Bridging the sim2real gap. Investigating deviations between experimental motion measurements and musculoskeletal simulation results-a systematic review.

Musculoskeletal simulations can be used to estimate biomechanical variables like muscle forces and joint torques from non-invasive experimental data using inverse and forward methods. Inverse kinematics followed by inverse dynamics (ID) uses body motion and external force measurements to compute joint movements and the corresponding joint loads, respectively. ID leads to residual forces and torques (residuals) that are not physically realistic, because of measurement noise and modeling assumptions. Forward dynamic simulations (FD) are found by tracking experimental data. They do not generate residuals but will move away from experimental data to achieve this. Therefore, there is a gap between reality (the experimental measurements) and simulations in both approaches, the sim2real gap. To answer (patho-) physiological research questions, simulation results have to be accurate and reliable; the sim2real gap needs to be handled. Therefore, we reviewed methods to handle the sim2real gap in such musculoskeletal simulations. The review identifies, classifies and analyses existing methods that bridge the sim2real gap, including their strengths and limitations. Using a systematic approach, we conducted an electronic search in the databases Scopus, PubMed and Web of Science. We selected and included 85 relevant papers that were sorted into eight different solution clusters based on three aspects: how the sim2real gap is handled, the mathematical method used, and the parameters/variables of the simulations which were adjusted. Each cluster has a distinctive way of handling the sim2real gap with accompanying strengths and limitations. Ultimately, the method choice largely depends on various factors: available model, input parameters/variables, investigated movement and of course the underlying research aim. Researchers should be aware that the sim2real gap remains for both ID and FD approaches. However, we conclude that multimodal approaches tracking kinematic and dynamic measurements may be one possible solution to handle the sim2real gap as methods tracking multimodal measurements (some combination of sensor position/orientation or EMG measurements), consistently lead to better tracking performances. Initial analyses show that motion analysis performance can be enhanced by using multimodal measurements as different sensor technologies can compensate each other's weaknesses.

Kinematic analysis of kinases and their oncogenic mutations - Kinases and their mutation kinematic analysis.

Protein kinases are crucial cellular enzymes that facilitate the transfer of phosphates from adenosine triphosphate (ATP) to their substrates, thereby regulating numerous cellular activities. Dysfunctional kinase activity often leads to oncogenic conditions. Chosen by using structural similarity to 5UG9, we selected 79 crystal structures from the PDB and based on the position of the phenylalanine side chain in the DFG motif, we classified these 79 crystal structures into 5 group clusters. Our approach applies our kinematic flexibility analysis (KFA) to explore the flexibility of kinases in various activity states and examine the impact of the activation loop on kinase structure. KFA enables the rapid decomposition of macromolecules into different flexibility regions, allowing comprehensive analysis of conformational structures. The results reveal that the activation loop of kinases acts as a "lock" that stabilizes the active conformation of kinases by rigidifying the adjacent α-helices. Furthermore, we investigate specific kinase mutations, such as the L858R mutation commonly associated with non-small cell lung cancer, which induces increased flexibility in active-state kinases. In addition, through analyzing the hydrogen bond pattern, we examine the substructure of kinases in different states. Notably, active-state kinases exhibit a higher occurrence of α-helices compared to inactive-state kinases. This study contributes to the understanding of biomolecular conformation at a level relevant to drug development.

Estimating 3D kinematics and kinetics from virtual inertial sensor data through musculoskeletal movement simulations.

