Computerised Muscle Modelling and Simulation for Interactive

Applications*

Martin Cervenka

1,∗ a

, Ondrej Havlicek

2 b

, Josef Kohout

1 c

and Libor V

1 d

The University of West Bohemia, Faculty of Applied Sciences, Department of Computer Science and Engineering,

Czech Republic

The University of West Bohemia, Faculty of Applied Sciences, NTIS - New Technologies for the Information Society,

Czech Republic

Keywords:

Muscle Modelling, Collision Detection, Collision Response, Position Based Dynamics, Discregrid, Scalar

Distance Field, as-Rigid-as-Possible, Radial Basis Functions.

Abstract:

The main challenges of collision detection and handling in muscle modelling are demonstrated. Then, a colli-

sion handling technique is tested, exploiting the issue of muscle penetrating the bone in some circumstances,

mainly when the movement is too rapid or the displacement of the bone is too high. Our approach also de-

tects the problem, using Discregrid to see the immediate direction change towards the penetrated bone. Some

alternatives to the described PBD (Position-Based dynamics) technique are presented: PBD with As-Rigid-

As-Possible modiﬁcation and radial basis function approach.

1 INTRODUCTION

Osteoporosis (Wade et al., 2014), osteoarthritis

(Oatis, 2017), patellar dislocation (Barzan et al.,

2017), or hemiplegic diseases (Zhang et al., 2021) are

leading researchers to develop a satisfactory model of

the musculoskeletal system. Creating such a model is

a complex procedure with many issues. The problem

of collision detection (CD) between muscle and bone

models and its response (CR) is critical.

In this paper, we follow our previous work and

newly present the parameter upper bound, where the

simulation still works as expected. Another contribu-

tion of this paper is exploring novel modelling meth-

ods to overcome the current limitations. This paper

also brieﬂy describes some techniques of CD and CR.

The paper is structured as follows. The next sec-

tion gives an idea of the whole muscle modelling

overview and the steps to obtain a usable comput-

erised muscle model. The state-of-the-art approaches

https://orcid.org/0000-0001-9625-1872

https://orcid.org/0000-0002-6944-7084

https://orcid.org/0000-0002-3231-2573

https://orcid.org/0000-0002-0213-3769

∗

This Work Was Supported by the Ministry of Educa-

tion, Youth and Sports of the Czech Republic, Project SGS-

2022-015.

∗∗

Corresponding author

to modelling and simulation of the muscles, based on

the position-based dynamics, are described in Sec-

tion 3. The description of existing CD and CR tech-

niques employed during these simulations follows.

Sections 5 and 6 present the current approach’s lim-

itations and propose several improvements to over-

come them. Discussion of future work and conclud-

ing remarks follow.

2 MUSCLE MODELLING

PIPELINE

The muscle modelling procedure involves many

steps, including acquiring relevant raw data and its

subsequent transformation into a useful form. The

last step is formulating the mathematical model,

where the main concern is (among others) the deﬁ-

nition of the muscle-bone interaction.

An example of a complex pipeline (consisting of

data acquisition, model building and inverse kinemat-

ics) includes the following steps:

1. obtaining raw data of the patient at rest (such as

medical images) representing anatomical objects

(bones, muscles, muscle attachment areas, etc.),

and movement data,

2. extraction and transformation of the raw data into

214

Cervenka, M., Havlicek, O., Kohout, J. and Váša, L.

Computerised Muscle Modelling and Simulation for Interactive Applications.

DOI: 10.5220/0011688000003417

In Proceedings of the 18th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2023) - Volume 1: GRAPP, pages

214-221

ISBN: 978-989-758-634-7; ISSN: 2184-4321

 2023 by SCITEPRESS – Science and Technology Publications, Lda. Under CC license (CC BY-NC-ND 4.0)

a useful form, using:

(a) segmentation – separation of different types of

tissues present in medical images (if they are

distinguishable). Segmentation can be manual,

semi-automatic or automatic (depending on the

complexity of the segmentation),

(b) extraction – the conversion of segmented data

into geometrical models,

different measurements and modalities into the

common reference space

(d) approximation and interpolation – reconstruc-

tion of missing parts or partially corrupted data.

