{
"cells": [
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"source": [
"# Body segment parameters\n",
"\n",
"> Marcos Duarte \n",
"> [Laboratory of Biomechanics and Motor Control](http://pesquisa.ufabc.edu.br/bmclab/) \n",
"> Federal University of ABC, Brazil"
]
},
{
"cell_type": "markdown",
"metadata": {
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"source": [
"\n",
"
\n",
"\"Le proporzioni del corpo umano secondo Vitruvio\", also known as the Vitruvian Man, drawing by Leonardo da Vinci circa 1490 based on the work of Marcus Vitruvius Pollio (1st century BC), depicting a man in supposedly ideal human proportions (image from Wikipedia).\n",
"
\n",
"In fact, Leonardo's drawing does not follow the proportions according Vitruvius, but rather the proportions he found after his own anthropometrical studies of the human body. Leonardo was unable to fit a human body inside a circle and a square with the same center, one of the Vitruvius' claims.\n",
"
\n",
"This is a remarkable historical evidence of not complying with established common knowledge and relying on experimental data for acquiring knowledge about nature, a tour de force for the scientific method."
]
},
{
"cell_type": "markdown",
"metadata": {
"toc": 1,
"id": "c-MFs5IoO6aa"
},
"source": [
"
"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "rkfhb8-gO6ab"
},
"source": [
"## Estimation of body segment parameters\n",
"\n",
"Body segment parameters (BSP) of the human body, such as length, area, volume, mass, density, center of mass, moment of inertia, and center of volume, are fundamental for the application of mechanics to the understanding of human movement. Anthropometry is the field concerned with the study of such measurements of the human body. Frequently, one cannot measure most of these parameters of each segment of an individual and these quantities are estimated by indirect methods. The main indirect methods are based in data of cadavers (e.g. Dempster's model), body image scanning of living subjects (e.g., Zatsiorsky-Seluyanov's model), and geometric measurements (e.g., Hanavan's model). \n",
"\n",
"For reviews available online of the different methods employed in the estimation of BSP, see [Drills et al. (1964)](http://www.oandplibrary.org/al/1964_01_044.asp) and [Bjørnstrup (1995)](http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.21.5223). \n",
"\n",
"Let's look on how to estimate some of the BSP using the anthropometric model of Dempster (1955) with some parameters adapted by Winter (2009) and the model of Zatsiorsky and Seluyanov (Zatsiorsky, 2002), from now on, Zatsiorsky, with parameters adjusted by de Leva (1996). There is at least one Python library for the calculation of human body segment parameters, see Dembia et al. (2014), it implements the Yeadon human inertia geometric model, but we will not use it here.\n",
"\n",
"For a table with BSP values, also referred as anthropometric table, typically: \n",
"\n",
"+ The mass of each segment is given as fraction of the total body mass. \n",
"+ The center of mass (CM) position in the sagittal plane of each segment is given as fraction of the segment length with respect to the proximal or distal joint position.\n",
"+ The radius of gyration (Rg) around the transverse axis (rotation at the sagittal plane) and around other axes of each segment is given as fraction of the segment length with respect to (w.r.t.) the center of mass or w.r.t. the proximal or w.r.t. the distal joint position.\n",
"\n",
"For a formal description of these parameters, see the notebook [Center of Mass and Moment of Inertia](https://nbviewer.jupyter.org/github/BMClab/bmc/blob/master/notebooks/CenterOfMassAndMomentOfInertia.ipynb)."
