A computational model for the adaptation of muscle and tendon length to average muscle length and minimum tendon strain

MRI quantitative muscle characterization in children with X-linked hypophosphatemia

INTRODUCTION

Children with X Linked Hypophosphatemia (XLH) suffer from carential ricket, bone deformities and lameness. No previous study demonstrated a morphological distinction in muscles in these patients. The aim of this prospective study was to characterize, using Magnetic Resonance Imaging (MRI), the muscle morphology of pelvis, thigh and leg in children with XLH and to compare it with typically developed (TD) children.

HYPOTHESIS

We hypothesized that lower limbs muscles in children with XLH are different from TD children and could explain limp walking.

MATERIAL AND METHODS

Three-dimensional reconstructions of the muscles were performed in 11 patients with XLH and 15 TD children. Muscle lengths, sections and volumes were calculated and normalized with height and weight. Mean age was 10.

RESULTS

Lengths were all smaller in children with XLH except for the Medius/minimus gluteus muscles (p=0.64). The difference seemed higher in muscles with a long tendinous part as semitendinosus (0.139 vs 0,164; p<0.01). All volumes were significantly inferior in children with XLH. This preliminary study showed significant differences in muscle structures between patients with XLH and TD children.

DISCUSSION

Medius/minimus gluteus seemed to be particularly developed in children with XLH. Nevertheless it is not possible to conclude if it is related to XLH or a consequence of bone deformities.

LEVEL OF PROOF

IV.

Gastrocnemius Medialis Muscle Geometry and Extensibility in Typically Developing Children and Children With Spastic Paresis Aged 6–13 Years

Gait of children with spastic paresis (SP) is frequently characterized by a reduced ankle range of motion, presumably due to reduced extensibility of the triceps surae (TS) muscle. Little is known about how morphological muscle characteristics in SP children are affected. The aim of this study was to compare gastrocnemius medialis (GM) muscle geometry and extensibility in children with SP with those of typically developing (TD) children and assess how GM morphology is related to its extensibility. Thirteen children with SP, of which 10 with a diagnosis of spastic cerebral palsy and three with SP of unknown etiology (mean age 9.7 ± 2.1 years; GMFCS: I–III), and 14 TD children (mean age 9.3 ± 1.7 years) took part in this study. GM geometry was assessed using 3D ultrasound imaging at 0 and 4 Nm externally imposed dorsal flexion ankle moments. GM extensibility was defined as its absolute length change between the externally applied 0 and 4 Nm moments. Anthropometric variables and GM extensibility did not differ between the SP and TD groups. While in both groups, GM muscle volume correlated with body mass, the slope of the regression line in TD was substantially higher than that in SP (TD = 3.3 ml/kg; SP = 1.3 ml/kg, p < 0.01). In TD, GM fascicle length increased with age, lower leg length and body mass, whereas in SP children, fascicle length did not correlate with any of these variables. However, the increase in GM physiological cross-sectional area as a function of body mass did not differ between SP and TD children. Increases in lengths of tendinous structures in children with SP exceeded those observed in TD children (TD = 0.85 cm/cm; SP = 1.16 cm/cm, p < 0.01) and even exceeded lower-leg length increases. In addition, only for children with SP, body mass (r = −0.61), height (r = −0.66), muscle volume (r = − 0.66), physiological cross-sectional area (r = − 0.59), and tendon length (r = −0.68) showed a negative association with GM extensibility. Such negative associations were not found for TD children. In conclusion, physiological cross-sectional area and length of the tendinous structures are positively associated with age and negatively associated with extensibility in children with SP.

Stretching Interventions in Children With Cerebral Palsy: Why Are They Ineffective in Improving Muscle Function and How Can We Better Their Outcome?

