A validated model of passive skeletal muscle to predict force and intramuscular pressure

Aponeurosis structure-function properties: Evidence of heterogeneity and implications for muscle function

Aponeurosis is a sheath-like connective tissue that aids in force transmission from muscle to tendon and can be found throughout the musculoskeletal system. The key role of aponeurosis in muscle-tendon unit mechanics is clouded by a lack of understanding of aponeurosis structure-function properties. This work aimed to determine the heterogeneous material properties of porcine triceps brachii aponeurosis tissue with materials testing and evaluate heterogeneous aponeurosis microstructure with scanning electron microscopy. We found that aponeurosis may exhibit more microstructural collagen waviness in the insertion region (near the tendon) compared to the transition region (near the muscle midbelly) (1.20 versus 1.12, p = 0.055), which and a less stiff stress-strain response in the insertion versus transition regions (p < 0.05). We also showed that different assumptions of aponeurosis heterogeneity, specifically variations in elastic modulus with location can alter the stiffness (by more than 10x) and strain (by approximately 10% muscle fiber strain) of a finite element model of muscle and aponeurosis. Collectively, these results suggest that aponeurosis heterogeneity could be due to variations in tissue microstructure and that different approaches to modeling tissue heterogeneity alters the behavior of computational models of muscle-tendon units. STATEMENT OF SIGNIFICANCE: Aponeurosis is a connective tissue found in many muscle tendon units that aids in force transmission, yet little is known about the specific material properties of aponeurosis. This work aimed to determine how the properties of aponeurosis tissue varied with location. We found that aponeurosis exhibits more microstructural waviness near the tendon compared to near the muscle midbelly, which was associated with differences in tissue stiffness. We also showed that different variations in aponeurosis modulus (stiffness) can alter the stiffness and stretch of a computer model of muscle tissue. These results show that assuming uniform aponeurosis structure and modulus, which is common, may lead to inaccurate models of the musculoskeletal system.

Automated model discovery for muscle using constitutive recurrent neural networks

The stiffness of soft biological tissues not only depends on the applied deformation, but also on the deformation rate. To model this type of behavior, traditional approaches select a specific time-dependent constitutive model and fit its parameters to experimental data. Instead, a new trend now suggests a machine-learning based approach that simultaneously discovers both the best model and best parameters to explain given data. Recent studies have shown that feed-forward constitutive neural networks can robustly discover constitutive models and parameters for hyperelastic materials. However, feed-forward architectures fail to capture the history dependence of viscoelastic soft tissues. Here we combine a feed-forward constitutive neural network for the hyperelastic response and a recurrent neural network for the viscous response inspired by the theory of quasi-linear viscoelasticity. Our novel rheologically-informed network architecture discovers the time-independent initial stress using the feed-forward network and the time-dependent relaxation using the recurrent network. We train and test our combined network using unconfined compression relaxation experiments of passive skeletal muscle and compare our discovered model to a neo Hookean standard linear solid, to an advanced mechanics-based model, and to a vanilla recurrent neural network with no mechanics knowledge. We demonstrate that, for limited experimental data, our new constitutive recurrent neural network discovers models and parameters that satisfy basic physical principles and generalize well to unseen data. We discover a Mooney-Rivlin type two-term initial stored energy function that is linear in the first invariant I1 and quadratic in the second invariant I2 with stiffness parameters of 0.60 kPa and 0.55 kPa. We also discover a Prony-series type relaxation function with time constants of 0.362s, 2.54s, and 52.0s with coefficients of 0.89, 0.05, and 0.03. Our newly discovered model outperforms both the neo Hookean standard linear solid and the vanilla recurrent neural network in terms of prediction accuracy on unseen data. Our results suggest that constitutive recurrent neural networks can autonomously discover both model and parameters that best explain experimental data of soft viscoelastic tissues. Our source code, data, and examples are available at https://github.com/LivingMatterLab.

