Dense Sampling of Single Participant (Participant01)

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 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
Biopsychosocial Model Fit

FA Trajectory

What is FA

  • FA is Fractional Anistropy.

  • Fractional Anistropy (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 0.0297955 0.0592515 Significant variability in the intercept across tracts
Variance of the random slope for WeeksSinceTBI linear -0.8273491 0.0783114 No significant variability in linear slope across tracts
Variance of the random slope for WeeksSinceTBI_z^2 quadratic 0.0009908 0.0023858 Significant variability in quadratic slope across tracts
Residual or unexplained variance 0.0037964 0.0043188 Unexplained variance is significant
Predicted FA value at baseline (when WeeksSinceTBI_z and HeadMotion_z are 0) 0.4803943 0.5200881 Predicted FA value at baseline is significant
Linear effect of WeeksSinceTBI on FA -0.0030775 -0.0013819 There is a significant descrease in FA as WeeksSinceTBI increases
Quadratic effect of WeeksSinceTBI on FA 0.0011730 0.0019734 There is a significant U-Shaped Relationship between FA and WeeksSinceTBI
Linear effect of Head Motion -0.0064268 -0.0042458 Lower FA is significantly associated with higher head motion

  • 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 0.0000253 0.0000496 Significant variability in the intercept across tracts
Variance of the random slope for WeeksSinceTBI linear -0.5579475 0.4291780 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) 0.0003135 0.0003482 Predicted RD value at baseline is significant
Linear effect of WeeksSinceTBI on RD 0.0000015 0.0000028 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 0.0000036 Lower RD 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).

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 0.0000427 0.0000860 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) 0.0007449 0.0008014 Predicted AD value at baseline is significant
Linear effect of WeeksSinceTBI on AD 0.0000012 0.0000022 There is a significant descrease in AD as WeeksSinceTBI increases
Linear effect of Head Motion -0.0000037 -0.0000008 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 0.0000247 5.13e-05 Significant variability in the intercept across tracts
Residual or unexplained variance 0.0000030 3.50e-06 Unexplained variance is significant
Predicted MD value at baseline (when WeeksSinceTBI_z and HeadMotion_z are 0) 0.0004606 4.97e-04 Predicted MD value at baseline is significant
Linear effect of WeeksSinceTBI on MD 0.0000017 2.30e-06 There is a significant descrease in MD as WeeksSinceTBI increases
Quadratic effect of WeeksSinceTBI on MD -0.0000013 -6.00e-07 There is a significant U-Shaped Relationship between MD and WeeksSinceTBI
Linear effect of Head Motion 0.0000002 2.00e-06 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

## Error in select(., -AIC_Quadratic, -AIC_Linear, -MetricColor): unused arguments (-AIC_Quadratic, -AIC_Linear, -MetricColor)
## Error in select(., Tract, Metric, ChangeTimePt): unused arguments (Tract, Metric, ChangeTimePt)
## Error: object 'WhenChangeHappens' not found

FA,RD by tract

## Error in select(., -AIC_Quadratic, -AIC_Linear, -MetricColor): unused arguments (-AIC_Quadratic, -AIC_Linear, -MetricColor)
## Error in select(., Tract, Metric, ChangeTimePt): unused arguments (Tract, Metric, ChangeTimePt)
## Error: object 'WhenChangeHappens' not found