]
},
{
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"outputs": [],
"source": [
"# Import the necessary libraries\n",
"import numpy as np\n",
"import pandas as pd\n",
"from IPython.display import display, Math, Latex\n",
"%matplotlib inline\n",
"import matplotlib.pyplot as plt\n",
"pd.set_option('max_colwidth', 100)"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "77NnQx7oO6ad"
},
"source": [
"### Dempster's model adapted by Winter"
]
},
{
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"execution_count": 11,
"metadata": {
"ExecuteTime": {
"end_time": "2020-04-17T14:59:00.841434Z",
"start_time": "2020-04-17T14:59:00.831073Z"
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"id": "IAP8B4oaO6ad",
"outputId": "a9c8165a-b94e-47ad-f309-9f6ad6f3ef13",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 665
}
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"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
""
],
"text/latex": "\\text{BSP segments from Dempster's model adapted by Winter (2009):}"
},
"metadata": {}
},
{
"output_type": "display_data",
"data": {
"text/plain": [
" Segment Definition Mass CM prox CM dist Rg CM \\\n",
"0 Hand WJC-KNU2 0.0060 0.506 0.494 0.297 \n",
"1 Forearm EJC-STYL 0.0160 0.430 0.570 0.303 \n",
"2 Upper arm SJC-EJC 0.0280 0.436 0.564 0.322 \n",
"3 Forearm hand EJC-STYL 0.0220 0.682 0.318 0.468 \n",
"4 Total arm SJC-STYL 0.0500 0.530 0.470 0.368 \n",
"5 Foot LMAL-MT2 0.0145 0.500 0.500 0.475 \n",
"6 Leg KJC-MMAL 0.0465 0.433 0.567 0.302 \n",
"7 Thigh GTR-KJC 0.1000 0.433 0.567 0.323 \n",
"8 Head neck C7T1-RIB1EAR 0.0810 1.000 0.000 0.495 \n",
"9 Thorax C7T1-T12L1-DIAP 0.2160 0.820 0.180 NaN \n",
"10 Abdomen T12L1-GTR 0.1390 0.440 0.560 NaN \n",
"11 Pelvis L4L5-GTR 0.1420 0.105 0.895 NaN \n",
"12 Trunk GTR-SJC 0.4970 0.500 0.500 NaN \n",
"13 Trunk head neck GTR-SJC 0.5780 0.660 0.340 0.503 \n",
"14 HAT GTR-SJC 0.6780 0.626 0.374 0.496 \n",
"15 Foot leg KJC-MMAL 0.0610 0.606 0.394 0.416 \n",
"16 Total leg GTR-MMAL 0.1610 0.447 0.553 0.326 \n",
"17 Thorax abdomen C7T1-L4L5 0.3550 0.630 0.370 NaN \n",
"18 Abdomen pelvis T12L1-GTR 0.2810 0.270 0.730 NaN \n",
"\n",
" Rg prox Rg dist \n",
"0 0.587 0.577 \n",
"1 0.526 0.647 \n",
"2 0.542 0.645 \n",
"3 0.827 0.565 \n",
"4 0.645 0.596 \n",
"5 0.690 0.690 \n",
"6 0.528 0.643 \n",
"7 0.540 0.653 \n",
"8 0.116 NaN \n",
"9 NaN NaN \n",
"10 NaN NaN \n",
"11 NaN NaN \n",
"12 NaN NaN \n",
"13 0.830 0.607 \n",
"14 0.798 0.621 \n",
"15 0.735 0.572 \n",
"16 0.560 0.650 \n",
"17 NaN NaN \n",
"18 NaN NaN "
],
"text/html": [
"\n",
"
"
],
"text/plain": [
" Definition Mass CM prox CM dist Rg CM Rg prox \\\n",
"Segment \n",
"Hand WJC-KNU2 0.0060 0.506 0.494 0.297 0.587 \n",
"Forearm EJC-STYL 0.0160 0.430 0.570 0.303 0.526 \n",
"Upper arm SJC-EJC 0.0280 0.436 0.564 0.322 0.542 \n",
"Forearm hand EJC-STYL 0.0220 0.682 0.318 0.468 0.827 \n",
"Total arm SJC-STYL 0.0500 0.530 0.470 0.368 0.645 \n",
"Foot LMAL-MT2 0.0145 0.500 0.500 0.475 0.690 \n",
"Leg KJC-MMAL 0.0465 0.433 0.567 0.302 0.528 \n",
"Thigh GTR-KJC 0.1000 0.433 0.567 0.323 0.540 \n",
"Head neck C7T1-RIB1EAR 0.0810 1.000 0.000 0.495 0.116 \n",
"Thorax C7T1-T12L1-DIAP 0.2160 0.820 0.180 NaN NaN \n",
"Abdomen T12L1-GTR 0.1390 0.440 0.560 NaN NaN \n",