Formulation and exploration of novel, intramuscular pressure based, muscle activation strategies in a spine model

Optimization models are often devised to assess spinal stability via estimating individual muscle forces. However, neglecting muscles' fluidic behavior remains an approximation due to the role of muscle pressure in force transmission. The purpose of this study was to leverage a validated Finite Element (FE) model of the spine, inclusive of Intra-Muscular Pressure (IMP), to explore muscle activation strategies towards maintaining equilibrium spinal stability. Three conventional strategies governing minimizing muscle effort, minimizing IVD compressive forces, and maintaining stability at all costs were first investigated to explore model's validity. Thereafter, two novel IMP-based strategies were devised and explored, specifically minimizing and maximizing IMP. The model was previously shown valid in light of in vivo and in silico observations with an average discrepancy of 6%. This being the case, the conventional strategies dictated efficacy in muscular activations whilst maintaining an equilibrium stable position, as quantified in the present paper, with a difference of 9.8% from documented data. In addition, the explored novel IMP-based strategies suggested the presence of a threshold individual muscles IMP, approximately 272 mmHg for the longissimus muscle for example, beyond which muscles potentially start to share radial loads with surrounding tissues, whilst limiting the contraction of the underlying muscles. In conclusion, this study theoretically supports the possibility of activation strategies based on muscular pressure, which the developed, verified, and validated FE spine model was leveraged to investigate. The explored novel IMP-based strategies may have significance in informing clinical applications such as motion analysis and functional electrical stimulation of muscles.

The effects of gravity and compression on interstitial fluid transport in the lower limb

Edema in the limbs can arise from pathologies such as elevated capillary pressures due to failure of venous valves, elevated capillary permeability from local inflammation, and insufficient fluid clearance by the lymphatic system. The most common treatments include elevation of the limb, compression wraps and manual lymphatic drainage therapy. To better understand these clinical situations, we have developed a comprehensive model of the solid and fluid mechanics of a lower limb that includes the effects of gravity. The local fluid balance in the interstitial space includes a source from the capillaries, a sink due to lymphatic clearance, and movement through the interstitial space due to both gravity and gradients in interstitial fluid pressure (IFP). From dimensional analysis and numerical solutions of the governing equations we have identified several parameter groups that determine the essential length and time scales involved. We find that gravity can have dramatic effects on the fluid balance in the limb with the possibility that a positive feedback loop can develop that facilitates chronic edema. This process involves localized tissue swelling which increases the hydraulic conductivity, thus allowing the movement of interstitial fluid vertically throughout the limb due to gravity and causing further swelling. The presence of a compression wrap can interrupt this feedback loop. We find that only by modeling the complex interplay between the solid and fluid mechanics can we adequately investigate edema development and treatment in a gravity dependent limb.

Société de Biomécanique Young Investigator Award 2021: Numerical investigation of the time-dependent stress-strain mechanical behaviour of skeletal muscle tissue in the context of pressure ulcer prevention

BACKGROUND

Pressure-induced tissue strain is one major pathway for Pressure Ulcer development and, especially, Deep Tissue Injury. Biomechanical investigation of the time-dependent stress-strain mechanical behaviour of skeletal muscle tissue is therefore essential. In the literature, a viscoelastic formulation is generally assumed for the experimental characterization of skeletal muscles, with the limitation that the underlying physical mechanisms that give rise to the time dependent stress-strain behaviour are not known. The objective of this study is to explore the capability of poroelasticity to reproduce the apparent viscoelastic behaviour of passive muscle tissue under confined compression.

METHODS

Experimental stress-relaxation response of 31 cylindrical porcine samples tested under fast and slow confined compression by Vaidya and collaborators were used. An axisymmetric Finite Element model was developed in ABAQUS and, for each sample a one-to-one inverse analysis was performed to calibrate the specimen-specific constitutive parameters, namely, the drained Young's modulus, the void ratio, hydraulic permeability, the Poisson's ratio, the solid grain's and fluid's bulk moduli.

FINDINGS

The peak stress and consolidation were recovered for most of the samples (N=25) by the poroelastic model (normalised root-mean-square error ≤0.03 for fast and slow confined compression conditions).

INTERPRETATION

The strength of the proposed model is its fewer number of variables (N=6 for the proposed poroelastic model versus N=18 for the viscohyperelastic model proposed by Vaidya and collaborators). The incorporation of poroelasticity to clinical models of Pessure Ulcer formation could lead to more precise and mechanistic explorations of soft tissue injury risk factors.