3. acquiring some general apriori knowledge, deter-

mined by human anatomies, such as

(a) how the attachment areas will be determined

(whether based on apriori knowledge only or

the measured muscle attachment areas),

(b) deﬁning how a bone is connected by a joint to

another bone or how a muscle is connected to a

set of bones (attachment areas), etc.,

muscles, such as internal muscle architecture

(e.g. ﬁgure arrangement: parallel, pennate,

etc.), optimal (resting) length and others.

4. creating a mathematical model that requires:

(a) deﬁning the space (discretised or continuous),

(b) deﬁning the shape of the data (triangular sur-

face mesh, tetrahedral volumetric mesh, scat-

tered data... / surface deﬁned by Fourier series,

implicit RBF,...)

bone models and thus determining whether or

not a transformation of the measured data is

necessary.

5. transformation of the simulation output from its

model representation into the ﬁnal form, e.g.,

from a triangular surface mesh into a set of in-

ternal ﬁbres.

We recommend the following papers for a more

detailed view: the foremost step is well described

by (Fukuda et al., 2017) for the attachment area ac-

quisition strategy, (Lee et al., 2014) to determine the

pennate angle from the source data. There are also

data from invasive measurements, e.g. Visible Hu-

man Project (the National Library of Medicine) or

The Chinese Visible Human (Zhang et al., 2004). The

second step (registration) is also well described in

(Zhao et al., 2013). There is also an approach from

(Li et al., 2008), with promising results. The other

steps are highly dependent on the considered applica-

tion, whether the purpose is a plausible visualisation

of muscles in movement (see. e.g. (Romeo et al.,

2018)) or to calculate some physical phenomena of

the muscle (see. e.g. (Modenese and Kohout, 2020)),

and whether the user should be able to change the

modelling or simulation parameters interactively or

not.

We focus on interactive applications which do

not require specialised hardware. Consequently, any

model developed in the fourth step needs to trade off

some accuracy for the speed of simulation. In this pa-

per, we consider position-based dynamics (PBD) suit-

able for generating models of such a kind.

3 POSITION BASED DYNAMICS

Position-based dynamics (PBD) (M

uller et al., 2007)

is a fast approach used mainly in the animation indus-

try to model elastic object (and cloth) deformations.

Nowadays, the PBD is making its way into physical

simulations as well. The original algorithm does not

consider the possibility of object anisotropy as far as

the algorithm has been developed for general objects.

The method accepts a manifold surface mesh and pro-

duces its deformed variant as the output.

The PBD also exists in the xPBD (eXtended ver-

sion of PBD, which respects the concept of elastic

potential energy) form. The xPBD incorporates elas-

tic potential energy and eliminates the necessity to

know the time step and iteration count (Macklin et al.,

2016).

Romeo et al.(Romeo et al., 2018) are the ﬁrst who

proposed using the xPBD algorithm for muscle mod-

elling problems. Their fundamental idea is to build an

internal structure above the surface mesh to respect

the anisotropy of the muscle (the internal structure

respects the general direction of the muscle ﬁbres).

They can form a volumetric model better suitable for

the PBD algorithm with an intelligent edge-creation

process. However, the paper needs to describe their

collision detection and handle thoroughly. According

to their video of the technique outcome, many col-

lisions occur, suggesting their approach did not ad-

dress the apparent requirement of avoiding muscle-

bone penetrations.

Angles et al. (Angles et al., 2019) developed a

PBD-based approach for muscle modelling in 2019.

Their approach virtually decomposes the muscle into

”rods” (which may approximate the muscle ﬁbres).

These rods can adjust their diameter wherever they

want to preserve their volume. Their main con-

tribution is the ability to provide real-time simula-

tion, which Romeo’s approach cannot because ”its

≈ 40s/frame of processing time causes it unﬁtting

to interactive applications” (Angles et al., 2019).

Computerised Muscle Modelling and Simulation for Interactive Applications

215

They adopt ”Particle simulation using CUDA” from

(Green, 2010) for collision detection between rods

and response. Again, the problem of muscle-bone

penetration is not addressed, though in this case, the

extension is relatively straightforward.