"Pelvis L4L5-GTR 0.1420 0.105 0.895 NaN NaN \n",
"Trunk GTR-SJC 0.4970 0.500 0.500 NaN NaN \n",
"Trunk head neck GTR-SJC 0.5780 0.660 0.340 0.503 0.830 \n",
"HAT GTR-SJC 0.6780 0.626 0.374 0.496 0.798 \n",
"Foot leg KJC-MMAL 0.0610 0.606 0.394 0.416 0.735 \n",
"Total leg GTR-MMAL 0.1610 0.447 0.553 0.326 0.560 \n",
"Thorax abdomen C7T1-L4L5 0.3550 0.630 0.370 NaN NaN \n",
"Abdomen pelvis T12L1-GTR 0.2810 0.270 0.730 NaN NaN \n",
"\n",
" Rg dist \n",
"Segment \n",
"Hand 0.577 \n",
"Forearm 0.647 \n",
"Upper arm 0.645 \n",
"Forearm hand 0.565 \n",
"Total arm 0.596 \n",
"Foot 0.690 \n",
"Leg 0.643 \n",
"Thigh 0.653 \n",
"Head neck NaN \n",
"Thorax NaN \n",
"Abdomen NaN \n",
"Pelvis NaN \n",
"Trunk NaN \n",
"Trunk head neck 0.607 \n",
"HAT 0.621 \n",
"Foot leg 0.572 \n",
"Total leg 0.650 \n",
"Thorax abdomen NaN \n",
"Abdomen pelvis NaN "
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"bsp_D = pd.read_csv('https://raw.githubusercontent.com/BMClab/BMC/master/data/BSP_DempsterWinter.txt', index_col=0, sep='\\t')\n",
"display(Latex('BSP values from Dempster\\'s model adapted by Winter (2009):'))\n",
"display(bsp_D)"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "rfzE36uAO6af"
},
"source": [
"### Zatsiorsky's model adjusted by de Leva\n",
"\n",
"The segments defined in the Zatsiorsky's model (Zatsiorsky, 2002) adjusted by de Leva (1996) are illustrated in the next figure.\n",
"\n",
""
]
},
{
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"execution_count": null,
"metadata": {
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{
"data": {
"text/latex": [
"BSP landmarks from Zatsiorsky's model adjusted by de Leva (1996):"
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
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{
"data": {
"text/html": [
"
\n",
"\n",
"
\n",
" \n",
"
\n",
"
\n",
"
Landmark Name
\n",
"
Abbreviation
\n",
"
Description
\n",
"
\n",
" \n",
" \n",
"
\n",
"
0
\n",
"
Acromion
\n",
"
ACRO
\n",
"
Most lateral point on the lateral edge of the acromial process of the scapula
\n",
"
\n",
"
\n",
"
1
\n",
"
Acropodion
\n",
"
TTIP
\n",
"
Tip of longest toe
\n",
"
\n",
"
\n",
"
2
\n",
"
Bispinous breadth
\n",
"
BB
\n",
"
Distance between two ASIS
\n",
"
\n",
"
\n",
"
3
\n",
"
Cervicale
\n",
"
CERV
\n",
"
Superior tip of the spine of the 7th certical vertebra
\n",
"
\n",
"
\n",
"
4
\n",
"
Dactylion (3rd)
\n",
"
DAC3
\n",
"
Tip of 3 rd digit
\n",
"
\n",
"
\n",
"
5
\n",
"
Gonion
\n",
"
GONI
\n",
"
Most lateral point on the posterior angle of mandible
\n",
"
\n",
"
\n",
"
6
\n",
"
Iliospinale
\n",
"
ASIS
\n",
"
Inferior point of one of the anterior superior iliac spines
\n",
"
\n",
"
\n",
"
7
\n",
"
Malleoli
\n",
"
MMAL, LMAL
\n",
"
Medial and lateral bony projections of the malleolus
\n",
"
\n",
"
\n",
"
8
\n",
"
Metacarpale (3rd)
\n",
"
MET3
\n",
"
Distal palpable point on the metacarpal of the 3rd digit on the dorsal hand
\n",
"
\n",
"
\n",
"
9
\n",
"
Mid-gonion
\n",
"
MIDG
\n",
"
Point midway between 2 gonion
\n",
"
\n",
"
\n",
"
10
\n",
"
Mid-hip
\n",
"
MIDH
\n",
"
Point midway between 2 hip joint centers
\n",
"
\n",
"
\n",
"
11
\n",
"
Mid-shoulder
\n",
"
MIDS
\n",
"
Point midway between 2 shoulder joint centers
\n",
"
\n",
"
\n",
"
12
\n",
"
Omphalion
\n",
"
OMPH
\n",
"
Center of navel
