Biomechanical Model of the Human Body in a Sitting Posture

In this example, a biomechanical model of the human body is developed for evaluating the dynamic response to the vertical vibrations in a sitting posture. It demonstrates how the Multibody Dynamics interface in COMSOL Multiphysics can be used to model various parts and connections in a human body and study the whole body vibrations (WBV). The problem statement and the model parameters are taken from Ref. 1.

The dynamic response of a human body in any vibration environment can be predicted using this biomechanical model. In the automobile industry, this model can be used in ride quality simulations as well as when designing vibration isolators such as the seats.

Model Definition

Geometry and Connections

The biomechanical model of a human body consists of different body parts such as head, torso, pelvis, thighs, viscera, and legs, as shown in Figure 1. All the body parts are treated as lumped masses and defined as rigid bodies. The values of mass and moment of inertia of each body part about its center of mass are given in Table 1.

Table 1: Mass and Moment of inertia of Different body parts
BODY Part	Mass (kg)	Moment of Inertia (kg-m2)
Head	7.24	0.411
Torso	19.90	1.627
Pelvis	11.01	0.692
Thighs	20.35	1.180
Viscera	12.92	-
Legs	-	-

The viscera are not allowed to rotate, and the legs are not allowed to translate or rotate. Hence corresponding values of mass and moment of inertia are not required in the above table.

Figure 1: Model geometry showing different body parts and connections between them. The center of mass of each body part and the locations of vibration excitation are also shown.

The connections between different body parts can be approximated using translational and rotational springs and dampers, applied on the relative motion between the two body parts. This type of connection is modeled using the elastic version of fixed joint. Once the elastic version of a joint is used, the translational and rotational stiffness and damping values between the two connected parts can be provided.

In this model, the source of vibration (seat) is not modeled explicitly and instead of that a base motion node is used. Here the input excitation is of 1 m/s2 in the vertical direction at three different locations. The body parts, which are directly in touch with the vibrating seat, are legs, thighs, and pelvis. The connections between these body parts and the vibrating seat are also modeled using fixed joint. The elasticity on these joints is included wherever it is required to model the cushioning effect of the seat.

The values of stiffness and damping coefficients, translational as well as rotational, for all the connections in the model are provided in table below.

Table 2: joint elasticity DETAILS
Fixed joint	translational stiffness (kN/m)	translational damping coefficient (kN-s/m)	rotational stiffness (kN-m/rad)	rotational damping coefficient (kN-m-s/rad)
Head-torso	113.7, 113.7	0.066, 0.066	0.915	0.340
Torso-pelvis	0.299, 0.299	1.79, 1.79	0.328	0.724
Pelvis-thigh	6.40, 6.40	0.061, 0.061	0.162	0.030
Thigh-leg	23.55, 23.55	0.154, 0.154	0.220	0.104
Viscera-torso	1.93, 0	0.079, 0	0	0
Viscera-pelvis	0, 18.37	0, 0.197	0	0
Seat-pelvis	0.905, 121.3	0.015, 0.047	0	0
Seat-thigh	0.614, 16.71	0.014, 8.01	0	0
Seat-leg	-	-	-	-

The legs are connected to the seat with the rigid version of fixed joint and hence it doesn’t need joint elasticity parameters.

Vibration transmissibility

In this example, first an eigenfrequency analysis is performed to determine the damped and undamped natural frequencies of vibration. Secondly a frequency response analysis is carried out around the natural frequencies to find out the vertical transmissibility (ratio of vertical acceleration of the head to the input acceleration of the seat), the rotational transmissibility (ratio of angular acceleration of the head to the input acceleration the seat) and the apparent mass (ratio of the force at the seat to the input acceleration of the seat).

The transmissibilities and apparent mass are directly related to the comfort feeling. Especially the vertical and rotational transmissibility affect the ride comfort and the vision.

Results and Discussion

Figure 2 shows one of the rotational eigenmodes of the undamped biomechanical model. In this mode, rotational movement of the head and torso segments can be seen. The viscera, pelvis, thighs and legs do not have considerable movement as compared to the other two.

Figure 2: One of the rotational eigenmodes of the undamped biomechanical model.

The first major translational eigenmode of the damped biomechanical model is shown in Figure 3. In this mode, there is a downward movement of head, pelvis, and viscera whereas other body parts do not move much.

Figure 4 shows the second major translational eigenmode. In this mode, body parts like head, torso, and pelvis move downward whereas viscera move upward.

Figure 3: First major translational eigenmode of the damped biomechanical model.

Figure 4: Second major translational eigenmode of the damped biomechanical model.

Figure 5 shows the variation of vertical transmissibility with the excitation frequency. The primary and secondary resonance are visible in the range of 4-6 Hz and 8-10 Hz respectively. The eigenmodes for these two translational modes are shown in Figure 3 and Figure 4.