The position-based dynamics for muscle mod-

elling is also described in the paper ”Fast and Real-

istic Approach to Virtual Muscle Deformation.” (Cer-

venka. and Kohout., 2020) where the PBD approach

has been proposed (ﬁnished the same year as Romeo’s

article (Romeo et al., 2018), working concurrently on

the same). The paper ”Muscle Deformation using

Position Based Dynamics” (Kohout and

Cervenka,

2021) follows, which tests the approach and compares

the results to an existing FEM technique. The primary

beneﬁt of our suggested system is that no interior is

needed. The anisotropy is computed on the surface

of the mesh only, utilising muscle ﬁbres on the mesh

surface, representing the ﬁbre direction. The voxeli-

sation technique has been used for collision detection

and response purposes.

4 COLLISION DETECTION AND

RESPONSE

Various approaches to detect and respond to an oc-

curring collision have been proposed. The most com-

mon algorithms exploit the D&C (divide & conquer)

paradigm. The bounding volume hierarchy is one of

them (Teschner et al., 2005), using a primitive (of-

ten an axis-aligned bounding box AABB or a sphere)

hierarchy to enclose the model and its parts. The spa-

tial hashing (Turk, 1990) is its generalisation over the

whole model space.

If there is a necessity to know not only if the col-

lision occurs but how far from the collision the model

is, the (signed) distance ﬁeld approach is an excel-

lent way to go. Numerous techniques can be used

to construct such a ﬁeld. The vast majority use vox-

elisation to obtain a cell array and then use an inter-

polation method to determine the value between the

cells. Some of these techniques are well described in

an older work by (Bærentzen and Aanæs, 2002).

In our research of the PBD approach, the ﬁrst de-

cision was to use a simple voxelisation method to

simplify the collision detection problem. This sim-

ple idea, however, leads to some things that could be

improved. Luckily, some ideas have emerged to en-

tirely improve or even ﬁx some problems, using more

complex collision detection algorithms. Havlicek

(Havlicek et al., 2022) changed the collision detec-

tion to Discregrid (using a signed distance ﬁeld) and

FLC (using a binary search tree), beating the voxeli-

sation approach in terms of accuracy. However, there

is still some work because even those methods only

work correctly in extreme conditions, mainly if the

movement is rapid.

The collision response is a complicated task

as well. Assume that two bones move towards

each other and narrowly miss each other (like shear

blades). If a muscle is attached to both of the bones

and appears to be in between the bones, there is no

such room for the bones to move into. This problem

often happens on a smaller scale, near joints, espe-

cially where two bones move close. Our former so-

lution (Cervenka and Skala, 2020) was to assume, in

this particular case, only one of the bones and move

a muscle in the direction opposite of it, but it proved

insufﬁcient. Havlicek (Havlicek et al., 2022) targets

this problem primarily, and he proposed a better ap-

proach of considering all adjacent bones and moving

opposite to the sum of all collision vectors. Even this

approach, however, does not always guarantee colli-

sion resolution.

Our current contribution, proposed in this paper,

follows our recent articles, mainly (Cervenka. and

Kohout., 2020; Kohout and

Cervenka, 2021) and also

(Havlicek et al., 2022).In the ﬁrst article, we devel-

oped a PBD-based approach for muscle modelling.

The issue with a muscle stuck inside a joint was

shown in that article. We believed that ”better col-

lision detection can ﬁx the issue” (Cervenka. and Ko-

hout., 2020). In the second article, the voxelisation

collision detection approach was proven inaccurate in

some cases, mainly in the case of more ”complicated”

(e.g. concave) bone surfaces, which are located near

the joint areas more frequently. The last article ex-

plores two existing collision detection algorithms for

the PBD approach: Discregrid and Flexible Collision

Library. The Discregrid was shown to be more suit-

able for the problem.

4.1 Discregrid

Discregrid library can be considered a Signed Dis-

tance Field generator written in C++. The algorithm

computes for each point in 3D space the shortest dis-

tance and direction towards a given nearby surface

represented by a triangular mesh. Also, assuming

that the input mesh is at least watertight, the method

can make the inside/outside decision because the al-

gorithm provides the sign. A ﬁnite bounded subspace

is required for the approach to work.

The bounded surface is ﬁrstly divided (like in the

voxelisation method) into a rectangular grid with a

user-deﬁned resolution, where each voxel is a 32-

node Serendipity type (Koschier and Bender, 2017).

GRAPP 2023 - 18th International Conference on Computer Graphics Theory and Applications

216

For each node, the distance and the direction to-

wards the nearest bounded surface are computed, see

(Bærentzen and Aanæs, 2002). The article describes

the problem of discontinuity of the mesh (where the

normal vectors have to be estimated differently).