\n",
"
\n",
"
\n",
"
13
\n",
"
Pternion
\n",
"
HEEL
\n",
"
Posterior point of the heel
\n",
"
\n",
"
\n",
"
14
\n",
"
Radiale
\n",
"
RADI
\n",
"
Lateral tip on the proximal head of the radius
\n",
"
\n",
"
\n",
"
15
\n",
"
Sphyrion (tibia)
\n",
"
TSPH
\n",
"
Distal tip of the tibia – distal to medial malleolus
\n",
"
\n",
"
\n",
"
16
\n",
"
Sphyrion fibulare
\n",
"
FSPH
\n",
"
Distal tip of the fibula – distal to lateral malleolus
\n",
"
\n",
"
\n",
"
17
\n",
"
Stylion
\n",
"
RSTY
\n",
"
Distal dip of the styloid process of the radius
\n",
"
\n",
"
\n",
"
18
\n",
"
Suprasternale
\n",
"
SUPR
\n",
"
Most caudal point on the jugular notch on the sternum
\n",
"
\n",
"
\n",
"
19
\n",
"
Tibiale (medial)
\n",
"
MTIB
\n",
"
Most proximal point on the medial superior border of the head of the tibia
\n",
"
\n",
"
\n",
"
20
\n",
"
Tibiale laterale
\n",
"
LTIB
\n",
"
Most proximal point on the lateral superior border of the head of the fibula
\n",
"
\n",
"
\n",
"
21
\n",
"
Trochanterion
\n",
"
TROC
\n",
"
Superior border on the greater trochanter of the femur
\n",
"
\n",
"
\n",
"
22
\n",
"
Vertex
\n",
"
VERT
\n",
"
Uppermost part of the head
\n",
"
\n",
"
\n",
"
23
\n",
"
Xiphion
\n",
"
XYPH
\n",
"
Lowermost end of the sternum
\n",
"
\n",
" \n",
"
\n",
"
"
],
"text/plain": [
" Landmark Name Abbreviation \\\n",
"0 Acromion ACRO \n",
"1 Acropodion TTIP \n",
"2 Bispinous breadth BB \n",
"3 Cervicale CERV \n",
"4 Dactylion (3rd) DAC3 \n",
"5 Gonion GONI \n",
"6 Iliospinale ASIS \n",
"7 Malleoli MMAL, LMAL \n",
"8 Metacarpale (3rd) MET3 \n",
"9 Mid-gonion MIDG \n",
"10 Mid-hip MIDH \n",
"11 Mid-shoulder MIDS \n",
"12 Omphalion OMPH \n",
"13 Pternion HEEL \n",
"14 Radiale RADI \n",
"15 Sphyrion (tibia) TSPH \n",
"16 Sphyrion fibulare FSPH \n",
"17 Stylion RSTY \n",
"18 Suprasternale SUPR \n",
"19 Tibiale (medial) MTIB \n",
"20 Tibiale laterale LTIB \n",
"21 Trochanterion TROC \n",
"22 Vertex VERT \n",
"23 Xiphion XYPH \n",
"\n",
" Description \n",
"0 Most lateral point on the lateral edge of the acromial process of the scapula \n",
"1 Tip of longest toe \n",
"2 Distance between two ASIS \n",
"3 Superior tip of the spine of the 7th certical vertebra \n",
"4 Tip of 3 rd digit \n",
"5 Most lateral point on the posterior angle of mandible \n",
"6 Inferior point of one of the anterior superior iliac spines \n",
"7 Medial and lateral bony projections of the malleolus \n",
"8 Distal palpable point on the metacarpal of the 3rd digit on the dorsal hand \n",
"9 Point midway between 2 gonion \n",
"10 Point midway between 2 hip joint centers \n",
"11 Point midway between 2 shoulder joint centers \n",
"12 Center of navel \n",
"13 Posterior point of the heel \n",
"14 Lateral tip on the proximal head of the radius \n",
"15 Distal tip of the tibia – distal to medial malleolus \n",
"16 Distal tip of the fibula – distal to lateral malleolus \n",
"17 Distal dip of the styloid process of the radius \n",
"18 Most caudal point on the jugular notch on the sternum \n",
"19 Most proximal point on the medial superior border of the head of the tibia \n",
"20 Most proximal point on the lateral superior border of the head of the fibula \n",
"21 Superior border on the greater trochanter of the femur \n",
"22 Uppermost part of the head \n",
