Determining individual muscle forces during maximal activity: Model development, parameter determination, and validation

Exploring the muscle architecture effect on the mechanical behaviour of mouse rotator cuff muscles

Incorporating detailed muscle architecture aspects into computational models can enable researchers to gain deeper insights into the complexity of muscle function, movement, and performance. In this study, we employed histological, multiphoton image processing, and finite element method techniques to characterise the mechanical dependency on the architectural behaviour of supraspinatus and infraspinatus mouse muscles. While mechanical tests revealed a stiffer passive behaviour in the supraspinatus muscle, the collagen content was found to be two times higher in the infraspinatus. This effect was unveiled by analysing the alignment of fibres during muscle stretch with the 3D models and the parameters obtained in the fitting. Therefore, a strong dependence of muscle behaviour, both active and passive, was found on fibre orientation rather than collagen content.

Elbow joint biomechanics during ADL focusing on total elbow arthroplasty - a scoping review

BACKGROUND

Overloading is hypothesized to be one of the failure mechanisms following total elbow arthroplasty (TEA). It is unclear whether the current post-operative loading instruction is compliant with reported failure mechanisms. Aim is therefore to evaluate the elbow joint load during activities of daily living (ADL) and compare these loads with reported failure limits from retrieval and finite element studies.

METHODS

A scoping review of studies until 23 November 2021 investigating elbow joint load during ADL were identified by searching PubMed/Medline and Web of Science. Studies were eligible when: (1) reporting on the elbow joint load in native elbows or elbows with an elbow arthroplasty in adults; (2) full-text article was available.

RESULTS

Twenty-eight studies with a total of 256 participants were included. Methodological quality was low in 3, moderate in 22 and high in 3 studies. Studies were categorized as 1) close to the body and 2) further away from the body. Tasks were then subdivided into: 1) cyclic flexion/extension, 2) push-up, 3) reaching, 4) self-care, 5) work. Mean flexion-extension joint load was 17 Nm, mean varus-valgus joint load 9 Nm, mean pronation-supination joint load 8 Nm and mean bone-on-bone contact force 337 N.

CONCLUSION

The results of our scoping review give a first overview of the current knowledge on elbow joint loads during ADL. Surprisingly, the current literature is not sufficient to formulate a postoperative instruction for elbow joint loading, which is compliant with failure limits of the prosthesis. In addition, our current instruction does not appear to be evidence-based. Our recommendations offer a starting point to assist clinicians in providing informed decisions about post-operative instructions for their patients.

Three-dimensional modelling of human quadriceps femoris forces

Quadriceps intramuscular anatomy is typically described in two dimensions. However, anatomical descriptions indicate fascicles in the quadriceps may have a three-dimensional orientation. The purpose of this investigation was to quantify the maximum force generating capacity of the individual quadriceps' muscles in three dimensions. Muscle architectural parameters were obtained from three cadaver specimens (two female) and input into a geometry-based multiple fascicle muscle force model. Vastus lateralis, vastus medialis, and rectus femoris had partitions which could be defined based on differences in the sense and direction of fascicles between partitions. Vastus lateralis and rectus femoris were bipennate due to partitions sharing an aponeurosis. Vastus lateralis deep and superficial partitions exerted posterior- (maximum: -29 ± 5 N) and anterior-directed (maximum: 58 ± 15 N) forces on their shared distal aponeurosis. Rectus femoris medial and lateral partitions exerted medial- (maximum: -38 ± 17 N) and lateral-directed (maximum: 19 ± 12 N) forces on their shared proximal aponeurosis. All vastus medialis fascicles ran along the proximal-distal axis. However, fascicles arising near the lesser trochanter also ran along the superficial-deep axis, while fascicles arising from the linea aspera ran along the medial-lateral axis. Thus, vastus medialis could be divided into longus and oblique partitions. Due to the large pennation angle, vastus medialis oblique could exert maximum medial-directed (-219 ± 93 N) and proximal-directed (279 ± 168 N) forces at approximately -40° and -70° knee flexion, respectively, indicating dual roles for vastus medialis oblique dependent on knee flexion angle.