The ﬁeld creation process is time-consuming

(about half a minute for bone meshes consisting of

up to 45 000 vertices with the grid resolution of

64 × 64 × 64 on standard hardware) and unfeasible

for deformable objects like muscles, where recalcu-

lation is often needed. There is no such problem with

the bone models because their movement is only rigid

(allowing for Discregrid results to be transformed us-

ing a global transformation).

In the case of muscle modelling, a situation may

happen when the muscle collides with a bone or an-

other muscle, even at the start of the simulation. This

situation is caused by the different modalities used for

the data measurements (see section 2). To ﬁx the is-

sue, the colliding surface vertices are pushed accord-

ing to the Discregrid result directional vectors so no

collision would occur at the start of the simulation.

5 MUSCLE SIMULATION

In this paper, we experimented with more types of

motion of the hip joint, not just ﬂexion but also ro-

tation and adduction. We also tested a hip extension

scenario in the described PBD approach to ﬁnd the

maximum amount of problematic cases possible. The

tests will be done on muscles and bones depicted in

Fig. 1.

Figure 1: One view from the side and one from the front

of a muscle group surrounding the hip joint in rest pose.

The vertices of the muscles are coloured by their distance

to the femur bone (pointing down) in millimetres given by

Discregrid.

5.1 Test of Motion Types

For the test of different motion types, we tested the

original hip ﬂexion (from 0

◦

to +90

◦

with the step of

◦

), hip rotation (from 0

◦

to +45

◦

and also to -45

◦

with the approximate degree of 1

◦

) and hip adduction

(from 0

◦

to +60

◦

with the approximate step of 2

◦

The results of hip ﬂexion are shown in Fig. 3.

Near the joint area, the muscle nearly touches the fe-

mur bone; however, no collision occurs. Fig. 4 shows

the results for the rotational motion. As before, the

muscle nearly touches the femur’s upper extremity

without collisions. The adduction is demonstrated in

Fig. 5. In this case, the muscle is further from the hip

joint, lowering the possibility of collisions. The col-

lision detection and response approach solved all the

apriori collisions, so no collisions happened.

5.2 Test of Motion Speeds

To test for bone movement speed impact, we chose

the extension movement. The initial step of 2

◦

was

increased to 4

◦

, 5

◦

and ﬁnally 10

◦

. We also increased

the target angle to +80

◦

for rapid movement to have

time and space to show up fully.

In this case, when the angle ﬁnally reaches 72

◦

with the angle step of 4

◦

, ﬁrst bone penetration occurs

(see Fig. 6). The muscle is not as fast as needed to

keep up with the bone movement, causing the distal

part of the muscle to enter the bone volume and go

through the whole cross-section. The muscle is also

being unnaturally pushed into itself by the bone.

Figure 2: Simpliﬁed 2D illustration of the sliding mecha-

nism. Points X

, X

and X

are being evaluated for the dis-

tance from the other muscle M. Consider the same thresh-

old distance for each of them (yellow margin). Point X

pushed to the position P

by previous PBD constraints but

returned towards the other muscle to the position P

′

. Point

is pushed away by the PBD so much it makes sense to

leave it to go ( L

> L

). Point X

is free to roam inside

the strip.

Figure 3: The result of the hip ﬂexion progressing from

right to left.

Computerised Muscle Modelling and Simulation for Interactive Applications

217

Figure 4: The result of the hip rotation progressing from the

centre to the sides.

Figure 5: The result of the hip adduction progressing right

to the left during the simulation.

5.3 Tunnelling Detection

The tunnelling problem (muscle ”jumps” in a single

iteration through the whole bone to the opposite side)

appears at places where the displacement of the bone

between two consecutive simulation frames exceeds

half the size of a muscle with which the bone collides.

According to (Havlicek et al., 2022), ”when [the fe-

mur] rotates about just 2

◦

(a typical step in simula-

tions), the displacement of the distal part of this bone

is nearly 3 cm”. In our experiments with the muscles

of the hip, i.e., no part of the muscle is near the dis-

tal portion of the bone, this problem arises when the

angle step is higher than 4

◦

This problem is relatively standard and does not

arise only with this particular approach. For example,

(Jan

ak, 2012) notes that ”if the movement of the ob-

ject is too fast in relation to the discrete time step, the

collision may not be detected”.

