Point Constraint Statistics
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When you save the notebook, an HTML file containing the code and output will be saved alongside it (click the Preview button or press Cmd+Shift+K to preview the HTML file). #Write cost functions
Load data and compute cost
All points for an 80%-of-max task
## Loading required package: GGally## Warning: package 'GGally' was built under R version 3.3.2## Loading required package: ggplot2## Warning: package 'ggplot2' was built under R version 3.3.2
#View all points as boxplots: 
## FDP FDS EIP
## Min. :0.01357 Min. :0.007762 Min. :0.001747
## 1st Qu.:0.14430 1st Qu.:0.069695 1st Qu.:0.260326
## Median :0.19247 Median :0.092336 Median :0.500613
## Mean :0.19100 Mean :0.091863 Mean :0.504462
## 3rd Qu.:0.24153 3rd Qu.:0.115783 3rd Qu.:0.758679
## Max. :0.33463 Max. :0.160963 Max. :0.999629
## EDC LUM DI
## Min. :0.001132 Min. :0.0003311 Min. :0.0001764
## 1st Qu.:0.412881 1st Qu.:0.2209727 1st Qu.:0.1004263
## Median :0.601081 Median :0.4262012 Median :0.1799842
## Mean :0.578074 Mean :0.4469257 Mean :0.1875894
## 3rd Qu.:0.758173 3rd Qu.:0.6677409 3rd Qu.:0.2629963
## Max. :0.999588 Max. :0.9990431 Max. :0.5156824
## PI
## Min. :0.001317
## 1st Qu.:0.090575
## Median :0.151913
## Mean :0.154694
## 3rd Qu.:0.212580
## Max. :0.387905what about parcoord axes being parallel (few line crossings between muscle actiavtions)?
cor(points_w_cost$FDP, points_w_cost$FDS)## [1] 0.9998411what about many crossings between two muscles?
cor(points_w_cost$LUM, points_w_cost$DI)## [1] -0.4982628cor(points_w_cost$EIP, points_w_cost$EDC)## [1] -0.06642129library(corrplot)
corrplot(cor(points_w_cost), order = "hclust", addrect=5)
Let’s grab the bottom 10% of L2W cost and see how the muscle activations are distributed
## FDP FDS EIP
## Min. :0.01357 Min. :0.007762 Min. :0.001936
## 1st Qu.:0.06686 1st Qu.:0.032769 1st Qu.:0.099902
## Median :0.08922 Median :0.043177 Median :0.191305
## Mean :0.08594 Mean :0.041834 Mean :0.205708
## 3rd Qu.:0.11054 3rd Qu.:0.053781 3rd Qu.:0.308059
## Max. :0.13065 Max. :0.062602 Max. :0.499439
## EDC LUM DI
## Min. :0.009153 Min. :0.005913 Min. :0.002266
## 1st Qu.:0.180492 1st Qu.:0.129539 1st Qu.:0.036946
## Median :0.283373 Median :0.248116 Median :0.059195
## Mean :0.269663 Mean :0.283379 Mean :0.074878
## 3rd Qu.:0.365629 3rd Qu.:0.424265 3rd Qu.:0.117655
## Max. :0.468751 Max. :0.692210 Max. :0.190278
## PI
## Min. :0.002277
## 1st Qu.:0.024293
## Median :0.051305
## Mean :0.054887
## 3rd Qu.:0.081641
## Max. :0.133341Limiting one muscle:
Our dataset can be used to simulate a 40% reduction in activation (due to muscle dysfunction, for example) in the two index finger muscles innervated by the radial nerve (EIP and EDC).
## FDP FDS EIP
## Min. :0.01357 Min. :0.007762 Min. :0.001936
## 1st Qu.:0.10158 1st Qu.:0.048847 1st Qu.:0.150776
## Median :0.13908 Median :0.067052 Median :0.299853
## Mean :0.13068 Mean :0.063065 Mean :0.300343
## 3rd Qu.:0.16418 3rd Qu.:0.078859 3rd Qu.:0.455278
## Max. :0.19852 Max. :0.095062 Max. :0.594677
## EDC LUM DI
## Min. :0.009153 Min. :0.005913 Min. :0.001012
## 1st Qu.:0.309293 1st Qu.:0.170160 1st Qu.:0.053976
## Median :0.443477 Median :0.325978 Median :0.112468
## Mean :0.408749 Mean :0.370912 Mean :0.116461
## 3rd Qu.:0.530161 3rd Qu.:0.545670 3rd Qu.:0.171332
## Max. :0.598835 Max. :0.962193 Max. :0.309409
## PI
## Min. :0.002277
## 1st Qu.:0.054151
## Median :0.092123
## Mean :0.094562
## 3rd Qu.:0.132383
## Max. :0.221263When flexor digitorum profundus has resting tonicity of 0.2:
## FDP FDS EIP EDC
## Min. :0.2001 Min. :0.09564 Min. :0.009423 Min. :0.5008
## 1st Qu.:0.2193 1st Qu.:0.10493 1st Qu.:0.332995 1st Qu.:0.6909
## Median :0.2442 Median :0.11709 Median :0.567915 Median :0.7637
## Mean :0.2492 Mean :0.11946 Mean :0.553988 Mean :0.7777
## 3rd Qu.:0.2753 3rd Qu.:0.13190 3rd Qu.:0.794048 3rd Qu.:0.8786
## Max. :0.3346 Max. :0.16096 Max. :0.999629 Max. :0.9996
## LUM DI PI
## Min. :0.004486 Min. :0.04966 Min. :0.0932
## 1st Qu.:0.256842 1st Qu.:0.18648 1st Qu.:0.1711
## Median :0.504870 Median :0.25665 Median :0.2142
## Mean :0.496704 Mean :0.25766 Mean :0.2171
## 3rd Qu.:0.730647 3rd Qu.:0.32410 3rd Qu.:0.2576
## Max. :0.999043 Max. :0.51568 Max. :0.3879Manual observations on the effects upon other muscles when FDP activation is kept above 0.2: - FDS becomes constrained between .09 and 0.16, with middle 50% of solutions in a range spanning only .02697 (between .13190 and .10493) - EDC goes from being redundant (with bounds of 0 and 1), to being only in the upper half (0.5 to 0.88)
Which muscle, when hypotonic, slices the FAS more—PI or DI?
