The muscle-force driven FE modeling approach was developed and used in this thesis (studiesItoIV) with the goal of creating sequential MSFE models with inte-grated and consistent kinematics and kinetics at the interface between the MS and FE models. The only kinematic input into the FE models of this thesis was the knee flexion angle estimated from IK shared identically between the MS and FE mod-els. The rest of the DoFs of the FE models were driven by the kinetics of the knee
Motion data
EMG-assisted MS analysisFinite Element (FE) Analysis
Assembling
Assembling the parts, writing inputs into the
FE models, executing FE
analyses FE model
parts
utputs
OpenSim (EMG-assisted CMC)
EMGs Enveloped EMGs
Marker
trajectories Inverse
kinematics Joint angles
Residual reduction algorithm
Adjusted model
Adjusted muscle excitation ranges
Knee flexion angle
Residual joint contact forces Knee external moments
(i.e., inverse dynamics) Muscle insertion points Muscles’ line
of action
Muscle forces Inputs into the FE model Ground
reaction forces
Reference points of femur and patella
Knee muscles The 12 DoFs muscle-force
driven FRPVE FE model
Subject’s MRI
Figure 5.1:Workflow of studyI, i.e., the EMG-assisted muscle-force driven FRPVE FE model of the knee. The arrows in orange show inputs to the workflow.
32
MRI of the subject
The 12 DoFs muscle-force driven FRPVE FE model
Kinematics (IK)
Joint moments (ID)
Muscle-tendon lengths
Muscle moment arms
Initial muscle-tendon parameters
The EMG-assisted MS model
The MS model with
the 12 DoFs knee The Gait2392 MS model (SO-based)
Motion data
Motion data EMGs Marker trajectories Ground reaction
forces
Calibration
Execution
Calibrated muscle-tendon
parameters EMG envelopes
Knee flexion angle
Residual joint contact forces Knee external moments
(i.e., inverse dynamics)
Muscle insertion points Muscles’ line of action
Muscle forces Inputs into the FE model
Femoral, tibial, patellar cartilagesand
Figure 5.2: Workflow of studyII. The concurrent 12 DoFs knee MSFE model (in blue), the SO-based sequential MSFE model (in green), and the EMG-assisted MSFE model (in red) were developed to explore the knee joint mechanics. The arrows in orange show inputs to the workflow.
Motion DataMarker trajectories Ground reactionforces EMGs Estimating the knee varus-valgus alignmentInverse kinematics Inverse dynamics Muscle-tendon parameters
Muscle moment arms Muscle-tendon lengths
Static-optimization based muscle forces Calibration
Execution Calibrated muscle-tendon parameters Musculoskeletalanalyses(SO-based)employing OpenSim API in MATLAB Enveloped EMGs(MOtoNMS)
Writing inputs to CEINMSRunning calibration and execution
Static-optimization based Joint contact forces Calibration trials
Execution trials
Estimated muscle forces Calculating muscle moments and otherinputs to the FE model Atlas-based finite elementmodeling toolbox Back to OpenSimAPI to calculate joint contact forces(joint contact force analysis toolbox) SO-based inputs EMG-assistedinputs Scaled Geometries(.inpfile)
Writing Abaqus inpfiles, executing models, and then reading the results OpenSim CEINMS MATLAB
FRPVE FE models
Measuring anatomical dimensions(used as reference) Measuring anatomical dimensions (used for scaling) SubjectsTemplate MRIs
Manual segmentation (MIMICS)Meshing (HyperMesh) Estimated joint contact forcesReference points
Figure5.3:Theworkflowofthesemi-automatedatlas-basedMSFEanalysispipelinedevelopedinstudyIIIandutilizedinstudyIV.Thearrowsinorangeshowinputstotheworkflow.
(estimated by the MS models) consisted of JCFs and knee moments (except for the knee flexion-extension moment). Hence, in addition to the knee external moments estimated from ID, the moments generated by the muscles should also be imported into the FE models. Following, more details are discussed.
First, let us consider the free-body diagram of the tibia illustrated in Figure 5.4.
As explained in section 3.1, the required external moment at each DoF of the MS model should be counterbalanced by the muscle forces. Specifically at the knee joint, equation 3.5 can be restated as follows:
τf lex/ext=
∑
N j=1fjrj,i (5.1)
whereτf lex/ext is the external flexion/extension moment applied to the knee joint (i.e., obtained from ID), fjis the generated force by thejthmuscle acting on the knee, rj,iis the moment arm of thejthmuscle around the flexion axis of the knee joint, and Nis the total number of muscles acting on the knee.