"23 Lowermost end of the sternum "
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"BSP_Zmarks = pd.read_csv('https://raw.githubusercontent.com/BMClab/BMC/master/data/BSPlandmarks_ZdeLeva.txt', sep='\\t')\n",
"display(Latex('BSP landmarks from Zatsiorsky\\'s model adjusted by de Leva (1996):'))\n",
"display(BSP_Zmarks)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"ExecuteTime": {
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"outputId": "2bdc6a04-ace1-4145-c13f-15a342374b88"
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"outputs": [
{
"data": {
"text/latex": [
"BSP female values from Zatsiorsky's model adjusted by de Leva (1996):"
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/html": [
"
"
],
"text/plain": [
" Endpoints Mass CM Long Rg Sag Rg Trans Rg Long\n",
"Segment \n",
"Head VERT-MIDG 0.0694 0.5976 0.362 0.376 0.312\n",
"Trunk SUPR-MIDH 0.4346 0.4486 0.372 0.347 0.191\n",
"Upper trunk SUPR-XYPH 0.1596 0.2999 0.716 0.454 0.659\n",
"Middle trunk XYPH-OMPH 0.1633 0.4502 0.482 0.383 0.468\n",
"Lower trunk OMPH-MIDH 0.1117 0.6115 0.615 0.551 0.587\n",
"Upper arm SJC-EJC 0.0271 0.5772 0.285 0.269 0.158\n",
"Forearm EJC-WJC 0.0162 0.4574 0.276 0.265 0.121\n",
"Hand WJC-MET3 0.0061 0.7900 0.628 0.513 0.401\n",
"Thigh HJC-KJC 0.1416 0.4095 0.329 0.329 0.149\n",
"Shank KJC-AJC 0.0433 0.4395 0.251 0.246 0.102\n",
"Foot HEEL-TTIP 0.0137 0.4415 0.257 0.245 0.124\n",
"Head 2 VERT-CERV 0.0694 0.5002 0.303 0.315 0.261\n",
"Trunk 2 CERV-MIDH 0.4346 0.5138 0.328 0.306 0.169\n",
"Trunk 3 MIDS-MIDH 0.4346 0.4310 0.384 0.358 0.197\n",
"Upper trunk 2 CERV-XYPH 0.1596 0.5066 0.505 0.320 0.465\n",
"Forearm 2 EJC-STYL 0.0162 0.4608 0.278 0.267 0.122\n",
"Hand 2 WJC-DAC3 0.0061 0.3624 0.288 0.235 0.184\n",
"Hand 3 STYL-DAC3 0.0061 0.3691 0.285 0.233 0.182\n",
"Hand 4 STYL-MET3 0.0061 0.7948 0.614 0.502 0.392\n",
"Shank 2 KJC-LMAL 0.0433 0.4459 0.255 0.249 0.103\n",
"Shank 3 KJC-SPHY 0.0433 0.4524 0.258 0.253 0.105"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"bsp_Zm = pd.read_csv('https://raw.githubusercontent.com/BMClab/BMC/master/data/BSPmale_ZdeLeva.txt', index_col=0, sep='\\t')\n",
"display(Latex('BSP male values from Zatsiorsky\\'s model adjusted by de Leva (1996):'))\n",
"display(bsp_Zm)"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "LTTOWhCLO6ah"
},
"source": [
"### Differences between the anthropometric models from Dempster and Zatsiorsky\n",
"\n",
"The anthropometric models from Dempster and Zatsiorsky are different in many aspects; regarding the subjetcs investigated in the studies, Dempster's model is based on the data of 8 cadavers of older male individuals (but two of the individuals were of unknown age) analyzed in the United States. Zatsiorsky's model is based on image scanning of 100 young men and 15 young women, at the time all students of a military school in the former Soviet Union.\n",
"\n",
"The difference between models for some segments is large (see table below): the mass fraction of the thigh segment for Zatsiorsky's model is more than 40% larger than for the Dempster's model, inversely, the trunk segment has about 15% lower mass fraction for Zatisorsky's model. Also, note that some of the segments don't have the same definition in the two models."