Let’s limit each to 20% of maximal distal fingertip force.
## FDP FDS EIP
## Min. :0.01357 Min. :0.007762 Min. :0.001747
## 1st Qu.:0.12208 1st Qu.:0.059204 1st Qu.:0.220062
## Median :0.16583 Median :0.079812 Median :0.440370
## Mean :0.16200 Mean :0.078000 Mean :0.469318
## 3rd Qu.:0.20481 3rd Qu.:0.098008 3rd Qu.:0.725786
## Max. :0.29395 Max. :0.140646 Max. :0.999629
## EDC LUM DI
## Min. :0.001132 Min. :0.0003311 Min. :0.0001764
## 1st Qu.:0.333529 1st Qu.:0.2754155 1st Qu.:0.0717440
## Median :0.496606 Median :0.5083091 Median :0.1300251
## Mean :0.480370 Mean :0.4957852 Mean :0.1308368
## 3rd Qu.:0.632880 3rd Qu.:0.7043622 3rd Qu.:0.1864969
## Max. :0.956826 Max. :0.9990431 Max. :0.2855284
## PI
## Min. :0.001317
## 1st Qu.:0.067947
## Median :0.116917
## Mean :0.111577
## 3rd Qu.:0.157552
## Max. :0.199896
## FDP FDS EIP
## Min. :0.01357 Min. :0.007762 Min. :0.001747
## 1st Qu.:0.11548 1st Qu.:0.055890 1st Qu.:0.195862
## Median :0.15946 Median :0.076669 Median :0.398982
## Mean :0.15664 Mean :0.075365 Mean :0.448702
## 3rd Qu.:0.20042 3rd Qu.:0.096050 3rd Qu.:0.702340
## Max. :0.29395 Max. :0.140646 Max. :0.999629
## EDC LUM DI
## Min. :0.001132 Min. :0.005877 Min. :0.0001764
## 1st Qu.:0.300929 1st Qu.:0.336927 1st Qu.:0.0601682
## Median :0.479448 Median :0.558418 Median :0.1115024
## Mean :0.465338 Mean :0.543292 Mean :0.1086178
## 3rd Qu.:0.626037 3rd Qu.:0.746026 3rd Qu.:0.1559808
## Max. :0.981464 Max. :0.999043 Max. :0.1997135
## PI
## Min. :0.001317
## 1st Qu.:0.059449
## Median :0.101185
## Mean :0.097346
## 3rd Qu.:0.134199
## Max. :0.205729## No id variables; using all as measure variables
## No id variables; using all as measure variables
## FDP FDS EIP
## Min. :0.01357 Min. :0.007762 Min. :0.001747
## 1st Qu.:0.11548 1st Qu.:0.055890 1st Qu.:0.195862
## Median :0.15946 Median :0.076669 Median :0.398982
## Mean :0.15664 Mean :0.075365 Mean :0.448702
## 3rd Qu.:0.20042 3rd Qu.:0.096050 3rd Qu.:0.702340
## Max. :0.29395 Max. :0.140646 Max. :0.999629
## EDC LUM DI
## Min. :0.001132 Min. :0.005877 Min. :0.0001764
## 1st Qu.:0.300929 1st Qu.:0.336927 1st Qu.:0.0601682
## Median :0.479448 Median :0.558418 Median :0.1115024
## Mean :0.465338 Mean :0.543292 Mean :0.1086178
## 3rd Qu.:0.626037 3rd Qu.:0.746026 3rd Qu.:0.1559808
## Max. :0.981464 Max. :0.999043 Max. :0.1997135
## PI
## Min. :0.001317
## 1st Qu.:0.059449
## Median :0.101185
## Mean :0.097346
## 3rd Qu.:0.134199
## Max. :0.205729showing the wide bounds with small IQR for a muscle at higher force (not 80%)
high_force_points <- read.csv("finger_forcevector_25.379547626496084_1484881649920.csv")
par(mfrow=c(3,3))
lapply(1:7,
function(x) {
hist(high_force_points[,x], xlim=c(0,1))
summary(high_force_points[,x])
}
)## [[1]]
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.06631 0.13230 0.16320 0.15970 0.19010 0.25230
##
## [[2]]
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.06907 0.10000 0.11430 0.11270 0.12690 0.15680
##
## [[3]]
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0004144 0.2560000 0.4773000 0.4917000 0.7363000 0.9996000
##
## [[4]]
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.3448 0.6543 0.7756 0.7600 0.8826 0.9996
##
## [[5]]
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.007945 0.371700 0.559700 0.553000 0.757300 0.996100
##
## [[6]]
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.8785 0.9350 0.9594 0.9552 0.9791 1.0000
##
## [[7]]
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 2.949e-05 1.344e-02 2.624e-02 2.844e-02 4.074e-02 8.130e-02