The scenario of the muscle movement is so rapid

that the whole muscle volume could go through the

entire bone model, which is possible (due to the al-

ready described displacement issue concerning the

change of the angle of the bone). Our solution would

be moving a muscle to the bone (rotate around the ex-

act centre of rotation and about the same angle), so

the muscle is closer to where it should lie. However,

before applying this correction, such an event must be

detected.

Generally, a continuous collision detection

method could be employed instead of the currently

used discrete one. However, such methods are

expensive. We, therefore, propose a simple (and fast)

test based on a comparison of the directional vectors

to the nearest bone surface, provided automatically

by the Discregrid.

If the direction of one muscle vertex suddenly

changes “too much”, we may expect that the penetra-

tion through the whole bone has happened. The “too

much” is deﬁned as when the angle between the direc-

tional vector from the previous step and the new one

is greater than 135

◦

, as described in Equ. 1, where

is the direction to the bone in this computational

step and d

′

is the direction to the bone in the previous

computational step,

is the euclidean norm of the

vector a. A tunnelling case can be seen in Fig. 6.

arccos



· d

′



> 135

◦

(1)



· d

′



> −0.75

Figure 6: Due to the lack of contraction modelling, the mus-

cles are being dragged during the hip extension (left and

centre images). Finally, under the degree of 72

◦

, ﬁrst tun-

nelling occurs (right) and is detected successfully by the

proposed algorithm.

5.4 Problem of Multiple Muscles

When multiple muscles are simulated in the scene,

they may also intersect each other. As noted in sec-

tion 4.1, building the Discregrid structure for the mus-

cle meshes is unusable for the interactive application

due to time requirements. An appropriate collision

handling system could be, e.g. a BVH structure (see

section 4), which would have to be updated each time

any muscle moves. As the nearby muscles often touch

each other - see Figure 1, this solution would proba-

bly be inefﬁcient. Therefore, we propose the ”sliding”

technique using the so-called ”virtual edges” to keep

the muscles at a certain distance from each other to

prevent collisions and unrealistic detachments.

5.4.1 Sliding over Surfaces

The main idea is to allow the muscles to slide over

each other using the virtual edges between the mus-

cles. We may keep chosen vertices up to a certain

distance away from the other muscles, i.e. a thresh-

old. The vertices to keep close to the other muscles

GRAPP 2023 - 18th International Conference on Computer Graphics Theory and Applications

218

can be selected by their initial distance and kept in a

list. This list could also be updated if the PBD dis-

placement of a particular vertex away from the other

muscle would be greater than its initial distance, let-

ting the point go. Similarly, collecting more vertices

into this list could be achieved via checking, for ex-

ample, the neighbourhood vertices, which would be

the likely candidates.

In case the PBD forces are less in magnitude than

this attraction force but still point away from the mus-

cle, the vertex would be pushed in the closest direc-

tion to the other muscle surface, effectively making

the point slide along the other muscle surface and

hopefully preventing it from colliding or unrealisti-

cally spanning out, as illustrated in Fig. 2.

This functionality is implemented preliminarily,

using the Discregrid library to preserve the distances

between a bone and a muscle. The resulting vir-

tual edges can be seen in Figure 7. The reason for

this measure is that the original idea implementation

would be beyond the scope of this paper.

Figure 7: An example of virtual edges between a muscle

and a bone with the participating vertices in blue and red,

respectively. The points in blue are muscle vertices, which

are close enough to the bone at the start of the simulation.

For each of them, the closest bone vertex (red) is found. The

pairs of vertices are connected with a straight line segment,

symbolizing a virtual edge.

6 FUTURE WORK

The PBD approach on its own brings some problems

to muscle modelling. The shape is not well preserved

(see Fig. 5, on the middle image, the bottom central

part of the gluteus maximus muscle is unrealistically

deformed), and bone penetration happens. Any prob-

lems stem from low solver iteration count, essential

for real-time model interaction. The options to solve

these are to:

• increases the number of PBD iterations, ef-

fectively slowing down the simulation, which

would become no longer interactive (Kohout and

Cervenka, 2021);

• uses the eXtended PBD, which converges more

consistently (the iteration count is not as signiﬁ-

cant) but does not solve the penetration issues;

• uses a different muscle model.