Finite element modeling of shape memory polyurethane foams for treatment of cerebral aneurysms

In this paper, a thermo-mechanical analysis of shape memory polyurethane foams (SMPUFs) with aiding of a finite element model (FEM) for treating cerebral aneurysms (CAs) is introduced. Since the deformation of foam cells is extremely difficult to observe experimentally due to their small size, a structural cell-assembly model is established in this work via finite element modeling to examine all-level deformation details. Representative volume elements of random equilateral Kelvin open-cell microstructures are adopted for the cell foam. Also, a user-defined material subroutine (UMAT) is developed based on a thermo-visco-elastic constitutive model for SMPUFs, and implemented in the ABAQUS software package. The model is able to capture thermo-mechanical responses of SMPUFs for a full shape memory thermodynamic cycle. One of the latest treatments of CAs is filling the inside of aneurysms with SMPUFs. The developed FEM is conducted on patient-specific basilar aneurysms treated by SMPUFs. Three sizes of foams are selected for the filling inside of the aneurysm and then governing boundary conditions and loadings are applied to the foams. The results of the distribution of stress and displacement in the absence and presence of the foam are compared. Due to the absence of similar results in the specialized literature, this paper is likely to fill a gap in the state of the art of this problem and provide pertinent results that are instrumental in the design of SMPUFs for treating CAs.

Systematic review of skeletal muscle passive mechanics experimental methodology

Understanding passive skeletal muscle mechanics is critical in defining structure-function relationships in skeletal muscle and ultimately understanding pathologically impaired muscle. In this systematic review, we performed an exhaustive literature search using PRISMA guidelines to quantify passive muscle mechanical properties, summarized the methods used to create these data, and make recommendations to standardize future studies. We screened over 7500 papers and found 80 papers that met the inclusion criteria. These papers reported passive muscle mechanics from single muscle fiber to whole muscle across 16 species and 54 distinct muscles. We found a wide range of methodological differences in sample selection, preparation, testing, and analysis. The systematic review revealed that passive muscle mechanics is species and scale dependent-specifically within mammals, the passive mechanics increases non-linearly with scale. However, a detailed understanding of passive mechanics is still unclear because the varied methodologies impede comparisons across studies, scales, species, and muscles. Therefore, we recommend the following: smaller scales may be maintained within storage solution prior to testing, when samples are tested statically use 2-3 min of relaxation time, stress normalization at the whole muscle level be to physiologic cross-sectional area, strain normalization be to sarcomere length when possible, and an exponential equation be used to fit the data. Additional studies using these recommendations will allow exploration of the multiscale relationship of passive force within and across species to provide the fundamental knowledge needed to improve our understanding of passive muscle mechanics.

Development and validation of a timely and representative finite element human spine model for biomechanical simulations

Numerous spine Finite Element (FE) models have been developed to assess spinal tolerances, spinal loadings and low back pain-related issues. However, justified simplifications, in terms of tissue decomposition and inclusion, for such a complex system may overlook crucial information. Thus, the purpose of this research was to develop and validate a comprehensive and representative spine FE model inclusive of an accurate representation of all major torso elements. A comprehensive model comprised of 273 tissues was developed via a novel FE meshing method to enhance computational feasibility. A comprehensive set of indirect validation tests were carried out to validate every aspect of the model. Under an increasing angular displacement of 24°-41°, the lumbar spine recorded an increasing moment from 5.5 to 9.3 Nm with an increase in IVD pressures from 0.41 to 0.66 MPa. Under forward flexion, vertical vertebral displacements simulated a 6% and 13% maximum discrepancy for intra-abdominal and intramuscular pressure results, all closely resembling previously documented in silico measured values. The developed state-of-the-art model includes most physiological tissues known to contribute to spinal loadings. Given the simulation's accuracy, confirmed by its validation tests, the developed model may serve as a reliable spinal assessment tool.

Investigating Passive Muscle Mechanics With Biaxial Stretch

Introduction

The passive stiffness of skeletal muscle can drastically affect muscle function in vivo, such as the case for fibrotic tissue or patients with cerebral palsy. The two constituents of skeletal muscle that dominate passive stiffness are the intracellular protein titin and the collagenous extracellular matrix (ECM). However, efforts to correlate stiffness and measurements of specific muscle constituents have been mixed, and thus the complete mechanisms for changes to muscle stiffness remain unknown. We hypothesize that biaxial stretch can provide an improved approach to evaluating passive muscle stiffness.