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

Intro to DBSI

Model Fit Decision Process

Biopsychosocial Model Fit
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 0.0043566 0.0086672 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 0.0000356 0.0010850 Significant variability in quadratic slope across tracts
Residual or unexplained variance 0.0040419 0.0046121 Unexplained variance is significant
Predicted fiber ratio at baseline (when WeeksSinceTBI_z and HeadMotion_z are 0) 0.9027314 0.9087640 Predicted fiber ratio value at baseline is significant
Linear effect of WeeksSinceTBI on fiber ratio 0.0002488 0.0011199 There is a significant descrease in fiber ratio as WeeksSinceTBI increases
Quadratic effect of WeeksSinceTBI on fiber ratio -0.0014286 -0.0005481 There is a significant U-Shaped Relationship between fiber ratio and WeeksSinceTBI
Linear effect of Head Motion -0.0015792 0.0009006 Lower fiber 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 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 0.0033265 0.0067385 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 0.0000092 0.0002958 Significant variability in quadratic slope across tracts
Residual or unexplained variance 0.0010922 0.0012463 Unexplained variance is significant
Predicted cellularity ratio at baseline (when WeeksSinceTBI_z and HeadMotion_z are 0) 0.0130703 0.0177028 Predicted cellularity ratio value at baseline is significant
Linear effect of WeeksSinceTBI on cellularity ratio -0.0006930 -0.0004313 The relationship between cellularity ratio and WeeksSinceTBI is not significant
Quadratic effect of WeeksSinceTBI on cellularity ratio 0.0001856 0.0004294 There is a significant U-Shaped Relationship between cellularity ratio and WeeksSinceTBI
Linear effect of Head Motion 0.0000634 0.0007141 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 0.0013141 0.0026005 Significant variability in the intercept across tracts
Residual or unexplained variance 0.0018833 0.0021420 Unexplained variance is significant
Predicted perfusion ratio at baseline (when WeeksSinceTBI_z and HeadMotion_z are 0) 0.0177221 0.0197025 Predicted perfusion ratio value at baseline is significant
Linear effect of WeeksSinceTBI on perfusion ratio -0.0007495 -0.0003920 As WeeksSinceTBI increases, perfusion ratio significantly increases
Linear effect of Head Motion -0.0004576 0.0007323 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 0.0040052 0.0082300 Significant variability in the intercept across tracts
Variance of the random slope for WeeksSinceTBI linear -0.5610355 0.5616602 No significant variability in linear slope across tracts
Variance of the random slope for WeeksSinceTBI_z^2 quadratic 0.0004696 0.0013443 Significant variability in quadratic slope across tracts
Residual or unexplained variance 0.0028161 0.0032249 Unexplained variance is significant
Predicted water ratio at baseline (when WeeksSinceTBI_z and HeadMotion_z are 0) 0.0345974 0.0404672 Predicted water ratio value at baseline is significant
Linear effect of WeeksSinceTBI on water ratio -0.0008029 0.0002169 The relationship between water ratio and WeeksSinceTBI is not significant
Quadratic effect of WeeksSinceTBI on water ratio 0.0005466 0.0011373 There is a significant U-Shaped Relationship between water ratio and WeeksSinceTBI
Linear effect of Head Motion -0.0011644 0.0005498 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 0.0058436 0.0120760 Significant variability in the intercept across tracts
Residual or unexplained variance 0.0028081 0.0031969 Unexplained variance is significant
Predicted hindered ratio at baseline (when WeeksSinceTBI_z and HeadMotion_z are 0) 0.0173905 0.0256085 Predicted hindered ratio value at baseline is significant
Linear effect of WeeksSinceTBI on hindered ratio 0.0004520 0.0009829 As WeeksSinceTBI increases, there is a significant increase in hindered ratio
Linear effect of Head Motion -0.0006343 0.0009977 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

## Error in select(., -AIC_Quadratic, -AIC_Linear, -MetricColor): unused arguments (-AIC_Quadratic, -AIC_Linear, -MetricColor)
## Error in select(., Tract, Metric, ChangeTimePt): unused arguments (Tract, Metric, ChangeTimePt)
## Error: object 'WhenChangeHappens' not found

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
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.

Plot
Quadratic Plot

With density 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 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%
Plot
GAM

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.

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

  1. 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.
  2. 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.
  3. 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.
Plot
GAM

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.

General Additive Model
  • EDF = 9 (EDF > 1 implies a non-linear relationship)
  • R-sq.(adj) = 0.6
  • Deviance explained = 56.9%
Plot
GAM