6.1 RBF Representation

The radial basis function model opens a new possi-

bility to develop a new approach to the deformation

of this model, which would allow smooth and rapid

muscle simulation. Collision detection and response,

volume preservation, and muscle anisotropy are the

challenges for future work.

The critical decision for the suitable model is to

select the suitable radial basis function and shape pa-

rameters (if any). A comprehensive study of some

well-known RBFs has already been made (see, e.g.

(Majdisova and Skala, 2017)), and the shape param-

eters were explored (e.g. in (Skala and Cervenka,

2019) or (Aﬁatdoust and Esmaeilbeigi, 2015)).

6.2 ARAP & PBD

Because of the deformed and unrealistic shape of

the model during the simulation, the As-Rigid-As-

Possible (ARAP) approach from computer graphics is

proposed for merge with PBD to deform an object re-

specting its original shape (Sorkine and Alexa, 2007)

to obtain ”the best of both worlds”.

As the preliminary experiment, we tried to use a

single PBD iteration to preserve the muscle’s original

volume, followed by a single iteration from ARAP,

which should restore the initial shape of the muscle.

The problem is that these two restrictions force most

vertices to go in the opposite direction, resulting in a

rough surface. (see results in Fig. 8). The volume

preservation constraint is not solvable by introducing

a new condition into the system since the interleaving

approach does not work.

Dvorak et al. (Dvo

ak et al., 2022) show how

to apply the ARAP approach to volume preservation.

However, their approach is not used directly for mus-

cle modelling problems. Our goal is to avoid the

introduction of an internal muscle structure to reach

lower computational complexity, meaning that their

approach would have to be altered drastically.

We see two options for ﬁxing the mentioned is-

sues. The ﬁrst is to start with PBD and replace the

shape preservation constraint with the shape preser-

vation constraint from the ARAP approach. A math-

Computerised Muscle Modelling and Simulation for Interactive Applications

219

Figure 8: ARAP approach with a simple volume preserva-

tion constraint. The initial model is in white, the user de-

formation is in yellow. The volume preserving model with

user deﬁned constraint is in lime blue, the green model is

the simple interweaving approach of the ARAP and PBD.

ematical reformulation of the shape constraint and

ﬁnding a gradient expression would be required for

the ARAP shape preservation constraint. The other

option is to start with ARAP and replace the interleav-

ing approach with gradient descent from PBD. Then,

a volume constraint can be added. Either way, both

methods should end up with the same result.

7 CONCLUSION

All of the described techniques for muscle mod-

elling provide good outcomes; however, each has

some drawbacks. Some are inaccurate (Hill-type

model (Hill, 1938), incorrect according to (Burzy

nski

et al., 2021), Via-points too approximate according

to (Modenese and Kohout, 2020)), some are accu-

rate but difﬁcult to set up or simply too slow to be

useful (Finite element methods used by, e.g. (Delp

and Blemker, 2005), proved difﬁcult to set up by

(Romeo et al., 2018)). Other methods are ”com-

promise solutions” in terms of accuracy and com-

putational complexity (Mass-Spring system, (Georgii

and Westermann, 2005; Aubel and Thalmann, 2001;

Jan

ak, 2012), PBD, As-Rigid-As-Possible (Sorkine

and Alexa, 2007; Fasser et al., 2021; Wang et al.,

2021)). As the reader can probably imagine, many

open problems still exist.

ACKNOWLEDGEMENTS

The authors thank their colleagues and students at the

University of West Bohemia for their discussions and

suggestions. This work was supported by the Ministry

of Education, Youth and Sports of the Czech Repub-

lic, project SGS-2022-015 New Methods for Medical,

Spatial, and Communication Data.

REFERENCES

Aﬁatdoust, F. and Esmaeilbeigi, M. (2015). Optimal vari-

able shape parameters using genetic algorithm for ra-

dial basis function approximation. Ain Shams Engi-

neering Journal, 6(2):639–647.

Angles, B., Rebain, D., Macklin, M., Wyvill, B., Barthe,

L., Lewis, J., Von Der Pahlen, J., Izadi, S., Valentin,

J., Bouaziz, S., and Tagliasacchi, A. (2019). Viper:

Volume invariant position-based elastic rods. Proc.

ACM Comput. Graph. Interact. Tech., 2(2).