IB2d: a Python and MATLAB implementation of the immersed boundary method

The development of fluid-structure interaction (FSI) software involves trade-offs between ease of use, generality, performance, and cost. Typically there are large learning curves when using low-level software to model the interaction of an elastic structure immersed in a uniform density fluid. Many existing codes are not publicly available, and the commercial software that exists usually requires expensive licenses and may not be as robust or allow the necessary flexibility that in house codes can provide. We present an open source immersed boundary software package, IB2d, with full implementations in both MATLAB and Python, that is capable of running a vast range of biomechanics models and is accessible to scientists who have experience in high-level programming environments. IB2d contains multiple options for constructing material properties of the fiber structure, as well as the advection-diffusion of a chemical gradient, muscle mechanics models, and artificial forcing to drive boundaries with a preferred motion.

A Mathematical Model and MATLAB Code for Muscle-Fluid-Structure Simulations

This article provides models and code for numerically simulating muscle-fluid-structure interactions (FSIs). This work was presented as part of the symposium on Leading Students and Faculty to Quantitative Biology through Active Learning at the society-wide meeting of the Society for Integrative and Comparative Biology in 2015. Muscle mechanics and simple mathematical models to describe the forces generated by muscular contractions are introduced in most biomechanics and physiology courses. Often, however, the models are derived for simplifying cases such as isometric or isotonic contractions. In this article, we present a simple model of the force generated through active contraction of muscles. The muscles' forces are then used to drive the motion of flexible structures immersed in a viscous fluid. An example of an elastic band immersed in a fluid is first presented to illustrate a fully-coupled FSI in the absence of any external driving forces. In the second example, we present a valveless tube with model muscles that drive the contraction of the tube. We provide a brief overview of the numerical method used to generate these results. We also include as Supplementary Material a MATLAB code to generate these results. The code was written for flexibility so as to be easily modified to many other biological applications for educational purposes.

The influence of squat depth on maximal vertical jump performance

An increase in the period over which a muscle generates force can lead to the generation of greater force and, therefore, for example in jumping, to greater jump height. The aim of this study was to examine the effect of squat depth on maximum vertical jump performance. We hypothesized that jump height would increase with increasing depth of squat due to the greater time available for the generation of muscular force. Ten participants performed jumps from preferred and deep squat positions. A computer model simulated jumps from the different starting postures. The participants showed no difference in jump height in jumps from deep and preferred positions. Simulated jumps produced similar kinematics to the participants' jumps. The optimal squat depth for the simulated jumps was the lowest position the model was able to jump from. Because jumping from a deep squat is rarely practised, it is unlikely that these jumps were optimally coordinated by the participants. Differences in experimental vertical ground reaction force patterns also suggest that jumps from a deep squat are not optimally coordinated. These results suggest there is the potential for athletes to increase jump performance by exploiting a greater range of motion.

Examining the Role of the Gastrocnemius during the Leg Curl Exercise

This study examined the moment-producing capabilities of the gastrocnemius during isokinetic knee flexion tasks. Nine healthy men were tested using a Biodex isokinetic dynamometer. Each one completed 3 maximum repetitions at 3 angular velocities, 30, 75, and 150º/s, with his ankle braced in either full dorsiflexion or full plantar flexion. A computer model was used to simulate the experimental tasks. Experimentally, the moment produced at the knee joint with the ankle dorsiflexed was significantly higher than the moment with the ankle plantar-flexed at all 3 angular velocities,p< 0.05. This suggests that lengthening the gastrocnemius allowed for greater contribution of the gastrocnemius to the total moment produced at the knee during isokinetic knee flexions. The simulations supported the experimental data and suggested that, with the ankle dorsiflexed, the gastrocnemius acts on a more favorable part of the muscle’s force-length curve compared with the plantar-flexed condition. The results of the experimental work, along with the simulations, demonstrated that lengthening the gastrocnemius significantly increased the moment produced at the knee joint during isokinetic knee flexion tasks. These results have implications for instructions given to persons who perform leg curls for muscle strengthening, and for the design of knee flexion exercise machines.