]
},
{
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"execution_count": null,
"metadata": {
"ExecuteTime": {
"end_time": "2020-04-17T14:59:00.905358Z",
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"outputId": "4e0239b2-8716-4ef1-f1c4-c062adfcd07f"
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"outputs": [
{
"data": {
"text/latex": [
"Mass fraction difference (in %) of Zatsiorsky's model w.r.t. Dempster's model"
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/html": [
"
\n",
"\n",
"
\n",
" \n",
"
\n",
"
\n",
"
Females
\n",
"
Males
\n",
"
\n",
"
\n",
"
Segment
\n",
"
\n",
"
\n",
"
\n",
" \n",
" \n",
"
\n",
"
Foot
\n",
"
-11.0
\n",
"
-6.0
\n",
"
\n",
"
\n",
"
Shank
\n",
"
3.0
\n",
"
-7.0
\n",
"
\n",
"
\n",
"
Thigh
\n",
"
48.0
\n",
"
42.0
\n",
"
\n",
"
\n",
"
Lower trunk
\n",
"
-12.0
\n",
"
-21.0
\n",
"
\n",
"
\n",
"
Middle trunk
\n",
"
5.0
\n",
"
17.0
\n",
"
\n",
"
\n",
"
Upper trunk
\n",
"
-28.0
\n",
"
-26.0
\n",
"
\n",
"
\n",
"
Trunk
\n",
"
-14.0
\n",
"
-13.0
\n",
"
\n",
"
\n",
"
Upper arm
\n",
"
-9.0
\n",
"
-3.0
\n",
"
\n",
"
\n",
"
Forearm
\n",
"
-14.0
\n",
"
1.0
\n",
"
\n",
"
\n",
"
Hand
\n",
"
-7.0
\n",
"
2.0
\n",
"
\n",
"
\n",
"
Head
\n",
"
-18.0
\n",
"
-14.0
\n",
"
\n",
" \n",
"
\n",
"
"
],
"text/plain": [
" Females Males\n",
"Segment \n",
"Foot -11.0 -6.0\n",
"Shank 3.0 -7.0\n",
"Thigh 48.0 42.0\n",
"Lower trunk -12.0 -21.0\n",
"Middle trunk 5.0 17.0\n",
"Upper trunk -28.0 -26.0\n",
"Trunk -14.0 -13.0\n",
"Upper arm -9.0 -3.0\n",
"Forearm -14.0 1.0\n",
"Hand -7.0 2.0\n",
"Head -18.0 -14.0"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"m_D = bsp_D.loc[['Foot', 'Leg', 'Thigh', 'Pelvis', 'Abdomen', 'Thorax', 'Trunk',\n",
" 'Upper arm', 'Forearm', 'Hand', 'Head neck'], 'Mass']\n",
"m_Zf = bsp_Zf.loc[['Foot', 'Shank', 'Thigh', 'Lower trunk', 'Middle trunk', 'Upper trunk',\n",
" 'Trunk', 'Upper arm', 'Forearm', 'Hand', 'Head'], 'Mass']\n",
"m_Zm = bsp_Zm.loc[['Foot', 'Shank', 'Thigh', 'Lower trunk', 'Middle trunk', 'Upper trunk',\n",
" 'Trunk', 'Upper arm', 'Forearm', 'Hand', 'Head'], 'Mass']\n",
"m_D.index = m_Zf.index # because of different names for some segments\n",
"\n",
"display(Latex(\"Mass fraction difference (in %) of Zatsiorsky's model w.r.t. Dempster's model\"))\n",
"d = pd.DataFrame({'Females': np.around(100 * (m_Zf - m_D) / m_D), \\\n",
" 'Males': np.around(100 * (m_Zm - m_D) / m_D)})\n",
"display(d)"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "Qv0HiiOaO6ah"
},
"source": [
"## Center of mass\n",
"\n",
"See the notebook [Center of Mass and Moment of Inertia](https://nbviewer.jupyter.org/github/BMClab/bmc/blob/master/notebooks/CenterOfMassAndMomentOfInertia.ipynb) for a description of center of mass.\n",
"\n",
"Using the data of the body segment parameters table, the center of mass of a single segment $i$ is (see figure below):\n",
"\n",
"\\begin{equation}\n",