Portable measurement systems using inertial sensors enable motion capture outside the lab, facilitating longitudinal and large-scale studies in natural environments. However, estimating 3D kinematics and kinetics from inertial data for a comprehensive biomechanical movement analysis is still challenging. Machine learning models or stepwise approaches performing Kalman filtering, inverse kinematics, and inverse dynamics can lead to inconsistencies between kinematics and kinetics. We investigated the reconstruction of 3D kinematics and kinetics of arbitrary running motions from inertial sensor data using optimal control simulations of full-body musculoskeletal models. To evaluate the feasibility of the proposed method, we used marker tracking simulations created from optical motion capture data as a reference and for computing virtual inertial data such that the desired solution was known exactly. We generated the inertial tracking simulations by formulating optimal control problems that tracked virtual acceleration and angular velocity while minimizing effort without requiring a task constraint or an initial state. To evaluate the proposed approach, we reconstructed three trials each of straight running, curved running, and a v-cut of 10 participants. We compared the estimated inertial signals and biomechanical variables of the marker and inertial tracking simulations. The inertial data was tracked closely, resulting in low mean root mean squared deviations for pelvis translation (≤20.2 mm), angles (≤1.8 deg), ground reaction forces (≤1.1 BW%), joint moments (≤0.1 BWBH%), and muscle forces (≤5.4 BW%) and high mean coefficients of multiple correlation for all biomechanical variables (≥0.99). Accordingly, our results showed that optimal control simulations tracking 3D inertial data could reconstruct the kinematics and kinetics of individual trials of all running motions. The simulations led to mutually and dynamically consistent kinematics and kinetics, which allows researching causal chains, for example, to analyze anterior cruciate ligament injury prevention. Our work proved the feasibility of the approach using virtual inertial data. When using the approach in the future with measured data, the sensor location and alignment on the segment must be estimated, and soft-tissue artifacts are potential error sources. Nevertheless, we demonstrated that optimal control simulation tracking inertial data is highly promising for estimating 3D kinematics and kinetics for a comprehensive biomechanical analysis.

Methods for integrating postural control into biomechanical human simulations: a systematic review.

Understanding of the human body's internal processes to maintain balance is fundamental to simulate postural control behaviour. The body uses multiple sensory systems' information to obtain a reliable estimate about the current body state. This information is used to control the reactive behaviour to maintain balance. To predict a certain motion behaviour with knowledge of the muscle forces, forward dynamic simulations of biomechanical human models can be utilized. We aim to use predictive postural control simulations to give therapy recommendations to patients suffering from postural disorders in the future. It is important to know which types of modelling approaches already exist to apply such predictive forward dynamic simulations. Current literature provides different models that aim to simulate human postural control. We conducted a systematic literature research to identify the different approaches of postural control models. The different approaches are discussed regarding their applied biomechanical models, sensory representation, sensory integration, and control methods in standing and gait simulations. We searched on Scopus, Web of Science and PubMed using a search string, scanned 1253 records, and found 102 studies to be eligible for inclusion. The included studies use different ways for sensory representation and integration, although underlying neural processes still remain unclear. We found that for postural control optimal control methods like linear quadratic regulators and model predictive control methods are used less, when models' level of details is increasing, and nonlinearities become more important. Considering musculoskeletal models, reflex-based and PD controllers are mainly applied and show promising results, as they aim to create human-like motion behaviour considering physiological processes.

SARS-CoV-2 main protease mutation analysis via a kinematic method.

The Severe Acute Respiratory Syndrome CoronaVirus 2 (SARS-CoV-2) is the virus responsible for the COVID-19 pandemic. COVID-19 continues to cause millions of deaths globally in part due to immune-evading mutations. SARS-CoV-2 main protease (Mpro) is an important enzyme for viral replication and potentially an effective drug target. Mutations affect the dynamics of enzymes and thereby their activity and ability to bind ligands. Here, we use kinematic flexibility analysis (KFA) to identify how mutations and ligand binding changes the conformational flexibility of Mpro. KFA decomposes macromolecules into regions of different flexibility near-instantly from a static structure, allowing conformational dynamics analysis at scale. Altogether, we analyzed 47 mutation sites across 69 Mpro-ligand complexes resulting in more than 3300 different structures which includes 69 mutated structures with all 47 sites mutated simultaneously and 3243 single residue mutated structures. We found that mutations generally increased the conformational flexibility of the protein. Understanding the impact of mutations on the flexibility of Mpro is essential for identifying potential drug targets in the treatment of SARS-CoV-2. Further studies in this area can offer valuable insights into the mechanisms of molecular recognition.