Figure 5: Vertical transmissibility versus excitation frequency.

Figure 6 shows the variation of rotational transmissibility with the excitation frequency. A high value of rotational transmissibility is not recommended as apart from reducing the comfort level it also directly affects the vision.

While vertical and rotation transmissibility depicts the endpoint characteristics of the model, apparent mass conveys the driving point characteristics, relating the force and the motion at the seat. Figure 7 shows the variation of apparent mass of the system with the excitation frequency.

Figure 6: Rotational transmissibility versus excitation frequency.

Figure 7: Apparent mass versus excitation frequency.

Notes About the COMSOL Implementation

•

To model a lumped mass, use subnode of the node and enter the inertia properties given at a certain point. Also make the density zero in the dummy domain.

•

To model a bushing, use nodeof the node and enter the stiffness and damping properties of the joint.

•

Use node to excite the system instead of modeling an actual vibrating base (seat).

•

The connections set up in the model and net system DOFs can be reviewed in the andsections at the physics node.

Reference

1. Tae-Hyeong Kim, Young-Tae Kim, and Yong-San Yoon, “Development of a biomechanical model of the human body in a sitting posture with vibration transmissibility in the vertical direction,” Int. J. Industrial Ergonomics, vol. 35, pp. 817–829, 2005.

Multibody_Dynamics_Module/Biomechanics/seated_human_body

Modeling Instructions

From the menu, choose .

New

In the window, click

Model Wizard

In the window, click

In the tree, select .

Click .

Click

In the tree, select .

Click

Global Definitions

Parameters 1

In the window, under click .

In the window for , locate the section.

Click

Browse to the model’s Application Libraries folder and double-click the file seated_human_body_parameters.txt.

Geometry 1

Import 1 (imp1)

In the toolbar, click

In the window for , locate the section.

Click .

Browse to the model’s Application Libraries folder and double-click the file seated_human_body.mphbin.

Click .

Form Union (fin)

In the window, under click .

In the window for , locate the section.

From the list, choose .

Click

Multibody Dynamics (mbd)

Do as follows to generate Rigid Domain nodes for all body parts.

In the window, under click .

In the window for , locate the section.

Select the check box. This automatically sets the density of all rigid domains to zero and adds a Mass and Moment of Inertia subnode to each Rigid Domain node.

Click in the upper-right corner of the section. From the menu, choose .

Rigid Domain: Pelvis

In the window, expand the node, then click .

In the window for , type Rigid Domain: Pelvis in the text field.

Mass and Moment of Inertia 1

In the window, expand the node, then click .

In the window for , locate the section.

In the m text field, type m_pelvis.

In the Iz text field, type I_pelvis.

Locate the section. From the list, choose .

From the list, choose .

Center of Mass: Point 1

In the window, click .

Select Point 11 only.

Rigid Domains

Similarly, model the other four body parts by assigning other Rigid Domain nodes in the group and resetting the inputs using the information given in the table below.


Name	Selection	Mass	Moment of Inertia	Center of Mass (Point)
Rigid Domain: Head	2	m_head	I_head	46
Rigid Domain: Torso	3	m_torso	I_torso	46
Rigid Domain: Viscera	4	m_viscera	0	55
Rigid Domain: Thigh	5	m_thigh	I_thigh	62

The rotational motion of the viscera is not included in the model. Therefore constrain the rotation of by using the subnode.

Rigid Domain: Viscera

In the window, click .

Prescribed Displacement/Rotation 1

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Use the node to model the legs.

Rigid Domain: Leg

In the window, under click .

In the window for , type Rigid Domain: Leg in the text field.

Add a Base Motion node to model the effects of a vibrating seat.

Base Motion: Seat

In the toolbar, click

and choose .

In the window for , type Base Motion: Seat in the text field.

Locate the section. From the list, choose .

Specify the ab vector as


0	x
vtt_in	y

Fixed Joint: Head-Torso

In the toolbar, click

and choose .

In the window for , type Fixed Joint: Head-Torso in the text field.

Locate the section. From the list, choose .

From the list, choose .

Locate the section. From the list, choose .

Center of Joint: Point 1

In the window, click .

Select Point 24 only.

Joint Elasticity 1

In the window, click .

In the window for , locate the section.

From the list, choose .

In the ku table, enter the following settings:


k1	0
0	k1

In the kθ text field, type kr1.

Locate the section. From the list, choose .

In the cu table, enter the following settings:


if(i_c==1,c1,0)	0
0	if(i_c==1,c1,0)

In the cθ text field, type if(i_c==1,cr1,0).

Fixed Joints

Similarly create eight more fixed joints between the different body parts by duplicating and resetting the inputs using the information given in the table below.