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
Tract Metric IndirectEffect_Estimate IndirectEffect_P_Value DirectEffect_Estimate DirectEffect_P_Value TotalEffect_Estimate TotalEffect_P_Value ProportionMediated_PercentEstimate ProportionMediated_P_Value MediationEffect
forceps major FA -0.33 0.00 -0.55 0 -0.88 0 37.49 0.00 Partial
forceps major AD -0.01 0.91 -0.87 0 -0.87 0 0.61 0.91 None
forceps major RD -0.37 0.00 -0.51 0 -0.88 0 41.87 0.00 Partial
forceps major MD -0.25 0.00 -0.62 0 -0.87 0 28.78 0.00 Partial
forceps minor FA -0.07 0.22 -0.81 0 -0.88 0 7.76 0.22 None
forceps minor AD -0.01 0.66 -0.86 0 -0.87 0 1.46 0.66 None
forceps minor RD -0.08 0.13 -0.80 0 -0.88 0 8.55 0.13 None
forceps minor MD -0.05 0.18 -0.82 0 -0.88 0 6.08 0.18 None
left atr FA -0.03 0.30 -0.84 0 -0.87 0 3.79 0.30 None
left atr AD -0.05 0.25 -0.82 0 -0.87 0 5.96 0.25 None
left atr RD -0.06 0.09 -0.81 0 -0.87 0 7.41 0.09 None
left atr MD -0.08 0.09 -0.79 0 -0.87 0 9.24 0.09 None
right atr FA -0.11 0.14 -0.77 0 -0.88 0 12.97 0.14 None
right atr AD 0.00 0.88 -0.87 0 -0.87 0 0.10 0.88 None
right atr RD -0.11 0.14 -0.78 0 -0.88 0 12.06 0.14 None
right atr MD -0.07 0.21 -0.81 0 -0.88 0 7.80 0.21 None
left cab FA 0.01 0.72 -0.88 0 -0.88 0 -0.91 0.72 None
left cab AD -0.03 0.37 -0.84 0 -0.87 0 3.60 0.37 None
left cab RD -0.03 0.36 -0.85 0 -0.88 0 3.67 0.36 None
left cab MD -0.06 0.24 -0.82 0 -0.88 0 6.70 0.24 None
right cab FA 0.01 0.75 -0.88 0 -0.87 0 -1.23 0.75 None
right cab AD -0.03 0.32 -0.84 0 -0.87 0 3.35 0.32 None
right cab RD -0.05 0.27 -0.82 0 -0.88 0 6.11 0.27 None
right cab MD -0.06 0.15 -0.82 0 -0.87 0 6.61 0.15 None
left cing FA -0.05 0.09 -0.82 0 -0.87 0 5.66 0.09 None
left cing AD 0.02 0.66 -0.89 0 -0.87 0 -2.00 0.66 None
left cing RD -0.06 0.07 -0.81 0 -0.87 0 6.99 0.07 None
left cing MD -0.01 0.71 -0.86 0 -0.87 0 1.43 0.71 None
right cing FA -0.20 0.09 -0.68 0 -0.88 0 22.73 0.09 None
right cing AD -0.05 0.30 -0.83 0 -0.87 0 5.22 0.30 None
right cing RD -0.21 0.12 -0.67 0 -0.88 0 23.62 0.12 None
right cing MD 0.04 0.66 -0.91 0 -0.87 0 -4.14 0.66 None
left cst FA -0.03 0.26 -0.84 0 -0.88 0 3.90 0.26 None
left cst AD 0.04 0.49 -0.91 0 -0.87 0 -4.03 0.49 None
left cst RD -0.05 0.31 -0.82 0 -0.88 0 6.03 0.31 None
left cst MD -0.03 0.58 -0.84 0 -0.87 0 3.67 0.58 None
right cst FA -0.04 0.25 -0.84 0 -0.88 0 5.09 0.25 None
right cst AD 0.01 0.96 -0.88 0 -0.87 0 -1.12 0.96 None
right cst RD -0.04 0.44 -0.84 0 -0.88 0 4.22 0.44 None
right cst MD -0.01 0.83 -0.87 0 -0.87 0 0.77 0.83 None
left ilf FA 0.00 0.97 -0.88 0 -0.88 0 0.17 0.97 None
left ilf AD -0.05 0.45 -0.82 0 -0.87 0 5.62 0.45 None
left ilf RD -0.11 0.09 -0.77 0 -0.88 0 12.47 0.09 None
left ilf MD -0.15 0.04 -0.72 0 -0.87 0 17.57 0.04 Partial