It should be noticed that Equation (5.1) is valid for the MS models with either a 1 DoF knee or a 12 DoFs knee joint. In other words, in the MS model with the 12 DoFs knee joint mechanism, the equations of motion at the knee are solved only for the knee flexion DoF, while ligaments are considered to passively stabilize the knee joint in other knee DoFs [24, 191]. Although the abduction/abduction and internal/external rotational DoFs are not included when solving equations of mo-tion [24, 27, 191], the estimated muscle forces apply moments in those two DoFs according to equation 3.5 based on their moment arms around those DoFs, corre-spondingly.
Figure 5.4: The free-body diagram of the foot and shank. Rf sis the internal force applied from the foot to the shank,Rs f is the internal force applied from the shank to the foot (which is equal and opposite to theRf s), and Rts is the internal force applied from the thigh to the shank (i.e., the knee JCF).
Following estimation of the muscle forces, the JCF at the knee (according to Figure 5.4) is calculated as:
JCFknee,tot =~Rts= M~a+~Rf s+
∑
N i=1~Fim,knee+
∑
M j=1~Fjm,ankle+
∑
P k=1~Fkl+W~ (5.2) whereJCFknee,totis the total JCF estimated by the MS model (equal to the internal forces between the shank and the thigh), M~a represents the inertial force of the shank due to linear acceleration,~Rf s is the force applied from the foot to the shank,
∑Ni=1~Fim,kneeis the sum of muscle forces passing through the knee joint,∑Mj=1~Fjm,ankle is the sum of muscle forces passing through the ankle joint,∑Pk=1~Fklis the sum of the ligament forces passing through the knee, andW~ is the weight of the shank (note that the effect of the GRF is implicitly included in Equation (5.2) via~Rf s. It should be mentioned that the∑Pk=1~Fkl exists only in the MS models with the 12 DoFs knee, and is zero in the MS model with a 1 DoF knee joint.
The resultant moment on the knee joint, which is the vector sum of the gen-erated moment by muscles and the external moments applied on the knee joint (i.e., those estimated from ID), should be counterbalanced by ligaments. Hence, the femur undergoes mediolateral and anteroposterior translations as well as abduc-tion/adduction and internal/external rotations to provide the required strains in the ligaments to generate the passive forces that counterbalance the resultant mo-ment on the knee joint. Each ligamo-ment applies a momo-ment equal to the cross product of its moment arm and its passive force. Similarly, the transverse components of the JCFs are counterbalanced by ligaments. Indeed, the secondary kinematics estimated by the FE model are due to the interaction of ligaments with the knee moments and JCFs.
To conclude, the forces in Equation (5.2) (i.e., the JCFknee,tot, the knee external moments (estimated from ID), and the moments generated by the muscles (Equa-tion 3.5 in abduc(Equa-tion/adduc(Equa-tion and internal/external rota(Equa-tional DoFs) should be transferred into the FE model to ensure the consistency of the loading and boundary conditions. To this end, the muscle-force driven approach was developed to favor-ably apply these three kinetic loads to the FE model of a sequential MSFE workflow.
Two different implementations of the muscle-force driven FE modeling approach will be explained later in section 5.6.3 (loading and boundary conditions).
5.3 PARTICIPANTS IN THE STUDIES
Studies I and II: One healthy individual (male, 33 years old, 78 kg, 1.77 m) partic-ipated in these studies. The exclusion criteria were the presence of any specific pain, diagnosed MS injuries, or record of surgeries concerning the lower limb of the sub-ject. The study procedures were approved by the ethics committee of the Northern Savo Hospital District (94/2011), and written informed consent was obtained from the participant.
Studies III and IV: Fifteen individuals (6 males and 9 females, 62.4±7.8 years old, and with body mass index 29.3±6.8) participated in studies IIIandIV. The inclu-sion criterion was previously diagnosed KOA according to the KOA clinical defi-nition (i.e., the existence of pain and an evident radiographic joint tissue deterio-ration) [192], at least in one of the medial or lateral femur, tibia, and patella. The
exclusion criteria were the existence of any record of lower limb surgeries or di-agnosed disorders such as ligament or tendon rupture or presence of pain in any body parts except for the knee. The most affected leg of each subject (in terms of OA severity) was selected for analyses (a total of 15 knees, one knee from each sub-ject). All the procedures were approved by the ethics committee of the Northern Savo Hospital District (permission No. 750/2018), and written informed consent was obtained from each subject.