Hyper-resistance at the joint is one of the most common symptoms in children with cerebral palsy (CP). Alterations to the structure and mechanical properties of the musculoskeletal system, such as a decreased muscle length and an increased joint stiffness are typically managed conservatively, by means of physiotherapy involving stretching exercises. However, the effectiveness of stretching-based interventions for improving function is poor. This may be due to the behavior of a spastic muscle during stretch, which is poorly understood. The main aim of this paper is to provide a mechanistic explanation as to why the effectiveness of stretching is limited in children with CP and consider clinically relevant means by which this shortcoming can be tackled. To do this, we review the current literature regarding muscle and tendon plasticity in response to stretching in children with CP. First, we discuss how muscle and tendon interact based on their morphology and mechanical properties to provide a certain range of motion at the joint. We then consider the effect of traditional stretching exercises on these muscle and tendon properties. Finally, we examine possible strategies to increase the effectiveness of stretching therapies and we highlight areas of further research that have the potential to improve the outcome of non-invasive interventions in children with cerebral palsy.

A cross-sectional study on the mechanical properties of the Achilles tendon with growth

PURPOSE

This study aimed to elucidate growth pattern of mechanical properties of the Achilles tendon and to examine if imbalance between growth of bone and muscle-tendon unit occurs during adolescence.

METHODS

Fourteen elementary school boys, 30 junior high school boys, 20 high school boys and 15 male adults participated in this study. Based on estimated age at peak height velocity (PHV), junior high school boys were separated into two groups (before or after PHV). An ultrasonography technique was used to determine the length, cross-sectional area, stiffness and Young's modulus of Achilles tendon. In addition, the maximum strain in "toe region" (strain_TP) was determined to describe the balance between growth of bone and muscle-tendon unit.

RESULTS

No group difference was observed in length, cross-sectional area and strain_TP among the groups. However, stiffness and Young's modulus in after PHV groups were significantly higher than those of elementary school boys and before PHV groups (p ≤ 0.05).

CONCLUSIONS

These results indicate that mechanical properties of Achilles tendon change dramatically at and/or around PHV to increased stiffness. The widely believed assumption that muscle-tendon unit is passively stretched due to rapid bone growth in adolescence is not supported.

Computational Modeling of Muscle Regeneration and Adaptation to Advance Muscle Tissue Regeneration Strategies

Skeletal muscle has an exceptional ability to regenerate and adapt following injury. Tissue engineering approaches (e.g. cell therapy, scaffolds, and pharmaceutics) aimed at enhancing or promoting muscle regeneration from severe injuries are a promising and active field of research. Computational models are beginning to advance the field by providing insight into regeneration mechanisms and therapies. In this paper, we summarize the contributions computational models have made to understanding muscle remodeling and the functional implications thereof. Next, we describe a new agent-based computational model of skeletal muscle inflammation and regeneration following acute muscle injury. Our computational model simulates the recruitment and cellular behaviors of key inflammatory cells (e.g. neutrophils and M1 and M2 macrophages) and their interactions with native muscle cells (muscle fibers, satellite stem cells, and fibroblasts) that result in the clearance of necrotic tissue and muscle fiber regeneration. We demonstrate the ability of the model to track key regeneration metrics during both unencumbered regeneration and in the case of impaired macrophage function. We also use the model to simulate regeneration enhancement when muscle is primed with inflammatory cells prior to injury, which is a putative therapeutic intervention that has not yet been investigated experimentally. Computational modeling of muscle regeneration, pursued in combination with experimental analyses, provides a quantitative framework for evaluating and predicting muscle regeneration and enables the rational design of therapeutic strategies for muscle recovery.

