	11.293	concave-up
left slft	hind_ratio_map	0.0121, Week: 5	0.0182, Week: 14	0.182, AIC: -264.978	0.24, AIC: -264.984	-6.37e-05	1.52e-04	-7.72e-06	Yes	9.833	concave-down
right slft	fiber_ratio_map	0.9005, Week: 14	0.9112, Week: 12	0.024, AIC: -240.765	0.024, AIC: -238.765	4.51e-05	3.91e-05	2.17e-07	No	-90.097	concave-up
right slft	cell_ratio_map	0.018, Week: 20	0.0216, Week: 5	0.119, AIC: -299.502	0.189, AIC: -299.734	-2.62e-05	-1.46e-04	4.29e-06	Yes	17.014	concave-up
right slft	perfusion_ratio_map	0.0135, Week: 27	0.0218, Week: 9	0.096, AIC: -250.499	0.097, AIC: -248.522	-8.25e-05	-5.18e-05	-1.1e-06	No	-23.534	concave-down
right slft	water_ratio_map	0.0392, Week: 11	0.0502, Week: 13	0.034, AIC: -238.697	0.034, AIC: -236.704	-5.09e-05	-3.08e-05	-7.2e-07	No	-21.390	concave-down
right slft	hind_ratio_map	0.009, Week: 9	0.0165, Week: 27	0.215, AIC: -259.718	0.218, AIC: -257.802	1.11e-04*	1.6e-04	-1.77e-06	No	45.407	concave-down
left unc	fiber_ratio_map	0.9016, Week: 7	0.9237, Week: 14	0.136, AIC: -204.103	0.139, AIC: -202.169	1.84e-05	1.41e-04	-4.39e-06	Yes	16.058	concave-down
left unc	cell_ratio_map	0.0098, Week: 17	0.0152, Week: 5	0.393, AIC: -279.568	0.396, AIC: -277.713	-1.16e-04***	-1.61e-04	1.61e-06	No	49.928	concave-up
left unc	perfusion_ratio_map	0.0115, Week: 14	0.0224, Week: 9	0.041, AIC: -241.048	0.057, AIC: -239.502	-6.37e-05	9.82e-05	-5.8e-06	Yes	8.465	concave-down
left unc	water_ratio_map	0.0194, Week: 14	0.033, Week: 20	0.033, AIC: -227.71	0.108, AIC: -227.873	1.02e-05	-4.35e-04	1.6e-05	Yes	13.637	concave-up
left unc	hind_ratio_map	0.0255, Week: 16	0.0403, Week: 18	0.188, AIC: -224.124	0.201, AIC: -222.537	1.5e-04	3.62e-04	-7.57e-06	Yes	23.890	concave-down
right unc	fiber_ratio_map	0.9025, Week: 1	0.9249, Week: 15	0.131, AIC: -198.884	0.171, AIC: -198.172	2.06e-04	7.97e-04	-2.12e-05	Yes	18.822	concave-down
right unc	cell_ratio_map	0.0085, Week: 14	0.0144, Week: 10	0.086, AIC: -274.629	0.113, AIC: -273.455	-3.27e-05	-1.5e-04	4.19e-06	Yes	17.865	concave-up
right unc	perfusion_ratio_map	0.0136, Week: 24	0.0201, Week: 9	0.172, AIC: -260.365	0.214, AIC: -259.771	9.69e-06	2.07e-04	-7.08e-06	Yes	14.640	concave-down
right unc	water_ratio_map	0.0219, Week: 21	0.0319, Week: 7	0.263, AIC: -238.851	0.286, AIC: -237.701	-1.83e-04*	-4.13e-04	8.24e-06	Yes	25.058	concave-up
right unc	hind_ratio_map	0.023, Week: 4	0.0404, Week: 1	0.004, AIC: -214.479	0.047, AIC: -213.662	1.53e-06	-4.23e-04	1.52e-05	Yes	13.905	concave-up

Quadratic

WeeksSinceInjury_DTIMetric(Mediator)_Depression

No mediation effect was found across tracts.

