Oliver Röhrle

OpenCMISS: A multi-physics & multi-scale computational infrastructure for the VPH/Physiome project

The VPH/Physiome Project is developing the model encoding standards CellML (cellml.org) and FieldML (fieldml.org) as well as web-accessible model repositories based on these standards (models.physiome.org). Freely available open source computational modelling software is also being developed to solve the partial differential equations described by the models and to visualise results. The OpenCMISS code (opencmiss.org), described here, has been developed by the authors over the last six years to replace the CMISS code that has supported a number of organ system Physiome projects. OpenCMISS is designed to encompass multiple sets of physical equations and to link subcellular and tissue-level biophysical processes into organ-level processes. In the Heart Physiome project, for example, the large deformation mechanics of the myocardial wall need to be coupled to both ventricular flow and embedded coronary flow, and the reaction-diffusion equations that govern the propagation of electrical waves through myocardial tissue need to be coupled with equations that describe the ion channel currents that flow through the cardiac cell membranes. In this paper we discuss the design principles and distributed memory architecture behind the OpenCMISS code. We also discuss the design of the interfaces that link the sets of physical equations across common boundaries (such as fluid-structure coupling), or between spatial fields over the same domain (such as coupled electromechanics), and the concepts behind CellML and FieldML that are embodied in the OpenCMISS data structures. We show how all of these provide a flexible infrastructure for combining models developed across the VPH/Physiome community.

A physiologically based, multi-scale model of skeletal muscle structure and function

Models of skeletal muscle can be classified as phenomenological or biophysical. Phenomenological models predict the muscle’s response to a specified input based on experimental measurements. Prominent phenomenological models are the Hill-type muscle models, which have been incorporated into rigid-body modeling frameworks, and three-dimensional continuum-mechanical models. Biophysically based models attempt to predict the muscle’s response as emerging from the underlying physiology of the system. In this contribution, the conventional biophysically based modeling methodology is extended to include several structural and functional characteristics of skeletal muscle. The result is a physiologically based, multi-scale skeletal muscle finite element model that is capable of representing detailed, geometrical descriptions of skeletal muscle fibers and their grouping. Together with a well-established model of motor-unit recruitment, the electro-physiological behavior of single muscle fibers within motor units is computed and linked to a continuum-mechanical constitutive law. The bridging between the cellular level and the organ level has been achieved via a multi-scale constitutive law and homogenization. The effect of homogenization has been investigated by varying the number of embedded skeletal muscle fibers and/or motor units and computing the resulting exerted muscle forces while applying the same excitatory input. All simulations were conducted using an anatomically realistic finite element model of the tibialis anterior muscle. Given the fact that the underlying electro-physiological cellular muscle model is capable of modeling metabolic fatigue effects such as potassium accumulation in the T-tubular space and inorganic phosphate build-up, the proposed framework provides a novel simulation-based way to investigate muscle behavior ranging from motor-unit recruitment to force generation and fatigue.

Bridging Scales: A Three-Dimensional Electromechanical Finite Element Model of Skeletal Muscle

This paper introduces a framework for skeletal muscles that couples outputs from a detailed biophysically based electrophysiological cell model to a three-dimensional continuum-based finite element model of muscle mechanics. Due to the unique manner in which a skeletal muscle is activated, specifically the fact that neighboring fibers are electrically isolated and can act independently of each other, a completely new and novel coupling framework has been created. Within this framework, the electrical activity within a fiber is modeled with a biophysically based cell model, which is itself an amalgamation of several existing cell models. From this amalgamated cell model, specific output parameters that describe the level of crossbridge activity are computed and stored within a lookup table. This lookup table is then used to map the appropriate level of activity to all fibers within the muscle. To link the level of activity to a three-dimensional finite flement model of a skeletal muscle, which is based on principles of continuum mechanics, an upscaling method is introduced to compensate for the fact that the finite element mesh does not attempt to separately represent each individual fiber. This upscaling method allows the stress equilibrium equations to be computed at each Gauss point based on different values of the cell model outputs in all the neighboring cells. Since adjacent fibers can operate independently, the cell model outputs used in the finite element solution of the finite elasticity equations are discontinuous. The behavior and performance of the entire coupling framework is carefully analyzed in some simple test cases analyzing the reduction of the discretization error with respect to a sequence of uniformly refined meshes and different activation patterns. The results show that the error-reduction factors obtained from the electromechanical framework using triquadratic Lagrange and tricubic Hermite basis functions in solving the Galerkin finite element stress equilibrium equations are very similar to those obtained from a mechanics-only continuum-based model. Following this, an example of this process applied to the lateral pterygoid muscle is presented. The proposed framework can be used, for example, to investigate the mechanical effects with respect to cellular changes or to analyze the effects of different neuromuscular activation patterns on the tissue response.