Adaptive Remodeling of Achilles Tendon: A Multi-scale Computational Model

While it is known that musculotendon units adapt to their load environments, there is only a limited understanding of tendon adaptation in vivo. Here we develop a computational model of tendon remodeling based on the premise that mechanical damage and tenocyte-mediated tendon damage and repair processes modify the distribution of its collagen fiber lengths. We explain how these processes enable the tendon to geometrically adapt to its load conditions. Based on known biological processes, mechanical and strain-dependent proteolytic fiber damage are incorporated into our tendon model. Using a stochastic model of fiber repair, it is assumed that mechanically damaged fibers are repaired longer, whereas proteolytically damaged fibers are repaired shorter, relative to their pre-damage length. To study adaptation of tendon properties to applied load, our model musculotendon unit is a simplified three-component Hill-type model of the human Achilles-soleus unit. Our model results demonstrate that the geometric equilibrium state of the Achilles tendon can coincide with minimization of the total metabolic cost of muscle activation. The proposed tendon model independently predicts rates of collagen fiber turnover that are in general agreement with in vivo experimental measurements. While the computational model here only represents a first step in a new approach to understanding the complex process of tendon remodeling in vivo, given these findings, it appears likely that the proposed framework may itself provide a useful theoretical foundation for developing valuable qualitative and quantitative insights into tendon physiology and pathology.

Agent-based computational model investigates muscle-specific responses to disuse-induced atrophy

Skeletal muscle is highly responsive to use. In particular, muscle atrophy attributable to decreased activity is a common problem among the elderly and injured/immobile. However, each muscle does not respond the same way. We developed an agent-based model that generates a tissue-level skeletal muscle response to disuse/immobilization. The model incorporates tissue-specific muscle fiber architecture parameters and simulates changes in muscle fiber size as a result of disuse-induced atrophy that are consistent with published experiments. We created simulations of 49 forelimb and hindlimb muscles of the rat by incorporating eight fiber-type and size parameters to explore how these parameters, which vary widely across muscles, influence sensitivity to disuse-induced atrophy. Of the 49 muscles modeled, the soleus exhibited the greatest atrophy after 14 days of simulated immobilization (51% decrease in fiber size), whereas the extensor digitorum communis atrophied the least (32%). Analysis of these simulations revealed that both fiber-type distribution and fiber-size distribution influence the sensitivity to disuse atrophy even though no single tissue architecture parameter correlated with atrophy rate. Additionally, software agents representing fibroblasts were incorporated into the model to investigate cellular interactions during atrophy. Sensitivity analyses revealed that fibroblast agents have the potential to affect disuse-induced atrophy, albeit with a lesser effect than fiber type and size. In particular, muscle atrophy elevated slightly with increased initial fibroblast population and increased production of TNF-α. Overall, the agent-based model provides a novel framework for investigating both tissue adaptations and cellular interactions in skeletal muscle during atrophy.

Critical damping conditions for third order muscle models: implications for force control

Experimental results presented in the literature suggest that humans use a position control strategy to indirectly control force rather than direct force control. Modeling the muscle-tendon system as a third-order linear model, we provide an explanation of why an indirect force control strategy is preferred. We analyzed a third-order muscle system and verified that it is required for a faithful representation of muscle-tendon mechanics, especially when investigating critical damping conditions. We provided numerical examples using biomechanical properties of muscles and tendons reported in the literature. We demonstrated that at maximum isotonic contraction, for muscle and tendon stiffness within physiologically compatible ranges, a third-order muscle-tendon system can be under-damped. Over-damping occurs for values of the damping coefficient included within a finite interval defined by two separate critical limits (such interval is a semi-infinite region in second-order models). An increase in damping beyond the larger critical value would lead the system to mechanical instability. We proved the existence of a theoretical threshold for the ratio between tendon and muscle stiffness above which critical damping can never be achieved; thus resulting in an oscillatory free response of the system, independently of the value of the damping. Under such condition, combined with high muscle activation, oscillation of the system can be compensated only by active control.