right ilf FA -0.22 0.03 -0.66 0 -0.88 0 24.88 0.03 Partial
right ilf AD -0.15 0.07 -0.72 0 -0.87 0 17.10 0.07 None
right ilf RD -0.32 0.00 -0.56 0 -0.88 0 36.01 0.00 Partial
right ilf MD -0.30 0.00 -0.58 0 -0.87 0 33.91 0.00 Partial
left slfp FA -0.05 0.28 -0.83 0 -0.88 0 6.17 0.28 None
left slfp AD 0.04 0.37 -0.91 0 -0.87 0 -4.16 0.37 None
left slfp RD -0.05 0.38 -0.83 0 -0.88 0 5.58 0.38 None
left slfp MD -0.01 0.72 -0.86 0 -0.87 0 1.69 0.72 None
right slfp FA -0.16 0.03 -0.72 0 -0.88 0 18.41 0.03 Partial
right slfp AD -0.02 0.45 -0.85 0 -0.87 0 2.29 0.45 None
right slfp RD -0.13 0.04 -0.76 0 -0.88 0 14.27 0.04 Partial
right slfp MD -0.04 0.29 -0.83 0 -0.88 0 4.95 0.29 None
left slft FA -0.07 0.12 -0.81 0 -0.88 0 8.30 0.12 None
left slft AD 0.01 0.80 -0.88 0 -0.87 0 -0.84 0.80 None
left slft RD -0.08 0.16 -0.80 0 -0.88 0 9.23 0.16 None
left slft MD -0.05 0.34 -0.83 0 -0.87 0 5.47 0.34 None
right slft FA -0.32 0.02 -0.57 0 -0.88 0 35.99 0.02 Partial
right slft AD 0.01 0.93 -0.88 0 -0.88 0 -1.07 0.93 None
right slft RD -0.30 0.01 -0.58 0 -0.88 0 33.97 0.01 Partial
right slft MD -0.16 0.08 -0.72 0 -0.88 0 17.93 0.08 None
left unc FA -0.01 0.75 -0.87 0 -0.88 0 1.23 0.75 None
left unc AD -0.08 0.22 -0.80 0 -0.87 0 8.64 0.22 None
left unc RD -0.09 0.11 -0.79 0 -0.88 0 9.90 0.11 None
left unc MD -0.12 0.04 -0.76 0 -0.88 0 13.56 0.04 Partial
right unc FA 0.01 0.96 -0.88 0 -0.87 0 -1.09 0.96 None
right unc AD -0.03 0.32 -0.84 0 -0.87 0 3.97 0.32 None
right unc RD -0.02 0.73 -0.86 0 -0.87 0 2.11 0.73 None
right unc MD -0.04 0.51 -0.83 0 -0.87 0 4.61 0.51 None
Accuracy
Tract Metric IndirectEffect_Estimate IndirectEffect_P_Value DirectEffect_Estimate DirectEffect_P_Value TotalEffect_Estimate TotalEffect_P_Value ProportionMediated_PercentEstimate ProportionMediated_P_Value MediationEffect
forceps major FA 0.00 0.64 -0.01 0.05 -0.01 0.01 -19.08 0.63 None
forceps major AD 0.00 0.59 -0.01 0.29 -0.01 0.01 21.22 0.60 None
forceps major RD 0.00 0.87 -0.01 0.15 -0.01 0.01 -10.40 0.86 None
forceps major MD 0.00 0.85 -0.01 0.33 -0.01 0.01 8.61 0.87 None
forceps minor FA 0.00 0.69 -0.01 0.07 -0.01 0.01 7.70 0.70 None
forceps minor AD 0.00 0.56 -0.01 0.03 -0.01 0.01 9.56 0.56 None
forceps minor RD 0.00 0.52 -0.01 0.09 -0.01 0.01 14.49 0.53 None
forceps minor MD 0.00 0.50 -0.01 0.05 -0.01 0.01 15.79 0.50 None
left atr FA 0.00 0.83 -0.01 0.05 -0.01 0.01 0.61 0.83 None
left atr AD 0.00 0.98 -0.01 0.01 -0.01 0.01 0.84 0.99 None
left atr RD 0.00 0.86 -0.01 0.05 -0.01 0.01 3.25 0.86 None
left atr MD 0.00 0.91 -0.01 0.03 -0.01 0.01 3.03 0.92 None
right atr FA 0.00 0.98 -0.01 0.06 -0.01 0.01 -0.12 0.98 None
right atr AD 0.00 0.52 -0.01 0.02 -0.01 0.01 9.62 0.52 None
right atr RD 0.00 0.57 -0.01 0.13 -0.01 0.01 17.90 0.58 None