Methods

We performed planar biaxial materials testing of passively stretched skeletal muscle and identified three previously published datasets of uniaxial materials testing. We developed and employed a constitutive model of passive skeletal muscle that includes aligned muscle fibers and dispersed ECM collagen fibers with a bimodal von Mises distribution. Parametric modeling studies and fits to experimental data (both biaxial and previously published) were completed.

Results

Biaxial data exhibited differences in time dependent behavior based on orientation (p < 0.0001), suggesting different mechanisms supporting load in the direction of muscle fibers (longitudinal) and in the perpendicular (transverse) directions. Model parametric studies and fits to experimental data exhibited the robustness of the model (<20% error) and how differences in tissue stiffness may not be observed in uniaxial longitudinal stretch, but are apparent in biaxial stretch.

Conclusion

This work presents novel materials testing data of passively stretched skeletal muscle and use of constitutive modeling and finite element analysis to explore the interaction between stiffness, constituent variability, and applied deformation in passive skeletal muscle. The results highlight the importance of biaxial stretch in evaluating muscle stiffness and in further considering the role of ECM collagen in modulating passive muscle stiffness.

An inverse model of the mechanical response of passive skeletal muscle: Implications for microstructure

The constitutive response of passive skeletal muscle is important for many human body modelling applications, but modelling the tension-compression asymmetry and the anisotropy observed in ex-vivo samples is challenging. Existing microstructural models do not capture the full three-dimensional response while models suitable for application in finite element environments mostly have a limited microstructural basis and cannot capture the observed Poisson's ratios. The aim of this paper is to derive an inverse model based on the microstructure of a skeletal muscle that can predict its passive mechanical response. The model parameters and predictions were derived and assessed by comparison with published experimental stress-strain response and Poisson's ratio data. Results show a close match for both predicted stress-strain response for fibre and cross-fibre direction deformations and similar Poisson's ratio values. Some microstructural observations which strengthen our understanding of the role of the collagen network and intramuscular pressure are also provided.

Internal fluid pressure influences muscle contractile force

Fluid fills intracellular, extracellular, and capillary spaces within muscle. During normal physiological activity, intramuscular fluid pressures develop as muscle exerts a portion of its developed force internally. These pressures, typically ranging between 10 and 250 mmHg, are rarely considered in mechanical models of muscle but have the potential to affect performance by influencing force and work produced during contraction. Here, we test a model of muscle structure in which intramuscular pressure directly influences contractile force. Using a pneumatic cuff, we pressurize muscle midcontraction at 260 mmHg and report the effect on isometric force. Pressurization reduced isometric force at short muscle lengths (e.g., -11.87% of P₀ at 0.9 L₀), increased force at long lengths (e.g., +3.08% of P₀ at 1.25 L₀), but had no effect at intermediate muscle lengths ∼1.1-1.15 L₀ This variable response to pressurization was qualitatively mimicked by simple physical models of muscle morphology that displayed negative, positive, or neutral responses to pressurization depending on the orientation of reinforcing fibers representing extracellular matrix collagen. These findings show that pressurization can have immediate, significant effects on muscle contractile force and suggest that forces transmitted to the extracellular matrix via pressurized fluid may be important, but largely unacknowledged, determinants of muscle performance in vivo.

Passive muscle tension increases in proportion to intramuscular fluid volume

During extended bouts of exercise, muscle can increase in volume by as much as 20% as vascular fluid moves into the tissue. Recent findings suggest that the fluid content of muscle can influence the mechanics of force production; however, the extent to which natural volume fluctuations should be expected to influence muscle mechanics in vivo remains unclear. Here, using osmotic perturbations of bullfrog muscle, we explored the impacts of physiologically relevant volume fluctuations on a fundamental property of muscle: passive force production. We found that passive force and fluid volume were correlated over a 20% increase in muscle volume, with small changes in volume having significant effects on force (e.g. a 5% volume increase results in a >10% passive force increase). A simple physical model of muscle morphology reproduces these effects. These findings suggest that physiologically relevant fluid fluxes could alter passive muscle mechanics in vivo and affect organismal performance.