Smoothed finite element methods in simulation of active contraction of myocardial tissue samples.

In modelling and simulation of cardiac mechanics, tetrahedral meshes are often used due to the easy availability of efficient meshing algorithms. This is beneficial in particular when complex geometries such as cardiac structures are considered. The gold standard in simulating the cardiac cycle is to solve the mechanical balance equations with the finite element method (FEM). However, using linear shape functions in the FEM in combination with nearly-incompressible material models is known to produce overly stiff approximations, whereas higher order elements are computationally more expensive. To overcome these problems, smoothed finite element methods (S-FEMs) have been proposed by Liu and co-workers. So far, S-FEMs in 3D have been utilised only in simulations of passive mechanics. In the present work, different S-FEMs are for the first time used for simulation of an active cardiac contraction on three-dimensional myocardial tissue samples. Further, node-based S-FEM (NS-FEM), face-based S-FEM (FS-FEM) and selective FS/NS-FEM are for the first time implemented as user subroutine in the commercial software Abaqus. Our results confirm that all S-FEMs perform softer than linear FEM and volumetric locking is reduced. The FS/NS-FEM produces solutions with the relative error in maximum displacement and rotation being less than 5% with respect to the reference solution obtained by the quadratic FEM for all considered mesh sizes, although linear shape functions are used. We therefore conclude that in particular FS/NS-FEM is an efficient and accurate numerical method in the simulation of an active cardiac muscle contraction.

Transmural fibre orientations based on Laplace-Dirichlet-Rule-Based-Methods and their influence on human heart simulations.

It is well known that the orthotropic tissue structure decisively influences the mechanical and electrical properties of the heart. Numerous approaches to compute the orthotropic tissue structure in computational heart models have been developed in the past decades. In this study, we investigate to what extent different Laplace-Dirichlet-Rule-Based-Methods (LDRBMs) influence the local orthotropic tissue structure and thus the electromechanical behaviour of the subsequent cardiac simulation. In detail, we are utilising three Laplace-Dirichlet-Rule-Based-Methods and compare: (i) the local myofibre orientation; (ii) important global characteristics (ejection fraction, peak pressure, apex shortening, myocardial volume reduction, fractional wall thickening); (iii) local characteristics (active fibre stress, fibre strain). We observe that the orthotropic tissue structures for the three LDRBMs show significant differences in the local myofibre orientation. The global characteristics myocardial volume reduction and peak pressure are rather insensitive to a change in local myofibre orientation, while the ejection fraction is moderately influenced by the different LDRBMs. Moreover, the apical shortening and fractional wall thickening exhibit a sensitive behaviour to a change in the local myofibre orientation. The highest sensitivity can be observed for the local characteristics.

Optimal Control of Dielectric Elastomer Actuated Multibody Dynamical Systems.

In this work, a simulation model for the optimal control of dielectric elastomer actuated flexible multibody dynamics systems is presented. The dielectric elastomer actuator (DEA) behaves like a flexible artificial muscle in soft robotics. It is modeled as an electromechanically coupled geometrically exact beam, where the electric charges serve as control variables. The DEA-beam is integrated as an actuator into multibody systems consisting of rigid and flexible components. The model also represents contact interaction via unilateral constraints between the beam actuator and, for example, a rigid body during the grasping process of a soft robot. With a mathematically concise and physically representative formulation, a reduced free energy function is developed for the electromechanically coupled beam. In the optimal control problem, an objective function is minimized while the electromechanically coupled dynamic balance equations for the multibody system have to be fulfilled together with the complementarity conditions for the contact and boundary conditions. The optimal control problem is solved via a direct transcription method, transforming it into a constrained nonlinear optimization problem. The electromechanically coupled geometrically exact beam is firstly semidiscretized with one-dimensional finite elements and then the multibody dynamics is temporally discretized with a variational integrator leading to the discrete Euler-Lagrange equations, which are further reduced with the null space projection. The discrete Euler-Lagrange equations and the boundary conditions serve as equality constraints, whereas the contact constraints are treated as inequality constraints in the optimization of the discretized objective. The constrained optimization problem is solved using the Interior Point Optimizer solver. The effectiveness of the developed model is demonstrated by three numerical examples, including a cantilever beam, a soft robotic worm, and a soft robotic grasper.