Using a Motion‐Capture System to Record Dynamic Articulation for Application in CAD/CAM Software

PURPOSE One of the current limitations of computer software programs for the virtual articulation of the opposing teeth is the static nature of the intercuspal position. Currently, software programs cannot identify eccentric occlusal contacts during masticatory cyclic movements of the mandible. MATERIALS AND METHODS Chewing trajectories with six degrees of freedom (DOF) were recorded and imposed on a computer model of one subjects maxillary and mandibular teeth. The computer model was generated from a set of high-resolution micro-CT images. To obtain natural chewing trajectories with six DOF, an optoelectronic motion-capturing system (VICON MX) was used. For this purpose, a special mandibular motion-tracking appliance was developed for this subject. RESULTS Mandibular movements while chewing elastic and plastic food samples were recorded and reproduced with the computer model. Examples of mandibular movements at intraoral points are presented for elastic and plastic food samples. The potential of such a kinematic computer model to analyze the dynamic nature of an occlusion was demonstrated by investigating the interaction of the second molars and the direction of the biting force during a chewing cycle. CONCLUSIONS The article described a methodology that measured mandibular movements during mastication for one subject. This produced kinematic input to 3D computer modeling for the production of a virtual dynamic articulation that is suitable for incorporation into dental CAD/CAM software.

Modeling the Chemoelectromechanical Behavior of Skeletal Muscle Using the Parallel Open-Source Software Library OpenCMISS

An extensible, flexible, multiscale, and multiphysics model for nonisometric skeletal muscle behavior is presented. The skeletal muscle chemoelectromechanical model is based on a bottom-up approach modeling the entire excitation-contraction pathway by strongly coupling a detailed biophysical model of a half-sarcomere to the propagation of action potentials along skeletal muscle fibers and linking cellular parameters to a transversely isotropic continuum-mechanical constitutive equation describing the overall mechanical behavior of skeletal muscle tissue. Since the multiscale model exhibits separable time scales, a special emphasis is placed on employing computationally efficient staggered solution schemes. Further, the implementation builds on the open-source software library OpenCMISS and uses state-of-the-art parallelization techniques taking advantage of the unique anatomical fiber architecture of skeletal muscles. OpenCMISS utilizes standardized data structures for geometrical aspects (FieldML) and cellular models (CellML). Both standards are designed to allow for a maximum flexibility, reproducibility, and extensibility. The results demonstrate the models capability of simulating different aspects of nonisometric muscle contraction and efficiently simulating the chemoelectromechanical behavior in complex skeletal muscles such as the tibialis anterior muscle.

Impact of transmural heterogeneities on arterial adaptation

Recent experimental and computational studies have shown that transmurally heterogeneous material properties through the arterial wall are critical to understanding the heterogeneous expressions of constituent degrading molecules. Given that expression of such molecules is thought to be intimately linked to local magnitudes of stress, modelling the transmural stress distribution is critical to understanding arterial adaption during disease. The aim of this study was to develop an arterial growth and remodelling framework that can incorporate both transmurally heterogeneous constituent distributions and residual stresses, into a 3-D finite element model. As an illustrative example, we model the development of a fusiform aneurysm and investigate the effects of elastinous and collagenous heterogeneities on the stress distribution during evolution. It is observed that the adaptive processes of growth and remodelling exhibit transmural variations. For physiological heterogeneous constituent distributions, a stress peak appears in the media towards the intima, and a stress plateau occurs towards the adventitia. These features can be primarily attributed to the underlying heterogeneity of elastinous constituents. During arterial adaption, the collagen strain is regulated to remain in its homoeostatic level; consequently, the partial stress of collagen has less influence on the total stress than the elastin. However, following significant elastin degradation, collagen plays the dominant role for the transmural stress profile and a marked stress peak occurs towards the adventitia. We conclude that to improve our understanding of the arterial adaption and the aetiology of arterial disease, there is a need to: quantify transmural constituent distributions during histopathological examinations, understand and model the role of the evolving transmural stress distribution.

A multiscale chemo-electro-mechanical skeletal muscle model to analyze muscle contraction and force generation for different muscle fiber arrangements