right atr MD 0.00 0.38 -0.01 0.13 -0.01 0.01 24.92 0.38 None
left cab FA 0.00 0.57 -0.01 0.05 -0.01 0.02 4.77 0.58 None
left cab AD 0.00 0.37 -0.01 0.09 -0.01 0.01 15.41 0.38 None
left cab RD 0.00 0.95 -0.01 0.01 -0.01 0.01 -0.75 0.95 None
left cab MD 0.00 0.63 -0.01 0.03 -0.01 0.01 8.99 0.64 None
right cab FA 0.00 0.77 -0.01 0.01 -0.01 0.01 -5.35 0.77 None
right cab AD 0.00 0.36 -0.01 0.04 -0.01 0.01 17.32 0.36 None
right cab RD 0.00 0.67 -0.01 0.04 -0.01 0.01 11.44 0.67 None
right cab MD 0.00 0.37 -0.01 0.05 -0.01 0.01 22.97 0.37 None
left cing FA 0.00 0.73 -0.01 0.01 -0.01 0.01 -3.83 0.73 None
left cing AD 0.00 0.59 -0.01 0.01 -0.01 0.01 10.93 0.58 None
left cing RD 0.00 0.77 -0.01 0.03 -0.01 0.01 5.14 0.77 None
left cing MD 0.00 0.22 -0.01 0.04 -0.01 0.01 23.25 0.22 None
right cing FA 0.00 0.52 -0.01 0.03 -0.01 0.01 -26.04 0.53 None
right cing AD 0.00 0.35 -0.01 0.00 -0.01 0.01 -23.35 0.37 None
right cing RD 0.00 0.53 -0.01 0.34 -0.01 0.01 30.45 0.53 None
right cing MD -0.01 0.05 0.00 0.46 -0.01 0.01 68.66 0.06 Full
left cst FA 0.00 0.86 -0.01 0.02 -0.01 0.01 2.41 0.86 None
left cst AD 0.00 0.51 -0.01 0.10 -0.01 0.02 17.84 0.52 None
left cst RD 0.00 0.27 -0.01 0.07 -0.01 0.01 17.24 0.28 None
left cst MD 0.00 0.19 -0.01 0.13 -0.01 0.01 33.70 0.20 None
right cst FA 0.00 0.60 -0.01 0.01 -0.01 0.01 -7.69 0.61 None
right cst AD 0.00 0.69 -0.01 0.01 -0.01 0.01 10.39 0.68 None
right cst RD 0.00 0.41 -0.01 0.04 -0.01 0.01 13.00 0.41 None
right cst MD 0.00 0.12 -0.01 0.03 -0.01 0.01 29.09 0.12 None
left ilf FA 0.00 0.99 -0.01 0.01 -0.01 0.01 -0.50 1.00 None
left ilf AD 0.00 0.45 -0.01 0.39 -0.01 0.01 30.76 0.46 None
left ilf RD 0.00 0.27 -0.01 0.01 -0.01 0.01 -19.84 0.28 None
left ilf MD 0.00 0.77 -0.01 0.06 -0.01 0.01 -10.22 0.77 None
right ilf FA 0.00 0.61 -0.01 0.11 -0.01 0.01 -27.07 0.60 None
right ilf AD -0.01 0.33 0.00 0.50 -0.01 0.01 54.21 0.33 None
right ilf RD 0.00 0.82 -0.01 0.43 -0.01 0.01 13.88 0.83 None
right ilf MD 0.00 0.62 -0.01 0.56 -0.01 0.01 39.65 0.63 None
left slfp FA 0.00 0.96 -0.01 0.02 -0.01 0.01 1.45 0.97 None
left slfp AD 0.00 0.24 -0.01 0.05 -0.01 0.01 21.53 0.24 None
left slfp RD 0.00 0.23 -0.01 0.06 -0.01 0.01 18.09 0.24 None
left slfp MD 0.00 0.16 -0.01 0.09 -0.01 0.01 26.13 0.17 None
right slfp FA 0.00 0.33 -0.01 0.02 -0.01 0.02 -24.46 0.34 None
right slfp AD 0.00 0.28 -0.01 0.00 -0.01 0.01 -26.95 0.29 None
right slfp RD 0.00 0.86 -0.01 0.04 -0.01 0.01 2.34 0.87 None
right slfp MD 0.00 0.52 -0.01 0.02 -0.01 0.01 11.47 0.53 None
left slft FA 0.00 0.31 -0.01 0.05 -0.01 0.01 15.04 0.32 None
left slft AD 0.00 0.63 -0.01 0.02 -0.01 0.01 6.82 0.63 None
left slft RD 0.00 0.19 -0.01 0.13 -0.01 0.01 26.32 0.20 None
left slft MD 0.00 0.23 -0.01 0.10 -0.01 0.01 23.56 0.24 None