Name	Source	Destination	Center of joint selection (points)
Fixed joint: Torso-Pelvis	Rigid Domain: Torso	Rigid Domain: Pelvis	39
Fixed joint: Pelvis-Thigh	Rigid Domain: Pelvis	Rigid Domain: Thigh	14
Fixed joint: Thigh-Leg	Rigid Domain: Thigh	Rigid Domain: Leg	64
Fixed joint: Viscera-Torso	Rigid Domain: Viscera	Rigid Domain: Torso	55
Fixed joint: Viscera-Pelvis	Rigid Domain: Viscera	Rigid Domain: Pelvis	55
Fixed joint: Seat-Pelvis	Base motion: Seat	Rigid Domain: Pelvis	13
Fixed joint: Seat-Thigh	Base motion: Seat	Rigid Domain: Thigh	61
Fixed joint: Seat-Leg	Base motion: Seat	Rigid Domain: Leg	69, 70

Joint Elasticity

Enter the joint elasticity parameters using the following table:


Name	KU (Diagonal Values)	KTH	CU (Diagonal Values)	CTH
Fixed joint: Torso-pelvis	k2, k2	kr2	If(i_c==I, c2, 0), If(i_c==I, c2, 0)	If(i_c==I, cr2, 0)
Fixed joint: Pelvis-thigh	k3, k3	kr3	If(i_c==I, c3, 0), If(i_c==I, c3, 0)	If(i_c==I, cr3, 0)
Fixed joint: Thigh-leg	k4, k4	kr4	If(i_c==I, c4, 0), If(i_c==I, c4, 0)	If(i_c==I, cr4, 0)
Fixed joint: Viscera-torso	kh5, 0	0	If(i_c==I, ch5, 0), 0	0
Fixed joint: Viscera-pelvis	0, kv6	0	0, If(i_c==I, cv6, 0)	0
Fixed joint: Seat-pelvis	kh7, kv7	0	If(i_c==I, ch7, 0), If(i_c==I, cv7, 0)	0
Fixed joint: Seat-thigh	kh8, kv8	0	If(i_c==I, ch8, 0), If(i_c==I, cv8, 0)	0

In this model, the legs are directly mounted to the vibrating base. Therefore, disable the joint elasticity of the Seat-Leg joint.

Fixed Joint: Seat-Leg

In the window, click .

In the window for , locate the section.

From the list, choose .

Enable the joint force computation for the Seat-Pelvis and the Seat-Thigh joints to compute the apparent mass.

Fixed Joint: Seat-Thigh

In the window, click .

In the window for , locate the section.

From the list, choose .

Fixed Joint: Seat-Pelvis

In the window, click .

In the window for , locate the section.

From the list, choose .

Mesh 1

In the window, under click .

In the window for , locate the section.

From the list, choose .

Click

Study 1: Eigenfrequency

In the window, click .

In the window for , type Study 1: Eigenfrequency in the text field.

Add a parametric sweep to find the undamped and damped natural frequencies of the system by changing the value of the damping controller parameter.

Parametric Sweep

In the toolbar, click

In the window for , locate the section.

Click

In the table, enter the following settings:


Parameter name	Parameter value list	Parameter unit
i_c (Damping controller)	0 1

Step 1: Eigenfrequency

In the window, click .

In the window for , locate the section.

Select the check box.

In the associated text field, type 12.

In the text field, type 0.

In the toolbar, click

Results

Mode Shape (mbd)

Follow the instructions below to plot the eigenmodes shown in Figure 2, Figure 3, and Figure 4.

In the window for , locate the section.

From the list, choose .

In the toolbar, click

Click the

button in the toolbar.

From the list, choose .

In the toolbar, click

Click the

button in the toolbar.

From the list, choose .

In the toolbar, click

Click the

button in the toolbar.

Add a new study to carry out the frequency response analysis of this system.

Add Study

In the toolbar, click

to open the window.

Go to the window.

Find the subsection. In the tree, select .

Click in the window toolbar.

In the toolbar, click

to close the window.

Study 2: Frequency Response

In the window, click .

In the window for , type Study 2: Frequency Response in the text field.

Step 1: Frequency Domain

In the window, under click .

In the window for , locate the section.

In the text field, type range(2,0.2,20).

Define the transmissibility variables to use them in the postprocessing.

Definitions

Variables 1

In the window, under right-click and choose .

In the window for , locate the section.

In the table, enter the following settings:


Name	Expression	Unit	Description
H_vert	abs(mbd.rd2.u_tty)/vtt_in		Vertical transmissibility
H_rot	abs(mbd.rd2.th_ttz)/vtt_in	rad/m	Rotational transmissibility
M_a	abs(mbd.fxj7.Fy+mbd.fxj8.Fy)/vtt_in	kg	Apparent mass