Use it or lose it: multiscale skeletal muscle adaptation to mechanical stimuli

Skeletal muscle undergoes continuous turnover to adapt to changes in its mechanical environment. Overload increases muscle mass, whereas underload decreases muscle mass. These changes are correlated with, and enabled by, structural alterations across the molecular, subcellular, cellular, tissue, and organ scales. Despite extensive research on muscle adaptation at the individual scales, the interaction of the underlying mechanisms across the scales remains poorly understood. Here, we present a thorough review and a broad classification of multiscale muscle adaptation in response to a variety of mechanical stimuli. From this classification, we suggest that a mathematical model for skeletal muscle adaptation should include the four major stimuli, overstretch, understretch, overload, and underload, and the five key players in skeletal muscle adaptation, myosin heavy chain isoform, serial sarcomere number, parallel sarcomere number, pennation angle, and extracellular matrix composition. Including this information in multiscale computational models of muscle will shape our understanding of the interacting mechanisms of skeletal muscle adaptation across the scales. Ultimately, this will allow us to rationalize the design of exercise and rehabilitation programs, and improve the long-term success of interventional treatment in musculoskeletal disease.

Haptic recognition of dystonia and spasticity in simulated multi-joint hypertonia

This paper investigates the capability of naïve individuals to recognize dystonic- or spastic- like conditions through physical manipulation of a virtual arm. Subjects physically interact with a two-joint, six-muscle hypertonic arm model, rendered on a two degrees-of-freedom robotic manipulandum. This paradigm aims to identify the limitation of manual manipulation during diagnosis of hypertonia. Our results indicate that there are difficulties to discriminate between the two conditions at low to medium level of severity. We found that the sample entropy of the executed motion and the force experienced during physical manipulation, tended to be higher during incorrectly identified trials than in those correctly assessed.

Therapist recognition of impaired muscle groups in simulated multi-joint hypertonia

It is common in today's clinical practice for a therapist to physically manipulate patients' limbs to assess hypertonic conditions (e.g. spasticity, rigidity, dystonia, among others). We present a study that evaluates the capabilities of expert therapists to correctly identify the location of a hypertonic impairment of an arm through standard manipulation. Therapists interacted with a hypertonic virtual arms rendered on a robotic device. Our results show that testing joints independently can cause misjudgment of the mechanical contributions of pluri-articular muscles to multi-joint impairment.

Haptic perception of multi-joint hypertonia during simulated patient-therapist physical tele-interaction

A potential solution to provide individualized physical therapy in remote areas is tele-interaction via robotic devices. To maintain stability during tele-interaction, transmission delay-compensation algorithms bound the impedance between the patient and the therapist. This can compromise the haptic perception of the patient being assessed, which can in turn lead to a bad diagnosis or intervention. We investigated how the perception of the severity of hypertonia (a common condition after neurological disorders) varied by modifying the connection impedance on a physical simulator. We found that assessing hypetonia using a low impedance connection may result in an overestimation of mild impairments.

Third-Order Muscle Models: The Role of Oscillatory Behavior In Force Control

This paper presents the analysis of a third-order linear differential equation representing a muscle-tendon system, including the identification of critical damping conditions. We analytically verified that this model is required for a faithful representation of muscle-skeletal muscles and provided numerical examples using the biomechanical properties of muscles and tendon reported in the literature. We proved the existence of a theoretical threshold for the ratio between tendon and muscle stiffness above which critical damping can never be achieved, thus resulting in an oscillatory free response of the system, independently of the value of the damping. Oscillation of the limb can be compensated only by active control, which requires creating an internal model of the limb mechanics. We demonstrated that, when admissible, over-damping of the muscle-tendon system occurs for damping values included within a finite interval between two separate critical limits. The same interval is a semi-infinite region in second-order models. Moreover, an increase in damping beyond the second critical point rapidly brings the system to mechanical instability.

Achilles tendon length and medial gastrocnemius architecture in children with cerebral palsy and equinus gait

BACKGROUND

The aim of this study was to examine both the tendon and muscle components of the medial gastrocnemius muscle-tendon unit in children with cerebral palsy (CP) and equinus gait, with or without contracture. We also examined a small number of children who had undergone prior surgical lengthening of the triceps surae to address equinus contracture.