right slft FA 0.00 0.80 -0.01 0.06 -0.01 0.01 -12.53 0.80 None
right slft AD 0.00 0.83 -0.01 0.01 -0.01 0.01 4.68 0.82 None
right slft RD 0.00 0.53 -0.01 0.28 -0.01 0.01 27.27 0.55 None
right slft MD 0.00 0.24 -0.01 0.38 -0.01 0.01 48.69 0.25 None
left unc FA 0.00 0.85 -0.01 0.01 -0.01 0.01 -3.59 0.86 None
left unc AD 0.00 0.23 -0.01 0.07 -0.01 0.01 28.32 0.24 None
left unc RD 0.00 0.53 -0.01 0.02 -0.01 0.01 -10.57 0.54 None
left unc MD 0.00 0.97 -0.01 0.03 -0.01 0.01 1.09 0.97 None
right unc FA 0.00 0.51 -0.01 0.15 -0.01 0.01 23.93 0.52 None
right unc AD 0.00 0.48 -0.01 0.04 -0.01 0.01 13.99 0.48 None
right unc RD 0.00 0.31 -0.01 0.27 -0.01 0.01 41.68 0.32 None
right unc MD 0.00 0.27 -0.01 0.20 -0.01 0.01 38.96 0.28 None
Antisaccade
Reaction Time
Tract Metric IndirectEffect_Estimate IndirectEffect_P_Value DirectEffect_Estimate DirectEffect_P_Value TotalEffect_Estimate TotalEffect_P_Value ProportionMediated_PercentEstimate ProportionMediated_P_Value MediationEffect
forceps major FA -0.16 0.45 -0.38 0.06 -0.54 0.01 29.53 0.44 None
forceps major AD 0.02 0.88 -0.56 0.04 -0.53 0.01 -4.24 0.88 None
forceps major RD -0.16 0.41 -0.37 0.11 -0.53 0.01 30.55 0.41 None
forceps major MD -0.09 0.58 -0.44 0.07 -0.53 0.01 17.47 0.58 None
forceps minor FA -0.02 0.98 -0.52 0.00 -0.53 0.01 3.06 0.97 None
forceps minor AD 0.06 0.27 -0.59 0.00 -0.53 0.01 -11.21 0.27 None
forceps minor RD 0.05 0.70 -0.58 0.00 -0.53 0.01 -8.87 0.71 None
forceps minor MD 0.07 0.43 -0.60 0.00 -0.53 0.01 -13.95 0.44 None
left atr FA -0.02 0.81 -0.52 0.01 -0.53 0.01 2.93 0.81 None
left atr AD 0.03 0.56 -0.57 0.01 -0.53 0.01 -6.30 0.55 None
left atr RD 0.01 0.96 -0.54 0.01 -0.53 0.01 -1.11 0.97 None
left atr MD 0.02 0.73 -0.56 0.01 -0.53 0.01 -4.53 0.73 None
right atr FA -0.04 0.86 -0.49 0.00 -0.54 0.01 7.93 0.85 None
right atr AD 0.06 0.37 -0.59 0.00 -0.53 0.01 -11.60 0.38 None
right atr RD 0.08 0.59 -0.61 0.00 -0.53 0.01 -15.20 0.61 None
right atr MD 0.14 0.24 -0.66 0.00 -0.52 0.01 -26.67 0.25 None
left cab FA 0.02 0.52 -0.56 0.01 -0.54 0.01 -4.44 0.52 None
left cab AD 0.09 0.25 -0.62 0.00 -0.53 0.01 -17.12 0.26 None
left cab RD 0.00 0.91 -0.54 0.00 -0.53 0.01 -0.60 0.91 None
left cab MD 0.06 0.42 -0.59 0.00 -0.53 0.01 -11.84 0.43 None
right cab FA 0.11 0.06 -0.63 0.00 -0.52 0.01 -21.77 0.07 None
right cab AD -0.01 0.92 -0.52 0.01 -0.53 0.01 2.28 0.92 None
right cab RD 0.14 0.12 -0.67 0.00 -0.52 0.01 -27.60 0.13 None
right cab MD 0.07 0.56 -0.60 0.01 -0.53 0.01 -12.72 0.57 None
left cing FA -0.07 0.21 -0.47 0.02 -0.53 0.01 12.48 0.22 None
left cing AD 0.05 0.55 -0.59 0.01 -0.53 0.01 -9.89 0.55 None
left cing RD -0.03 0.61 -0.50 0.01 -0.53 0.01 5.80 0.61 None
left cing MD 0.07 0.23 -0.61 0.01 -0.53 0.01 -13.55 0.23 None