"r_{i} = r_{i,p} + \\text{bsp[i,cmp]} \\cdot (r_{i,d}-r_{i,p})\n",
"\\label{}\n",
"\\end{equation}\n",
"\n",
"Where $r_{i,p}$ and $\\:r_{i,d}$ are the positions of the proximal and distal landmarks used to define the $i$ segment. \n",
"Note that $r$ is a vector and may have more than one dimension. The equation for the center of mass is valid in each direction and the calculations are performed independently in each direction. In addition, there is no need to include the mass of the segment in the equation above; the mass of the segment is used only when there is more than one segment.\n",
"\n",
"For example, given the following coordinates ($x, y$) for the MT2, ankle, knee and hip joints:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"ExecuteTime": {
"end_time": "2020-04-17T14:59:00.910452Z",
"start_time": "2020-04-17T14:59:00.907440Z"
},
"id": "2kmMP41ZO6ah",
"outputId": "69f3942f-2dea-4eb5-ae03-00b66c923c8c"
},
"outputs": [
{
"data": {
"text/plain": [
"array([[1.011, 0.013],\n",
" [0.849, 0.11 ],\n",
" [0.864, 0.549],\n",
" [0.721, 0.928]])"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"r = np.array([[101.1, 1.3], [84.9, 11.0], [86.4, 54.9], [72.1, 92.8]])/100\n",
"display(np.around(r, 3))"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "VBVuD6COO6ai"
},
"source": [
"The position of the center of mass of each segment and of the lower limb are:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"ExecuteTime": {
"end_time": "2020-04-17T14:59:00.918168Z",
"start_time": "2020-04-17T14:59:00.911546Z"
},
"id": "jRgLCrpxO6ai",
"outputId": "1e5fea9f-bfc9-41eb-e742-66b69a72d4a3"
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Foot CM: [0.93 0.062] m\n",
"Leg CM: [0.858 0.359] m\n",
"Thigh CM: [0.783 0.764] m\n",
"Lower limb CM: [0.818 0.584] m\n"
]
}
],
"source": [
"M = bsp_D.loc[['Foot', 'Leg', 'Thigh'], 'Mass'].sum()\n",
"rcm_foot = r[1] + bsp_D.loc['Foot', 'CM prox']*(r[0]-r[1])\n",
"rcm_leg = r[2] + bsp_D.loc['Leg', 'CM prox']*(r[1]-r[2])\n",
"rcm_thigh = r[3] + bsp_D.loc['Thigh','CM prox']*(r[2]-r[3])\n",
"rcm = (bsp_D.loc['Foot','Mass']*rcm_foot + bsp_D.loc['Leg','Mass']*rcm_leg + \\\n",
" bsp_D.loc['Thigh','Mass']*rcm_thigh)/M\n",
"print('Foot CM: ', np.around(rcm_foot, 3), 'm')\n",
"print('Leg CM: ', np.around(rcm_leg, 3), 'm')\n",
"print('Thigh CM: ', np.around(rcm_thigh, 3), 'm')\n",
"print('Lower limb CM: ', np.around(rcm, 3), 'm')"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "PGuLMUOAO6ai"
},
"source": [
"And here is a geometric representation of part of these calculations:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"ExecuteTime": {
"end_time": "2020-04-17T14:59:01.252974Z",
"start_time": "2020-04-17T14:59:00.919088Z"
},
"id": "vl6tfK4aO6ai",
"outputId": "75df3b5a-9675-4e73-89b7-666ca2dd0d7c"
},
"outputs": [
{
"data": {
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\n",
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