METHODS

Ultrasound was used to measure Achilles tendon length and muscle-tendon architectural parameters in children of ages 5 to 12 years. Muscle and tendon parameters were compared among 4 groups: Control group (N=40 limbs from 21 typically developing children), Static Equinus group (N=23 limbs from 15 children with CP and equinus contracture), Dynamic Equinus group (N=12 limbs from 7 children with CP and equinus gait without contracture), and Prior Surgery group (N=10 limbs from 6 children with CP who had prior gastrocnemius recession or tendo-achilles lengthening). The groups were compared using analysis of variance and Scheffe post hoc tests.

RESULTS

The CP groups had longer Achilles tendons and shorter muscle bellies than the Control group (P<0.001). Normalized tendon length was also longer in the Prior Surgery group compared with the Static Equinus group (P<0.001). The Prior Surgery group had larger pennation angles than the CP groups (P< or =0.009) and tended to have shorter muscle fascicle lengths (P< or =0.005 compared with Control and Static Equinus, P=0.08 compared with Dynamic Equinus). Similar results were observed for pennation angles and normalized muscle fascicle lengths throughout the range of motion.

CONCLUSIONS

Children with spastic CP and equinus gait have longer-than-normal Achilles tendons and shorter-than-normal muscle bellies. These characteristics are observed even in children with dynamic equinus, before contracture has developed. Surgery further lengthens the tendon, restoring dorsiflexion but not normal muscle-tendon architecture. These architectural features likely affect function, possibly contributing to functional deficits such as plantarflexor weakness after surgery.

LEVEL OF EVIDENCE

Level II, prospective comparative study.

Effects of Splinting on Wrist Contracture After Stroke

BACKGROUND AND PURPOSE

Splints are commonly applied to the wrist and hand to prevent and treat contracture after stroke. However, there have been few randomized trials of this intervention. We sought to determine whether wearing a hand splint, which positions the wrist in either a neutral or an extended position, reduces wrist contracture in adults with hemiplegia after stroke.

METHODS

Sixty-three adults who had experienced a stroke within the preceding 8 weeks participated. They were randomized to either a control group (routine therapy) or 1 of 2 intervention groups (routine therapy plus splint in either a neutral or an extended wrist position). Splints were worn overnight for, on average, between 9 and 12 hours, for 4 weeks. The primary outcome, measured by a blinded assessor, was extensibility of the wrist and long finger flexor muscles (angle of wrist extension at a standardized torque).

RESULTS

Neither splint appreciably increased extensibility of the wrist and long finger flexor muscles. After 4 weeks, the effect of neutral wrist splinting was to increase wrist extensibility by a mean of 1.4 degrees (95% CI, -5.4 degrees to 8.2 degrees), and splinting the wrist in extension reduced wrist extensibility by a mean of 1.3 degrees (95% CI, -4.9 degrees to 2.4 degrees) compared with the control condition.

CONCLUSIONS

Splinting the wrist in either the neutral or extended wrist position for 4 weeks did not reduce wrist contracture after stroke. These findings suggest that the practice of routine wrist splinting soon after stroke should be discontinued.

An axisymmetric computational model of skin expansion and growth

Skin expansion is the principal technique used in plastic surgery to repair large cutaneous defects, typically after tumour removal, burn care, craniofacial surgery and post-mastectomy breast reconstruction. It allows a gain of new tissue by means of gradual expansion of a prosthesis, surgically implanted beneath the patient's skin. Nevertheless, wide clinical use is not supported by a deep quantitative knowledge of the phenomena occurring during the expansion. A finite element model of the skin expansion was developed to evaluate the stresses and the strains of the skin due to the expander inflation and validated by proper in vitro experiments; furthermore, a growth model based on the mechanical stimulus was implemented to estimate the skin area gain. The developed computational approach, composed of the skin expansion model interaction and the growth law, proved its validity to investigate skin expansion phenomena: its use suggests a new predictive tool to optimize clinical procedures and the expander devices' design.