right cing FA -0.16 0.61 -0.38 0.04 -0.54 0.01 29.99 0.60 None
right cing AD -0.09 0.34 -0.44 0.02 -0.53 0.01 17.22 0.34 None
right cing RD 0.07 0.79 -0.60 0.01 -0.53 0.01 -12.98 0.80 None
right cing MD 0.26 0.05 -0.78 0.00 -0.52 0.01 -49.43 0.06 None
left cst FA -0.04 0.33 -0.50 0.01 -0.54 0.01 7.86 0.33 None
left cst AD 0.15 0.11 -0.68 0.01 -0.54 0.01 -27.00 0.12 None
left cst RD 0.00 1.00 -0.53 0.01 -0.53 0.01 0.66 0.99 None
left cst MD 0.11 0.36 -0.64 0.00 -0.53 0.01 -21.14 0.37 None
right cst FA -0.03 0.67 -0.51 0.01 -0.54 0.01 5.66 0.66 None
right cst AD 0.05 0.64 -0.58 0.01 -0.54 0.01 -8.52 0.64 None
right cst RD 0.06 0.37 -0.59 0.00 -0.52 0.01 -12.25 0.39 None
right cst MD 0.14 0.11 -0.66 0.00 -0.52 0.01 -26.16 0.12 None
left ilf FA 0.00 0.77 -0.54 0.03 -0.54 0.01 0.22 0.78 None
left ilf AD 0.07 0.57 -0.61 0.01 -0.54 0.01 -13.85 0.58 None
left ilf RD -0.05 0.60 -0.49 0.01 -0.54 0.01 9.30 0.60 None
left ilf MD -0.03 0.84 -0.51 0.01 -0.53 0.01 5.10 0.84 None
right ilf FA 0.14 0.58 -0.67 0.01 -0.53 0.01 -25.95 0.59 None
right ilf AD 0.10 0.65 -0.64 0.02 -0.53 0.01 -19.24 0.66 None
right ilf RD 0.23 0.43 -0.76 0.01 -0.53 0.01 -44.33 0.44 None
right ilf MD 0.22 0.44 -0.75 0.02 -0.53 0.01 -40.59 0.45 None
left slfp FA 0.01 0.87 -0.54 0.01 -0.53 0.01 -2.02 0.88 None
left slfp AD 0.07 0.32 -0.60 0.02 -0.53 0.01 -12.42 0.32 None
left slfp RD 0.07 0.41 -0.60 0.01 -0.53 0.01 -14.00 0.41 None
left slfp MD 0.09 0.31 -0.62 0.01 -0.53 0.01 -17.85 0.32 None
right slfp FA -0.13 0.40 -0.41 0.01 -0.54 0.01 23.42 0.39 None
right slfp AD -0.10 0.29 -0.44 0.02 -0.54 0.01 18.01 0.29 None
right slfp RD -0.05 0.72 -0.49 0.01 -0.54 0.01 8.61 0.71 None
right slfp MD 0.02 0.80 -0.55 0.00 -0.53 0.01 -3.75 0.81 None
left slft FA 0.09 0.12 -0.61 0.00 -0.53 0.01 -16.50 0.13 None
left slft AD -0.02 0.76 -0.51 0.02 -0.53 0.01 3.32 0.76 None
left slft RD 0.11 0.17 -0.64 0.00 -0.53 0.01 -20.49 0.18 None
left slft MD 0.06 0.53 -0.59 0.01 -0.53 0.01 -10.75 0.54 None
right slft FA -0.13 0.63 -0.41 0.03 -0.54 0.01 23.82 0.63 None
right slft AD 0.03 0.79 -0.56 0.01 -0.54 0.01 -4.76 0.79 None
right slft RD 0.02 0.91 -0.55 0.02 -0.53 0.01 -3.73 0.92 None
right slft MD 0.18 0.31 -0.71 0.00 -0.53 0.01 -33.16 0.31 None
left unc FA -0.01 0.72 -0.53 0.01 -0.54 0.01 2.47 0.72 None
left unc AD 0.13 0.22 -0.67 0.01 -0.53 0.01 -24.86 0.22 None
left unc RD -0.02 0.80 -0.51 0.01 -0.53 0.01 4.58 0.79 None
left unc MD 0.03 0.75 -0.56 0.00 -0.53 0.01 -5.65 0.76 None
right unc FA 0.18 0.29 -0.70 0.00 -0.52 0.01 -33.98 0.30 None
right unc AD 0.09 0.23 -0.62 0.00 -0.54 0.01 -16.43 0.23 None
right unc RD 0.29 0.06 -0.81 0.00 -0.52 0.01 -55.37 0.07 None
right unc MD 0.26 0.03 -0.79 0.00 -0.53 0.01 -49.70 0.04 Partial
Accuracy