Modeling Skeletal Muscle Stress and Intramuscular Pressure: A Whole Muscle Active-Passive Approach

Clinical treatments of skeletal muscle weakness are hindered by a lack of an approach to evaluate individual muscle force. Intramuscular pressure (IMP) has shown a correlation to muscle force in vivo, but patient to patient and muscle to muscle variability results in difficulty of utilizing IMP to estimate muscle force. The goal of this work was to develop a finite element model of whole skeletal muscle that can predict IMP under passive and active conditions to further investigate the mechanisms of IMP variability. A previously validated hypervisco-poroelastic constitutive approach was modified to incorporate muscle activation through an inhomogeneous geometry. Model parameters were optimized to fit model stress to experimental data, and the resulting model fluid pressurization data were utilized for validation. Model fitting was excellent (root-mean-square error or RMSE <1.5 kPa for passive and active conditions), and IMP predictive capability was strong for both passive (RMSE 3.5 mmHg) and active (RMSE 10 mmHg at in vivo lengths) conditions. Additionally, model fluid pressure was affected by length under isometric conditions, as increases in stretch yielded decreases in fluid pressurization following a contraction, resulting from counteracting Poisson effects. Model pressure also varied spatially, with the highest gradients located near aponeuroses. These findings may explain variability of in vivo IMP measurements in the clinic, and thus help reduce this variability in future studies. Further development of this model to include isotonic contractions and muscle weakness would greatly benefit this work.

In Silico and In Vivo Studies Detect Functional Repair Mechanisms in a Volumetric Muscle Loss Injury

IMPACT STATEMENT

Despite medical advances, volumetric muscle loss (VML) injuries to craniofacial muscles represent an unmet clinical need. We report an implantable tissue-engineered construct that leads to substantial tissue regeneration and functional recovery in a preclinical model of VML injury that is dimensionally relevant to unilateral cleft lip repair, and a series of corresponding computational models that provide biomechanical insight into mechanism(s) responsible for the VML-induced functional deficits and recovery following tissue-engineered muscle repair implantation. This unique combined approach represents a critical first step toward establishing a crucial biomechanical basis for the development of efficacious regenerative technologies, considering the spectrum of VML injuries.

Intramuscular Pressure of Human Tibialis Anterior Muscle Reflects in vivo Muscular Activity

Intramuscular pressure (IMP) is the fluid hydrostatic pressure generated within a muscle and reflects the mechanical forces produced by a muscle. By providing accurate quantification of interstitial fluid pressure, the measurement of IMP may be useful to detect changes in skeletal muscle function not identified with established techniques. However, the relationship between IMP and muscle activity has never been studied in vivo in healthy human muscles. To determine if IMP is able to evaluate electromechanical performance of muscles in vivo, we tested the following hypotheses on the human tibialis anterior (TA) muscle: (i) IMP increases in proportion to muscle activity as measured by electrical [Compound Muscle Action Potential (CMAP)] and mechanical (ankle torque) responses to activation by nerve stimulation and (ii) the onset delay of IMP (IMPD) is shorter than the ankle torque electromechanical delay (EMD). Twelve healthy adults [six females; mean (SD) = 28.1 (5.0) years old] were recruited. Ankle torque, TA IMP, and CMAP responses were collected during maximal stimulation of the fibular nerve at different intensity levels of electrical stimulation, and at different frequencies of supramaximal stimulation, i.e., at 2, 5, 10, and 20 Hz. The IMP response at different stimulation intensities was correlated with the CMAP amplitude (r² = 0.94). The area of the IMP response at different stimulation intensities was also significantly correlated with the area of the CMAP (r² = 0.93). Increasing stimulation intensity resulted in an increase of the IMP response (P < 0.001). Increasing stimulation frequency caused torque (P < 0.001) as well as the IMP (P < 0.001) to increase. The ankle torque EMD [median (interquartile range) = 41.8 (14.4) ms] was later than the IMPD [33.0 (23.6) ms]. These findings support the hypotheses and suggest that IMP captures active mechanical properties of muscle in vivo and can be used to detect muscular changes due to drugs, diseases, or aging.