A computationally efficient strategy to estimate muscle forces in a finite element musculoskeletal model of the lower limb

Abstract Finite element musculoskeletal (FEMS) approaches using concurrent musculoskeletal and finite element models driven by motion data such as marker-based motion trajectory can provide insight into the interactions between the knee joint secondary kinematics, contact mechanics, and muscle forces in subject-specific biomechanical investigations. However, these data-driven FEMS systems have two major disadvantages that make them challenging to apply in clinical environments: they are computationally expensive and they require expensive and inconvenient equipment for data acquisition. In this study, we developed an FEMS model of the lower limb driven solely by inertial measurement unit sensors that includes the tissue geometries of the entire knee joint and combines muscle modeling and elastic foundation theory-based contact analysis of knee into a single framework. The model requires only the angular velocities and accelerations measured by the sensors as input, and the target outputs (knee contact mechanics, secondary kinematics, and muscle forces) are predicted from the convergence results of iterative calculations of muscle force optimization and knee contact mechanics. To evaluate its accuracy, the model was compared with in vivo experimental data during gait. The maximum contact pressure (12.6 MPa) in the rigid body contact analysis occurred on the medial side of the cartilage at the maximum loading response. The proposed computationally efficient framework drastically reduced the computational time (97.5% reduction) in comparison with the conventional deformable finite element analysis. The developed framework combines measurement convenience and computational efficiency and shows promise for clinical applications.

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Development of a Lower Limb Finite Element Musculoskeletal Gait Simulation Framework Driven Solely by Inertial Measurement Unit Sensors

Biomechanics ◽

10.3390/biomechanics1030025 ◽

2021 ◽

Vol 1 (3) ◽

pp. 293-306

Author(s):

Sentong Wang ◽

Kazunori Hase ◽

Susumu Ota

Keyword(s):

Finite Element ◽

Knee Joint ◽

Contact Mechanics ◽

Lower Limb ◽

Inertial Measurement Unit ◽

Measurement Unit ◽

Muscle Forces ◽

Inertial Measurement ◽

Medial Side ◽

Subject Specific

Finite element musculoskeletal (FEMS) approaches using concurrent musculoskeletal and finite element models driven by motion data such as marker-based motion trajectory can provide insight into the interactions between the knee joint secondary kinematics, contact mechanics, and muscle forces in subject-specific biomechanical investigations. However, these data-driven FEMS systems have a major disadvantage that makes them challenging to apply in clinical environments, i.e., they require expensive and inconvenient equipment for data acquisition. In this study, we developed an FEMS model of the lower limb driven solely by inertial measurement unit sensors that include the tissue geometries of the entire knee joint, and that combine modeling of 16 muscles into a single framework. The model requires only the angular velocities and accelerations measured by the sensors as input. The target outputs (knee contact mechanics, secondary kinematics, and muscle forces) are predicted from the convergence results of iterative calculations of muscle force optimization and knee contact mechanics. To evaluate its accuracy, the model was compared with in vivo experimental data during gait. The maximum contact pressure (11.3 MPa) occurred on the medial side of the cartilage at the maximum loading response. The developed framework combines measurement convenience and accurate modeling, and shows promise for clinical applications aimed at understanding subject-specific biomechanics.

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The development of a segment-based musculoskeletal model of the lower limb: introducing F ree B ody

Royal Society Open Science ◽

10.1098/rsos.140449 ◽

2015 ◽

Vol 2 (6) ◽

pp. 140449 ◽

Cited By ~ 21

Author(s):

Daniel J. Cleather ◽

Anthony M. J. Bull

Keyword(s):

Lower Limb ◽

Musculoskeletal Model ◽

The Body ◽

Contact Forces ◽

Biomechanical Analysis ◽

Simultaneous Optimization ◽

Muscle Forces ◽

Phase Errors ◽

Vertical Jumping ◽

Joint Contact

Traditional approaches to the biomechanical analysis of movement are joint-based; that is the mechanics of the body are described in terms of the forces and moments acting at the joints, and that muscular forces are considered to create moments about the joints. We have recently shown that segment-based approaches, where the mechanics of the body are described by considering the effect of the muscle, ligament and joint contact forces on the segments themselves, can also prove insightful. We have also previously described a simultaneous, optimization-based, musculoskeletal model of the lower limb. However, this prior model incorporates both joint- and segment-based assumptions. The purpose of this study was therefore to develop an entirely segment-based model of the lower limb and to compare its performance to our previous work. The segment-based model was used to estimate the muscle forces found during vertical jumping, which were in turn compared with the muscular activations that have been found in vertical jumping, by using a Geers' metric to quantify the magnitude and phase errors. The segment-based model was shown to have a similar ability to estimate muscle forces as a model based upon our previous work. In the future, we will evaluate the ability of the segment-based model to be used to provide results with clinical relevance, and compare its performance to joint-based approaches. The segment-based model described in this article is publicly available as a GUI-based M atlab ® application and in the original source code (at www.msksoftware.org.uk ).