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

Emotion Measures

Trajectory

Model Fit Decision Process

Biopsychosocial Model Fit
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

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

Tract Metric IndirectEffect_Estimate IndirectEffect_P_Value DirectEffect_Estimate DirectEffect_P_Value TotalEffect_Estimate TotalEffect_P_Value ProportionMediated_PercentEstimate ProportionMediated_P_Value MediationEffect
forceps major FA -0.34 0.05 -0.23 0.28 -0.57 0.01 59.14 0.06 None
forceps major AD -0.18 0.25 -0.37 0.16 -0.55 0.01 32.76 0.26 None
forceps major RD -0.48 0.02 -0.08 0.73 -0.56 0.01 85.36 0.03 Full
forceps major MD -0.46 0.01 -0.10 0.69 -0.56 0.01 82.44 0.02 Full
forceps minor FA -0.08 0.57 -0.49 0.03 -0.57 0.01 14.50 0.57 None
forceps minor AD -0.01 0.85 -0.55 0.02 -0.56 0.01 2.52 0.86 None
forceps minor RD -0.09 0.42 -0.48 0.05 -0.57 0.01 15.28 0.43 None
forceps minor MD -0.06 0.47 -0.50 0.03 -0.56 0.01 10.79 0.47 None
left atr FA -0.02 0.62 -0.54 0.03 -0.56 0.01 4.31 0.63 None
left atr AD -0.04 0.63 -0.52 0.03 -0.56 0.01 7.01 0.63 None
left atr RD -0.04 0.59 -0.52 0.05 -0.56 0.01 7.99 0.59 None
left atr MD -0.06 0.55 -0.50 0.06 -0.56 0.01 10.30 0.56 None
right atr FA -0.12 0.46 -0.46 0.05 -0.57 0.01 20.19 0.47 None
right atr AD -0.01 0.67 -0.55 0.02 -0.56 0.01 2.50 0.67 None
right atr RD -0.14 0.28 -0.43 0.08 -0.57 0.01 24.05 0.29 None
right atr MD -0.11 0.22 -0.46 0.07 -0.57 0.01 18.84 0.23 None
left cab FA -0.01 0.69 -0.55 0.02 -0.56 0.01 1.92 0.69 None
left cab AD -0.11 0.07 -0.45 0.03 -0.56 0.01 20.24 0.08 None
left cab RD -0.03 0.70 -0.54 0.01 -0.57 0.00 4.57 0.70 None
left cab MD -0.10 0.21 -0.47 0.02 -0.57 0.01 18.30 0.21 None
right cab FA 0.07 0.29 -0.62 0.01 -0.55 0.01 -11.82 0.29 None
right cab AD -0.06 0.12 -0.49 0.04 -0.56 0.01 11.45 0.13 None
right cab RD -0.02 0.84 -0.55 0.04 -0.56 0.01 3.20 0.85 None
right cab MD -0.07 0.31 -0.49 0.05 -0.56 0.01 12.82 0.32 None
left cing FA -0.03 0.68 -0.54 0.01 -0.56 0.01 4.49 0.68 None
left cing AD 0.00 0.82 -0.56 0.02 -0.56 0.01 0.49 0.83 None
left cing RD -0.04 0.60 -0.52 0.02 -0.56 0.01 7.00 0.60 None
left cing MD -0.03 0.72 -0.53 0.03 -0.56 0.01 5.88 0.73 None
right cing FA -0.22 0.46 -0.35 0.36 -0.57 0.01 38.83 0.47 None
right cing AD -0.01 0.67 -0.55 0.02 -0.56 0.01 1.68 0.67 None
right cing RD -0.35 0.27 -0.22 0.49 -0.57 0.01 61.42 0.28 None
right cing MD -0.11 0.43 -0.46 0.17 -0.57 0.01 19.45 0.44 None
left cst FA 0.00 0.95 -0.56 0.02 -0.56 0.01 -0.13 0.95 None
left cst AD -0.01 0.84 -0.55 0.10 -0.56 0.01 1.97 0.85 None
left cst RD -0.01 0.92 -0.56 0.03 -0.56 0.01 1.08 0.93 None
left cst MD -0.02 0.84 -0.55 0.06 -0.56 0.01 2.81 0.85 None
right cst FA -0.02 0.82 -0.55 0.03 -0.57 0.01 3.14 0.82 None
right cst AD 0.01 0.84 -0.57 0.03 -0.56 0.01 -1.30 0.85 None
right cst RD -0.01 0.93 -0.56 0.04 -0.56 0.01 1.11 0.94 None
right cst MD 0.01 0.89 -0.57 0.05 -0.56 0.01 -1.81 0.88 None
left ilf FA 0.00 0.77 -0.57 0.01 -0.57 0.01 0.17 0.77 None
left ilf AD -0.23 0.07 -0.32 0.21 -0.56 0.01 42.09 0.08 None
left ilf RD -0.13 0.19 -0.44 0.03 -0.57 0.01 22.60 0.19 None
left ilf MD -0.26 0.04 -0.30 0.11 -0.56 0.01 45.82 0.05 Full
right ilf FA -0.30 0.16 -0.27 0.40 -0.57 0.01 52.63 0.17 None
right ilf AD -0.27 0.12 -0.29 0.32 -0.56 0.01 47.85 0.13 None
right ilf RD -0.49 0.04 -0.08 0.80 -0.57 0.01 85.53 0.05 Full
right ilf MD -0.48 0.03 -0.09 0.77 -0.56 0.01 84.73 0.03 Full
left slfp FA -0.03 0.66 -0.53 0.01 -0.57 0.00 5.99 0.66 None
left slfp AD -0.03 0.50 -0.53 0.05 -0.56 0.01 6.14 0.51 None
left slfp RD -0.06 0.44 -0.50 0.02 -0.57 0.01 11.45 0.44 None
left slfp MD -0.07 0.39 -0.50 0.05 -0.57 0.01 12.19 0.40 None
right slfp FA -0.21 0.15 -0.37 0.08 -0.58 0.00 36.63 0.15 None
right slfp AD -0.02 0.69 -0.55 0.01 -0.56 0.01 2.67 0.68 None
right slfp RD -0.18 0.06 -0.39 0.03 -0.58 0.01 31.93 0.06 None
right slfp MD -0.07 0.35 -0.50 0.02 -0.57 0.01 12.15 0.35 None
left slft FA -0.09 0.25 -0.48 0.02 -0.57 0.01 16.22 0.26 None
left slft AD -0.03 0.47 -0.53 0.03 -0.56 0.02 5.72 0.48 None
left slft RD -0.14 0.15 -0.43 0.03 -0.57 0.01 24.57 0.16 None
left slft MD -0.12 0.15 -0.44 0.04 -0.56 0.01 21.45 0.16 None
right slft FA -0.42 0.04 -0.16 0.51 -0.57 0.01 72.38 0.04 Full
right slft AD 0.00 0.76 -0.57 0.04 -0.56 0.01 -0.65 0.77 None
right slft RD -0.46 0.01 -0.11 0.63 -0.57 0.01 80.80 0.02 Full
right slft MD -0.31 0.07 -0.26 0.39 -0.57 0.01 54.90 0.08 None
left unc FA -0.01 0.51 -0.56 0.02 -0.57 0.01 1.42 0.52 None
left unc AD -0.06 0.67 -0.50 0.10 -0.56 0.01 10.76 0.68 None
left unc RD -0.07 0.39 -0.50 0.04 -0.57 0.01 11.78 0.40 None
left unc MD -0.09 0.40 -0.47 0.06 -0.56 0.01 16.33 0.41 None
right unc FA -0.02 0.85 -0.54 0.10 -0.56 0.01 3.69 0.86 None
right unc AD -0.02 0.69 -0.54 0.03 -0.56 0.01 4.06 0.70 None
right unc RD -0.03 0.75 -0.53 0.16 -0.56 0.01 6.01 0.75 None
right unc MD -0.04 0.72 -0.52 0.10 -0.56 0.01 7.26 0.73 None

WeeksSinceInjury_DTIMetric(Mediator)_Depression

No mediation effect was found across tracts.