Quadratic

Mediation with Inflammation Metrics

For this analysis, we only consider tracts for which DTI-metric mediations were significant across both cognitive and emotion measures.
The mediation models were generally described by:

Weeks Since Injury(Independent Variable) -> DTIMetric (FA, AD, RD, MD in each tract) -> Cognitive/Emotion Measure (Dependent Variable)
***

Mediation models were subject to 5000 boostrapped simulations to ensure model convergence and stability.

Data Snapshot

DV	DV_Spec	Mediator	Mediator_Spec	IndirectEffect_Estimate	IndirectEffect_P_Value	DirectEffect_Estimate	DirectEffect_P_Value	TotalEffect_Estimate	TotalEffect_P_Value	ProportionMediated_PercentEstimate	ProportionMediated_P_Value	MediationEffect
NUMSYM_RT	Cog	FA	forceps major	-0.33	0.00	-0.55	0.00	-0.88	0.00	37.49	0.00	Partial
NUMSYM_RT	Cog	RD	forceps major	-0.37	0.00	-0.51	0.00	-0.88	0.00	41.87	0.00	Partial
NUMSYM_RT	Cog	MD	forceps major	-0.25	0.00	-0.62	0.00	-0.87	0.00	28.78	0.00	Partial
ANXIETY	Emo	MD	right ilf	-0.48	0.03	-0.09	0.77	-0.56	0.01	84.73	0.03	Full
ANXIETY	Emo	FA	right slft	-0.42	0.04	-0.16	0.51	-0.57	0.01	72.38	0.04	Full
ANXIETY	Emo	RD	right slft	-0.46	0.01	-0.11	0.63	-0.57	0.01	80.80	0.02	Full

Comprehensive Profile of White Matter Changes Following Traumatic Brain Injury in a Densely Sampled Participant

Changes in Diffusion Metrics and Inflammation Indices and their Impact of Cognition and Emotion

11/09/2024

Dense Sampling of Single Participant (Participant01)

Notes

Data Snapshot

Head Motion

DTI Trajectory

Theoretical framework for quadratic model fit

Model Fit Decision Process

FA Trajectory

What is FA

Objective assessment of quadratic model fit

Linear Model

Quadratic Model

Which model is better?

Is a random slope model necessary?

Confidence Intervals Generated by Bootstrapping (n=1000)

RD Trajectory

What is RD

Objective assessment of quadratic model fit

Linear Model

Quadratic Model

Which model is better?

Is a random slope model necessary?

Confidence Intervals Generated by Bootstrapping (n=1000)

AD Trajectory

What is AD

Objective assessment of quadratic model fit

Linear Model

Quadratic Model

Which model is better?

Is a random slope model necessary?

Confidence Intervals Generated by Bootstrapping (n=1000)

MD Trajectory

What is MD

Objective assessment of quadratic model fit

Linear Model

Quadratic Model

Which model is better?

Is a random slope model necessary?

Confidence Intervals Generated by Bootstrapping (n=1000)

DTI: Summary models

DTI: Descriptive Table

All metrics by Tract

FA,RD by tract

DTI: Select Tract Plots

Commissural Tracts

Forceps Major

FA

RD

Projection Tracts

Right Anterior Thalamic Radiation

FA

RD

Association Tracts

Right Superior Longitudinal Fasiculus

FA

RD

dBSI Trajectory

Intro to DBSI

Model Fit Decision Process

Fiber Ratio Trajectory

What is Fiber Ratio

Objective assessment of quadratic model fit

Linear Model

Quadratic Model

Which model is better?

Is a random slope model necessary?

Confidence Intervals Generated by Bootstrapping (n=1000)

Cellularity Ratio Trajectory

What is Cellularity Ratio

Objective assessment of quadratic model fit

Linear Model

Quadratic Model

Which model is better?

Is a random slope model necessary?

Confidence Intervals Generated by Bootstrapping (n=1000)

Perfusion Ratio Trajectory

What is Perfusion Ratio