Aubel, A. and Thalmann, D. (2001). Interactive modeling

of the human musculature. In Proceedings Computer

Animation 2001. Fourteenth Conference on Computer

Animation (Cat. No.01TH8596), pages 167 – 255.

Barzan, M., Carty, C., Maine, S., Brito da Luz, S., Lloyd,

D., and Modenese, L. (2017). Subject-speciﬁc knee

kinematics during walking in children and adolescents

with recurrent patellar dislocation. In 23rd Australian

& New Zealand Orthopaedic Research Society.

Burzy

nski, S., Sabik, A., Witkowski, W., and Łuczkiewicz,

P. (2021). Inﬂuence of the femoral offset on the mus-

cles passive resistance in total hip arthroplasty. PLOS

ONE, 16(5):1–12.

Bærentzen, A. and Aanæs, H. (2002). Generating Signed

Distance Fields From Triangle Meshes. Informatics

and Mathematical Modelling.

Cervenka., M. and Kohout., J. (2020). Fast and realistic

approach to virtual muscle deformation. In Proceed-

ings of the 13th International Joint Conference on

Biomedical Engineering Systems and Technologies -

HEALTHINF,, pages 217–227. INSTICC, SciTePress.

Cervenka, M. and Skala, V. (2020). Behavioral study of

various radial basis functions for approximation and

interpolation purposes. In 2020 IEEE 18th World Sym-

posium on Applied Machine Intelligence and Infor-

matics (SAMI), pages 135–140.

Delp, S. and Blemker, S. (2005). Three-dimensional repre-

sentation of complex muscle architectures and geome-

tries. Annals of biomedical engineering, 33:661–73.

Dvo

ak, J., K

cerekov

a, Z., Van

cek, P., Hruda, L., and

sa, L. (2022). As-rigid-as-possible volume track-

ing for time-varying surfaces. Computers & Graphics,

102:329–338.

GRAPP 2023 - 18th International Conference on Computer Graphics Theory and Applications

220

Fasser, M. ., Jokeit, M., Kalthoff, M., Gomez Romero,

D. A., Trache, T., Snedeker, J. G., Farshad, M.,

and Widmer, J. (2021). Subject-speciﬁc alignment

and mass distribution in musculoskeletal models of

the lumbar spine. Frontiers in Bioengineering and

Biotechnology, 9. Cited By :2.

Fukuda, N., Otake, Y., Takao, M., Yokota, F., Ogawa, T.,

Uemura, K., Nakaya, R., Tamura, K., Grupp, R., Far-

vardin, A., Sugano, N., and Sato, Y. (2017). Estima-

tion of attachment regions of hip muscles in ct im-

age using muscle attachment probabilistic atlas con-

structed from measurements in eight cadavers. Inter-

national Journal of Computer Assisted Radiology and

Surgery, 12.

Georgii, J. and Westermann, R. (2005). Mass-spring sys-

tems on the gpu. Simulation Modelling Practice and

Theory, 13:693–702.

Green, S. (2010). Particle simulation using cuda. In Particle

Simulation using CUDA.

Havlicek, O., Cervenka, M., and Kohout, J. (2022). Colli-

sion detection and response approaches for computer

muscle modelling. accepted for the IEEE 16th Inter-

national Scientiﬁc Conference on Informatics.

Hill, A. (1938). The heat of shortening and the dynamic

constants of muscle. Proc. R. Soc. Lond. B, 126:612–

745.

Jan

ak, T. (2012). Fast soft-body models for musculoskele-

tal modelling. Technical report, University of West

Bohemia, Faculty of Applied Sciences.

Kohout, J. and

Cervenka, M. (2021). Muscle deformation

using position based dynamics. In Ye, X., Soares,

F., De Maria, E., G

omez Vilda, P., Cabitza, F., Fred,

A., and Gamboa, H., editors, Biomedical Engineer-

ing Systems and Technologies, pages 486–509, Cham.

Springer International Publishing.

Koschier, D. and Bender, J. (2017). Density maps for im-

proved sph boundary handling. In Proceedings of

the ACM SIGGRAPH / Eurographics Symposium on

Computer Animation, SCA ’17, New York, NY, USA.

Association for Computing Machinery.

Lee, D., Li, Z., Sohail, Q. Z., Jackson, K., Fiume, E., and

Agur, A. (2014). A three-dimensional approach to

pennation angle estimation for human skeletal mus-

cle. Computer methods in biomechanics and biomed-

ical engineering, 18:1–11.