Effects of PTH glandular and external dosing patterns on bone cell activity using a two-state receptor model-Implications for bone disease progression and treatment.

Temporal aspects of ligand specificity have been shown to play a significant role in the case of pulsatile hormone secretion, as exemplified by parathyroid hormone (PTH) binding to its receptor (PTH1R), a G-protein-coupled receptor expressed on surfaces of osteoblasts and osteocytes. The latter binding reaction regulates intracellular signalling and subsequently modulates skeletal homeostasis via bone remodelling. PTH glandular secretion patterns dictate bone cellular activity. In healthy humans, 70% of PTH is secreted in a tonic fashion, whereas 30% is secreted in low-amplitude and high-frequency bursts occurring every 10-20 min, superimposed on the tonic secretion. Changes in the PTH secretion patterns have been associated with various bone diseases. In this paper, we analyse PTH glandular secretion patterns for healthy and pathological states and their link to bone cellular responsiveness (αR). We utilise a two-state receptor ligand binding model of PTH to PTH1R together with a cellular activity function which is able to distinguish various aspects of the stimulation signal including peak dose, time of ligand exposure, and exposure period. Formulating and solving several constrained optimisation problems, we investigate the potential of pharmacological manipulation of the diseased glandular secretion and via clinical approved external PTH injections to restore healthy bone cellular responsiveness. Based on the mean experimentally reported data, our simulation results indicate cellular responsiveness in healthy subjects is sensitive to the tonic baseline stimulus and it is 28% of the computed maximum responsiveness. Simulation results for pathological cases of glucocorticoid-induced osteoporosis, hyperparathyroidism, initial and steady state hypocalcemia clamp tests indicate αR values significantly larger than the healthy baseline (1.7, 2.2, 4.9 and 1.9-times, respectively). Manipulation of the pulsatile glandular secretion pattern, while keeping the mean PTH concentration constant, allowed restoration of healthy baseline values from these catabolic bone diseases. Conversely, PTH glandular diseases that led to maximum bone cellular responsiveness below the healthy baseline value can't be restored to baseline via glandular manipulation. However, external PTH injections allowed restoration of these latter cases.

Change the direction: 3D optimal control simulation by directly tracking marker and ground reaction force data.

Optimal control simulations of musculoskeletal models can be used to reconstruct motions measured with optical motion capture to estimate joint and muscle kinematics and kinetics. These simulations are mutually and dynamically consistent, in contrast to traditional inverse methods. Commonly, optimal control simulations are generated by tracking generalized coordinates in combination with ground reaction forces. The generalized coordinates are estimated from marker positions using, for example, inverse kinematics. Hence, inaccuracies in the estimated coordinates are tracked in the simulation. We developed an approach to reconstruct arbitrary motions, such as change of direction motions, using optimal control simulations of 3D full-body musculoskeletal models by directly tracking marker and ground reaction force data. For evaluation, we recorded three trials each of straight running, curved running, and a v-cut for 10 participants. We reconstructed the recordings with marker tracking simulations, coordinate tracking simulations, and inverse kinematics and dynamics. First, we analyzed the convergence of the simulations and found that the wall time increased three to four times when using marker tracking compared to coordinate tracking. Then, we compared the marker trajectories, ground reaction forces, pelvis translations, joint angles, and joint moments between the three reconstruction methods. Root mean squared deviations between measured and estimated marker positions were smallest for inverse kinematics (e.g., 7.6 ± 5.1 mm for v-cut). However, measurement noise and soft tissue artifacts are likely also tracked in inverse kinematics, meaning that this approach does not reflect a gold standard. Marker tracking simulations resulted in slightly higher root mean squared marker deviations (e.g., 9.5 ± 6.2 mm for v-cut) than inverse kinematics. In contrast, coordinate tracking resulted in deviations that were nearly twice as high (e.g., 16.8 ± 10.5 mm for v-cut). Joint angles from coordinate tracking followed the estimated joint angles from inverse kinematics more closely than marker tracking (e.g., root mean squared deviation of 1.4 ± 1.8 deg vs. 3.5 ± 4.0 deg for v-cut). However, we did not have a gold standard measurement of the joint angles, so it is unknown if this larger deviation means the solution is less accurate. In conclusion, we showed that optimal control simulations of change of direction running motions can be created by tracking marker and ground reaction force data. Marker tracking considerably improved marker accuracy compared to coordinate tracking. Therefore, we recommend reconstructing movements by directly tracking marker data in the optimal control simulation when precise marker tracking is required.