Re-recession of the lateral rectus muscles in patients with recurrent exotropia

PURPOSE

We undertook a retrospective evaluation of changes in deviation and ocular motility after surgical rerecession of the lateral rectus (LR) muscles as a treatment for recurrent exotropia (XT).

METHODS

We describe 16 consecutive patients (age 6 to 35 years; median, 10 years; 13 children and 3 adults) with an average amount of recurrent alignment, amount of rerecession, distance from insertion to the limbus, postoperative alignment, and versions.

RESULTS

In most cases, bilateral LR muscles were rerecessed to a distance of 15 mm from the limbus, but in 5 cases with larger amount of deviation, these muscles were rerecessed to 17 mm from the limbus. A relation was found between the amount of rerecession and change in far alignment in prism diopters (r=0.46, P=0.07), but not for near deviation. The success rate (esotropia<or=10 PD or exotropia<or=8 PD) 1 to 7 days after surgery and in long-term follow-up (6-96 months; median, 25.5 months) was 100%. No significant underaction of the LR muscles was noted.

CONCLUSIONS

The results support the notion that bilateral LR rerecession to 17 mm from the limbus successfully corrects recurrent exotropia up to 33 PD and that it is particularly effective in children and adults without producing significant limitation of abduction.

The magnitude of muscle strain does not influence serial sarcomere number adaptations following eccentric exercise

It is generally accepted that eccentric exercise, when performed by a muscle that is unaccustomed to that type of contraction, results in a delayed onset of muscle soreness (DOMS). A prolonged exposure to eccentric exercise leads to the disappearance of the signs and symptoms associated with DOMS, which has been referred to as the repeated bout effect (RBE). Although the mechanisms underlying the RBE remain unclear, several mechanisms have been proposed, including the serial sarcomere number addition following exercise induced muscle damage. In the traditional DOMS and RBE protocols, muscle injury has been treated as a global parameter, with muscle force and strain assumed to be uniform throughout the muscle. To assess the effects of muscle-tendon unit strain, fiber strain, torque and injury on serial sarcomere number adaptations, three groups of New Zealand White (NZW) rabbits were subjected to chronic repetitive eccentric exercise bouts of the ankle dorsiflexors for 6 weeks. These eccentric exercise protocols consisted of identical muscle tendon unit (MTU) strain, but other mechanical factors were systematically altered. Following chronic eccentric exercise, serial sarcomere number adaptations were not identical between the three eccentric exercise protocols, and serial sarcomere number adaptations were not uniform across all regions of the muscle. Peak torque and relaxation fiber strain were the best predictors of serial sarcomere number across all three protocols. Therefore, MTU strain does not appear to be the primary cause for sarcomerogenesis, and differential adaptations within the muscle may be explained by the nonuniform architecture of the muscle, resulting in differential local fiber strains.

Modelling of anisotropic growth in biological tissues. A new approach and computational aspects

In this contribution, we develop a theoretical and computational framework for anisotropic growth phenomena. As a key idea of the proposed phenomenological approach, a fibre or rather structural tensor is introduced, which allows the description of transversely isotropic material behaviour. Based on this additional argument, anisotropic growth is modelled via appropriate evolution equations for the fibre while volumetric remodelling is realised by an evolution of the referential density. Both the strength of the fibre as well as the density follow Wolff-type laws. We however elaborate on two different approaches for the evolution of the fibre direction, namely an alignment with respect to strain or with respect to stress. One of the main benefits of the developed framework is therefore the opportunity to address the evolutions of the fibre strength and the fibre direction separately. It is then straightforward to set up appropriate integration algorithms such that the developed framework fits nicely into common, finite element schemes. Finally, several numerical examples underline the applicability of the proposed formulation.