The biomechanics of an overarm throwing task: a simulation model examination of optimal timing of muscle activations

A series of overarm throws, constrained to the parasagittal plane, were simulated using a muscle model actuated two-segment model representing the forearm and hand plus projectile. The parameters defining the modeled muscles and the anthropometry of the two-segment models were specific to the two young male subjects. All simulations commenced from a position of full elbow flexion and full wrist extension. The study was designed to elucidate the optimal inter-muscular coordination strategies for throwing projectiles to achieve maximum range, as well as maximum projectile kinetic energy for a variety of projectile masses. A proximal to distal (PD) sequence of muscle activations was seen in many of the simulated throws but not all. Under certain conditions moment reversal produced a longer throw and greater projectile energy, and deactivation of the muscles resulted in increased projectile energy. Therefore, simple timing of muscle activation does not fully describe the patterns of muscle recruitment which can produce optimal throws. The models of the two subjects required different timings of muscle activations, and for some of the tasks used different coordination patterns. Optimal strategies were found to vary with the mass of the projectile, the anthropometry and the muscle characteristics of the subjects modeled. The tasks examined were relatively simple, but basic rules for coordinating these tasks were not evident.

Timing accuracy in human throwing

This study examines the precision required in the timing of muscle activations and projectile release to hit a target of 20 cm in diameter oriented horizontally either 6 or 8 m away. Over-arm throws, constrained to the sagittal plane, were simulated using a muscle-actuated, two-segment model representing the forearm and hand plus projectile. The parameters defining the modeled muscles and the anthropometry were specific to two male subjects. An objective function specified that throws must be both fast and accurate. Once an optimal solution had been found, the sensitivity of these timings was investigated. The times of activation or release were changed and the simulation model re-run with the new timings, and it was determined whether the projectile would still have struck the target. For one set of simulations, to hit the target at 8 m, the optimal throw was achieved with a time delay between the onset of wrist activation and elbow extensor activation [Proximal-distal (PD) delay] of 49 ms and a release time of 83.4 ms. At this optimal point in the solution space, the launch window was 1.2 ms (assuming the original PD delay). The launch window was the time available within which the projectile must be released and still strike the target. The window during which the wrist flexors could be activated was 10. 41 ms (assuming the projectile was released at the pre-planned optimal time). The control scheme which required the least timing precision had a PD delay of 56 ms and a release time of 89.4 ms. Errors in timing could occur in activation and release simultaneously under this scheme, the timing windows were 4 ms in PD delay and 2.4 ms in release. Similar results were found for a second set of simulations. These simulations revealed the precise timings required in muscle activations and release required for fast accurate throws.

Producing physiologically realistic individual muscle force estimations by imposing constraints when using optimization techniques

Static optimization techniques have been used to estimate individual muscle forces in order to assess joint loads and muscle function. This study examined the validity of such techniques. Forces in the individual muscles, causing elbow flexion, were estimated using four different objective functions, minimizing the sum of the muscle stress either squared or cubed, and minimizing the sum of the relative muscle forces either squared or cubed. Constraints were placed on the maximum muscle forces based on physiological considerations. The resulting force estimates were compared with those from a validated muscle model that took account of the physiological properties of the muscles. The objective functions produced physiologically unrealistic muscle force estimations, unless the maximum muscle forces were constrained. By imposing constraints, individual muscle force predictions were restricted to those that were within physiologically realistic bounds. Using this procedure for sub-maximal activity resulted in some muscle activity being equal to the constraint, which, whilst possible, is still unrealistic. Therefore, by imposing constraints, the muscle forces can be kept within physiological boundaries, but the inferred recruitment is not necessarily the solution that the 'body' selects, but reflects a set of muscle forces that meet the solution to the optimization problem.

Estimating the contribution of muscles to joint torque based on motor-unit activity

Because most joints in the human arm are crossed by a number of muscles which exceeds the number of degrees of freedom for those joints, the motor system can use a variety of muscle activation patterns for the same torque in each joint. We have developed a mode to estimate the contribution of individual muscles to the total torque in a joint based on intramuscular EMG recordings. EMG activity recorded with surface electrodes may be contaminated with cross-talk from other muscles. Moreover, it may not be representative for the activation of a muscle when there are several subpopulations of motor units in the muscle. We derive a relation between the recruitment threshold of a motor unit in a subpopulation for force in various directions and the relative contribution by that subpopulation to joint torque. A set of linear equations can then be constructed which relates the contribution of each subpopulation (and therefore of each muscle) to the total joint torque. If the activition of individual subpopulations is modulated differently for forces in various directions, the relative contribution of the individual subpopulations to the total joint torque can be estimated.