Support Pressure Acting on the Epicardial Surface of a Rat Left Ventricle-A Computational Study.

The present computational study investigates the effects of an epicardial support pressure mimicking a heart support system without direct blood contact. We chose restrictive cardiomyopathy as a model for a diseased heart. By changing one parameter representing the amount of fibrosis, this model allows us to investigate the impairment in a diseased left ventricle, both during diastole and systole. The aim of the study is to determine the temporal course and value of the support pressure that leads to a normalization of the cardiac parameters in diseased hearts. These are quantified via the end-diastolic pressure, end-diastolic volume, end-systolic volume, and ejection fraction. First, the amount of fibrosis is increased to model diseased hearts at different stages. Second, we determine the difference in the left ventricular pressure between a healthy and diseased heart during a cardiac cycle and apply for the epicardial support as the respective pressure difference. Third, an epicardial support pressure is applied in form of a piecewise constant step function. The support is provided only during diastole, only during systole, or during both phases. Finally, the support pressure is adjusted to reach the corresponding parameters in a healthy rat. Parameter normalization is not possible to achieve with solely diastolic or solely systolic support; for the modeled case with 50% fibrosis, the ejection fraction can be increased by 5% with purely diastolic support and 14% with purely systolic support. However, the ejection fraction reaches the value of the modeled healthy left ventricle (65.6%) using a combination of diastolic and systolic support. The end-diastolic pressure of 13.5 mmHg cannot be decreased with purely systolic support. However, the end-diastolic pressure reaches the value of the modeled healthy left ventricle (7.5 mmHg) with diastolic support as well as with the combination of the diastolic and systolic support. The resulting negative diastolic support pressure is -4.5 mmHg, and the positive systolic support pressure is 90 mmHg. We, thereby, conclude that ventricular support during both diastole and systole is beneficial for normalizing the left ventricular ejection fraction and the end-diastolic pressure, and thus it is a potentially interesting therapy for cardiac insufficiency.

Kinematic Vibrational Entropy Assessment and Analysis of SARS CoV-2 Main Protease.

The three-dimensional conformations of a protein influence its function and select for the ligands it can interact with. The total free energy change during protein-ligand complex formation includes enthalphic and entropic components, which together report on the binding affinity and conformational states of the complex. However, determining the entropic contribution is computationally burdensome. Here, we apply kinematic flexibility analysis (KFA) to efficiently estimate vibrational frequencies from static protein and protein-ligand structures. The vibrational frequencies, in turn, determine the vibrational entropies of the structures and their complexes. Our estimates of the vibrational entropy change caused by ligand binding compare favorably to values obtained from a dynamic Normal Mode Analysis (NMA). Higher correlation factors can be achieved by increasing the distance cutoff in the potential energy model. Furthermore, we apply our new method to analyze the entropy changes of the SARS CoV-2 main protease when binding with different ligand inhibitors, which is relevant for the design of potential drugs.

Comparison of stress and stress-strain approaches for the active contraction in a rat cardiac cycle model.