The presented chemo-electro-mechanical skeletal muscle model relies on a continuum-mechanical formulation describing the muscles deformation and force generation on the macroscopic muscle level. Unlike other three-dimensional models, the description of the activation-induced behavior of the mechanical model is entirely based on chemo-electro-mechanical principles on the microscopic sarcomere level. Yet, the multiscale model reproduces key characteristics of skeletal muscles such as experimental force-length and force-velocity data on the macroscopic whole muscle level. The paper presents the methodological approaches required to obtain such a multiscale model, and demonstrates the feasibility of using such a model to analyze differences in the mechanical behavior of parallel-fibered muscles, in which the muscle fibers either span the entire length of the fascicles or terminate intrafascicularly. The presented results reveal that muscles, in which the fibers span the entire length of the fascicles, show lower peak forces, more dispersed twitches and fusion of twitches at lower stimulation frequencies. In detail, the model predicted twitch rise times of 38.2 and 17.2 ms for a 12 cm long muscle, in which the fibers span the entire length of the fascicles and with twelve fiber compartments in series, respectively. Further, the twelve-compartment model predicted peak twitch forces that were 19% higher than in the single-compartment model. The analysis of sarcomere lengths during fixed-end single twitch contractions at optimal length predicts rather small sarcomere length changes. The observed lengths range from 75 to 111% of the optimal sarcomere length, which corresponds to a region with maximum filament overlap. This result suggests that stability issues resulting from activation-induced stretches of non-activated sarcomeres are unlikely in muscles with passive forces appearing at short muscle length.

Multiscale musculoskeletal modelling, data–model fusion and electromyography-informed modelling

This paper proposes methods and technologies that advance the state of the art for modelling the musculoskeletal system across the spatial and temporal scales; and storing these using efficient ontologies and tools. We present population-based modelling as an efficient method to rapidly generate individual morphology from only a few measurements and to learn from the ever-increasing supply of imaging data available. We present multiscale methods for continuum muscle and bone models; and efficient mechanostatistical methods, both continuum and particle-based, to bridge the scales. Finally, we examine both the importance that muscles play in bone remodelling stimuli and the latest muscle force prediction methods that use electromyography-assisted modelling techniques to compute musculoskeletal forces that best reflect the underlying neuromuscular activity. Our proposal is that, in order to have a clinically relevant virtual physiological human, (i) bone and muscle mechanics must be considered together; (ii) models should be trained on population data to permit rapid generation and use underlying principal modes that describe both muscle patterns and morphology; and (iii) these tools need to be available in an open-source repository so that the scientific community may use, personalize and contribute to the database of models.

Reconstruction of muscle fascicle architecture from iodine-enhanced microCT images: A combined texture mapping and streamline approach.

Skeletal muscle models are used to investigate motion and force generation in both biological and bioengineering research. Yet, they often lack a realistic representation of the muscles internal architecture which is primarily composed of muscle fibre bundles, known as fascicles. Recently, it has been shown that fascicles can be resolved with micro-computed tomography (µCT) following staining of the muscle tissue with iodine potassium iodide (I2KI). Here, we present the reconstruction of the fascicular spatial arrangement and geometry of the superficial masseter muscle of a dog based on a combination of pattern recognition and streamline computation. A cadaveric head of a dog was incubated in I2KI and µCT-scanned. Following segmentation of the masseter muscle a statistical pattern recognition algorithm was applied to create a vector field of fascicle directions. Streamlines were then used to transform the vector field into a realistic muscle fascicle representation. The lengths of the reconstructed fascicles and the pennation angles in two planes (frontal and sagittal) were extracted and compared against a tracked fascicle field obtained through cadaver dissection. Both fascicle lengths and angles were found to vary substantially within the muscle confirming the complex and heterogeneous nature of skeletal muscle described by previous studies. While there were significant differences in the pennation angle between the experimentally derived and µCT-reconstructed data, there was congruence in the fascicle lengths. We conclude that the presented approach allows for embedding realistic fascicle information into finite element models of skeletal muscles to better understand the functioning of the musculoskeletal system.

The role of oral soft tissues in swallowing function: what can tongue pressure tell us?

Tongue pressure data taken from healthy subjects during normal oral activities such as mastication, speech and swallowing are providing us with new ways of understanding the role of the tongue in craniofacial growth and function. It has long been recognized that the sequential contact between the tongue and the palate plays a crucial role in the oropharyngeal phase of swallowing. However, because the focus of most research on intraoral pressure has been on the generation of positive pressure by the tongue on the hard palate and teeth, generation and coordination of absolute intraoral pressures and regional pressure gradients has remained unexplored. Ongoing research in our laboratory has uncovered highly variable individual pressure patterns during swallowing, which can nonetheless be divided into four stages: preparatory, primary propulsive, intermediate and terminal. These stages may further be sub-classified according to pressure patterns generated at the individual level as tipper or dipper patterns in the preparatory stage, roller or slapper in the primary propulsive and monophasic or biphasic during the intermediate stage. Interestingly, while an increase in bolus viscosity can result in significant changes to pressure patterns in some individuals, it has little effect in others. Highly individual responses to increased viscosity are also observed with swallowing duration. The above, together with other findings, have important implications for our understanding of the aetiology of widely differing conditions such as protrusive and retrusive malocclusions, dysphagia and sleep apnoea, as well as the development of novel food products.