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A finite element model of the lower limb during stance phase of gait cycle including the muscle forces

BioMedical Engineering OnLine ◽

10.1186/s12938-017-0428-6 ◽

2017 ◽

Vol 16 (1) ◽

Cited By ~ 4

Author(s):

Arnaud Diffo Kaze ◽

Stefan Maas ◽

Pierre-Jean Arnoux ◽

Claude Wolf ◽

Dietrich Pape

Keyword(s):

Finite Element ◽

Finite Element Model ◽

Lower Limb ◽

Stance Phase ◽

Gait Cycle ◽

Element Model ◽

Muscle Forces

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The Effects of External Loads and Muscle Forces on the Knee Joint Ligaments during Walking: A Musculoskeletal Model Study

Applied Sciences ◽

10.3390/app11052356 ◽

2021 ◽

Vol 11 (5) ◽

pp. 2356

Author(s):

Carlo Albino Frigo ◽

Lucia Donno

Keyword(s):

Knee Joint ◽

Cruciate Ligament ◽

Musculoskeletal Model ◽

Optimization Approach ◽

Muscle Forces ◽

Collateral Ligaments ◽

Flexion Extension ◽

Lateral Collateral Ligaments ◽

Gastrocnemius Muscles ◽

External Loads

A musculoskeletal model was developed to analyze the tensions of the knee joint ligaments during walking and to understand how they change with changes in the muscle forces. The model included the femur, tibia, patella and all components of cruciate and collateral ligaments, quadriceps, hamstrings and gastrocnemius muscles. Inputs to the model were the muscle forces, estimated by a static optimization approach, the external loads (ground reaction forces and moments) and the knee flexion/extension movement corresponding to natural walking. The remaining rotational and translational movements were obtained as a result of the dynamic equilibrium of forces. The validation of the model was done by comparing our results with literature data. Several simulations were carried out by sequentially removing the forces of the different muscle groups. Deactivation of the quadriceps produced a decrease of tension in the anterior cruciate ligament (ACL) and an increase in the posterior cruciate ligament (PCL). By removing the hamstrings, the tension of ACL increased at the late swing phase, while the PCL force dropped to zero. Specific effects were observed also at the medial and lateral collateral ligaments. The removal of gastrocnemius muscles produced an increase of tension only on PCL and lateral collateral ligaments. These results demonstrate how musculoskeletal models can contribute to knowledge about complex biomechanical systems as the knee joint.

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Investigation ofin-vivohinge knee behaviour using a dynamic finite element model of the lower limb

Computer Methods in Biomechanics & Biomedical Engineering ◽

10.1080/10255842.2012.713644 ◽

2012 ◽

Vol 15 (sup1) ◽

pp. 326-327 ◽

Cited By ~ 1

Author(s):

L. Zach ◽

S. Konvickova ◽

P. Ruzicka

Keyword(s):

Finite Element ◽

Finite Element Model ◽

Lower Limb ◽

Element Model ◽

Dynamic Finite Element

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Considerations when loading spinal finite element models with predicted muscle forces from inverse static analyses

Journal of Biomechanics ◽

10.1016/j.jbiomech.2013.03.003 ◽

2013 ◽

Vol 46 (7) ◽

pp. 1376-1378 ◽

Cited By ~ 11

Author(s):

Rui Zhu ◽

Thomas Zander ◽

Marcel Dreischarf ◽

Georg N. Duda ◽

Antonius Rohlmann ◽

...