Li, H., Sumner, R., and Pauly, M. (2008). Global correspon-

dence optimization for non-rigid registration of depth

scans. Computer Graphics Forum, 27.

Macklin, M., M

uller, M., and Chentanez, N. (2016). Xpbd:

Position-based simulation of compliant constrained

dynamics. In Proceedings of the 9th International

Conference on Motion in Games, MIG ’16, page

49–54, New York, NY, USA. Association for Com-

puting Machinery.

Majdisova, Z. and Skala, V. (2017). Radial basis function

approximations: comparison and applications. Ap-

plied Mathematical Modelling, 51:728–743.

Modenese, L. and Kohout, J. (2020). Automated generation

of three-dimensional complex muscle geometries for

use in personalised musculoskeletal models. Annals

of Biomedical Engineering, 48.

uller, M., Heidelberger, B., Hennix, M., and Ratcliff,

J. (2007). Position based dynamics. Journal of

Visual Communication and Image Representation,

18(2):109–118.

Oatis, C. A. (2017). Biomechanics of skeletal muscle. Lip-

pincott Williams & Wilkins.

Romeo, M., Monteagudo, C., and S

anchez-Quir

os, D.

(2018). Muscle Simulation with Extended Position

Based Dynamics. In Garc

ıa-Fern

andez, I. and Ure

na,

C., editors, Spanish Computer Graphics Conference

(CEIG). The Eurographics Association.

Skala, V. and Cervenka, M. (2019). Novel rbf approxima-

tion method based on geometrical properties for sig-

nal processing with a new rbf function: Experimental

comparison. In 2019 IEEE 15th International Scien-

tiﬁc Conference on Informatics.

Sorkine, O. and Alexa, M. (2007). As-Rigid-As-Possible

Surface Modeling. In Belyaev, A. and Garland, M.,

editors, Geometry Processing. The Eurographics As-

sociation.

Teschner, M., Kimmerle, S., Heidelberger, B., Zachmann,

G., Raghupathi, L., Fuhrman, A., Cani, M.-P., Faure,

F., Magnenat-Thalmann, N., Strasser, W., and Volino,

P. (2005). Collision Detection for Deformable Ob-

jects. Computer Graphics Forum.

Turk, G. (1990). Interactive collision detection for molec-

ular graphics. Technical report, University of North

Carolina at Chapel Hill, USA.

Wade, S., Strader, C., Fitzpatrick, L., Anthony, M., and

O’Malley, C. (2014). Estimating prevalence of os-

teoporosis: Examples from industrialized countries.

Archives of osteoporosis, 9:182.

Wang, B., Matcuk, G., and Barbi

c, J. (2021). Modeling

of personalized anatomy using plastic strains. ACM

Trans. Graph., 40(2).

Zhang, G., Wang, C., Liu, Q., Wei, J., Luo, C., Duan, L.,

Long, J., Zhang, X., and Wang, G. (2021). Develop-

ment of skeletal muscle model for bridge-style move-

ment rehabilitation. Journal of Physics: Conference

Series, 2026:012061.

Zhang, S.-X., Heng, P.-A., Liu, Z.-J., Tan, L.-W., Qiu, M.-

G., Li, Q.-Y., Liao, R.-X., Li, K., Cui, G.-Y., Guo,

Y.-L., Yang, X.-P., Liu, G.-J., Shan, J.-L., Liu, J.-J.,

Zhang, W.-G., Chen, X.-H., Chen, J.-H., Wang, J.,

Chen, W., Lu, M., You, J., Pang, X.-L., Xiao, H., Xie,

Y.-M., and Cheng, J. C.-Y. (2004). The chinese vis-

ible human (cvh) datasets incorporate technical and

imaging advances on earlier digital humans. Journal

of Anatomy, 204(3):165–173.

Zhao, Y., Clapworthy, G., Kohout, J., Dong, F., Tao, Y.,

Wei, S., and Mcfarlane, N. (2013). Laplacian muscu-

loskeletal deformation for patient-speciﬁc simulation

and visualisation. In 2013 17th International Confer-

ence on Information Visualisation, pages 505–510.

Computerised Muscle Modelling and Simulation for Interactive Applications

221