Keyword(s):

Finite Element ◽

Finite Element Models ◽

Muscle Forces

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Computationally Efficient Magnetic Resonance Imaging Based Surface Contact Modeling as a Tool to Evaluate Joint Injuries and Outcomes of Surgical Interventions Compared to Finite Element Modeling

Journal of Biomechanical Engineering ◽

10.1115/1.4026485 ◽

2014 ◽

Vol 136 (4) ◽

Cited By ~ 4

Author(s):

Joshua E. Johnson ◽

Phil Lee ◽

Terence E. McIff ◽

E. Bruce Toby ◽

Kenneth J. Fischer

Keyword(s):

Finite Element ◽

Finite Element Modeling ◽

Joint Mechanics ◽

Computationally Efficient ◽

Efficient Manner ◽

Element Modeling ◽

Joint Injuries ◽

Surface Contact ◽

Joint Contact ◽

Contact Pressures

Joint injuries and the resulting posttraumatic osteoarthritis (OA) are a significant problem. There is still a need for tools to evaluate joint injuries, their effect on joint mechanics, and the relationship between altered mechanics and OA. Better understanding of injuries and their relationship to OA may aid in the development or refinement of treatment methods. This may be partially achieved by monitoring changes in joint mechanics that are a direct consequence of injury. Techniques such as image-based finite element modeling can provide in vivo joint mechanics data but can also be laborious and computationally expensive. Alternate modeling techniques that can provide similar results in a computationally efficient manner are an attractive prospect. It is likely possible to estimate risk of OA due to injury from surface contact mechanics data alone. The objective of this study was to compare joint contact mechanics from image-based surface contact modeling (SCM) and finite element modeling (FEM) in normal, injured (scapholunate ligament tear), and surgically repaired radiocarpal joints. Since FEM is accepted as the gold standard to evaluate joint contact stresses, our assumption was that results obtained using this method would accurately represent the true value. Magnetic resonance images (MRI) of the normal, injured, and postoperative wrists of three subjects were acquired when relaxed and during functional grasp. Surface and volumetric models of the radiolunate and radioscaphoid articulations were constructed from the relaxed images for SCM and FEM analyses, respectively. Kinematic boundary conditions were acquired from image registration between the relaxed and grasp images. For the SCM technique, a linear contact relationship was used to estimate contact outcomes based on interactions of the rigid articular surfaces in contact. For FEM, a pressure-overclosure relationship was used to estimate outcomes based on deformable body contact interactions. The SCM technique was able to evaluate variations in contact outcomes arising from scapholunate ligament injury and also the effects of surgical repair, with similar accuracy to the FEM gold standard. At least 80% of contact forces, peak contact pressures, mean contact pressures and contact areas from SCM were within 10 N, 0.5 MPa, 0.2 MPa, and 15 mm2, respectively, of the results from FEM, regardless of the state of the wrist. Depending on the application, the MRI-based SCM technique has the potential to provide clinically relevant subject-specific results in a computationally efficient manner compared to FEM.

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AN ALGORITHM TO CALCULATE THE COMPONENTS OF ALL MUSCLE FORCES DURING EACH PHASES OF THE GAIT CYCLE, FOR THE PELVIC-FEMUR COMPLEX

Journal of Mechanics in Medicine and Biology ◽

10.1142/s0219519405001680 ◽

2005 ◽

Vol 05 (04) ◽

pp. 539-548 ◽

Cited By ~ 1

Author(s):

SANTANU MAJUMDER ◽

AMIT ROYCHOWDHURY ◽

SUBRATA PAL

Keyword(s):

Finite Element ◽

Hip Joint ◽

Computational Models ◽

Gait Cycle ◽

Muscle Force ◽

Fe Analysis ◽

Muscle Forces ◽

Force Magnitude ◽

Flexion Extension ◽

Force Components

With the help of finite element (FE) computational models of femur, pelvis or hip joint to perform quasi-static stress analysis during the entire gait cycle, muscle force components (X, Y, Z) acting on the hip joint and pelvis are to be known. Most of the investigators have presented only the net muscle force magnitude during gait. However, for the FE software, either muscle force components (X, Y, Z) or three angles for the muscle line of action are required as input. No published algorithm (with flowchart) is readily available to calculate the required muscle force components for FE analysis. As the femur rotates about the hip center during gait, the lines of action for 27 muscle forces are also variable. To find out the variable lines of action and muscle force components (X, Y, Z) with directions, an algorithm was developed and presented here with detailed flowchart. We considered the varying angles of adduction/abduction, flexion/extension during gait. This computer program, obtainable from the first author, is able to calculate the muscle force components (X, Y, Z) as output, if the net magnitude of muscle force, hip joint orientations during gait and muscle origin and insertion coordinates are provided as input.

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