In the last decades, different strategies to model the active electromechanically coupled behaviour of the cardiac tissue were proposed in order to simulate electromechanics of the heart under healthy and pathological conditions. The main objective of this work is to compare two approaches for modelling the active contraction during the electromechanically coupled rat cardiac cycle -- the stress and the stress-strain approach. Firstly, a cylindrical benchmark is considered and secondly, for a generic model of a rat left ventricle, a simulation including the Windkessel model, excitation via Purkinje fibre network and mechano-electrical feedback is performed. The model is calibrated with experimental data for rats, partly from own measurements via cardiac ultrasound, partly from the literature. Further, possibilities to reach higher ejection fractions are discussed and considered for an exemplary rat left ventricle. Within each approach, we observe regionally different active stresses and fibre stretches. Moreover, the transmural active stress and fibre stretch distribution is influenced by the pressure load on the endocardial surface. The active stress approach is not sensitive to the fibre stretch and transmurally varying fibre stretch in the left ventricular domain is observed. The active stress-strain approach leads to transmurally more homogeneous fibre stretch at the end-systolic state.

A Transmural Path Model Improves the Definition of the Orthotropic Tissue Structure in Heart Simulations.

In the past decades, the structure of the heart, human as well as other species, has been explored in a detailed way, e.g., via histological studies or diffusion tensor magnetic resonance imaging. Nevertheless, the assignment of the characteristic orthotropic structure in a patient-specific finite element model remains a challenging task. Various types of rule-based models, which define the local fiber and sheet orientation depending on the transmural depth, have been developed. However, the correct assessment of the transmural depth is not trivial. Its accuracy has a substantial influence on the overall mechanical and electrical properties in rule-based models. The main purpose of this study is the development of a finite element-based approach to accurately determine the transmural depth on a general unstructured grid. Instead of directly using the solution of the Laplace problem as the transmural depth, we make use of a well-established model for the assessment of the transmural thickness. It is based on two hyperbolic first-order partial differential equations for the definition of a transmural path, whereby the transmural thickness is defined as the arc length of this path. Subsequently, the transmural depth is determined based on the position on the transmural path. Originally, the partial differential equations were solved via finite differences on structured grids. In order to circumvent the need of two grids and mapping between the structured (to determine the transmural depth) and unstructured (electromechanical heart simulation) grids, we solve the equations directly on the same unstructured tetrahedral mesh. We propose a finite-element-based discontinuous Galerkin approach. Based on the accurate transmural depth, we assign the local material orientation of the orthotropic tissue structure in a usual fashion. We show that this approach leads to a more accurate definition of the transmural depth. Furthermore, for the left ventricle, we propose functions for the transmural fiber and sheet orientation by fitting them to literature-based diffusion tensor magnetic resonance imaging data. The proposed functions provide a distinct improvement compared to existing rules from the literature.

Passive mechanical properties in healthy and infarcted rat left ventricle characterised via a mixture model.

During the cardiac cycle, electrical excitation is coupled with mechanical response of the myocardium. Besides the active contraction, passive mechanics plays an important role, and its behaviour differs in healthy and diseased hearts as well as among different animal species. The aim of this study is the characterisation of passive mechanical properties in healthy and infarcted rat myocardium by means of mechanical testing and subsequent parameter fitting. Elasticity assessments via uniaxial extension tests are performed on healthy and infarcted tissue samples from left ventricular rat myocardium. In order to fully characterise the orthotropic cardiac tissue, our experimental data are combined with other previously published tests in rats - shear tests on healthy myocardium and equibiaxial tests on infarcted tissue. In a first step, we calibrate the Holzapfel-Ogden strain energy function in the healthy case. Sa far, this orthotropic constitutive law for the passive myocardium has been fitted to experimental data in several species, however there is a lack of an appropriate parameter set for the rat. With our determined parameters, a finite element simulation of the end-diastolic filling is performed. In a second step, we propose a model for the infarcted tissue. It is represented as a mixture of intact myocardium and a transversely isotropic scar structure. In our mechanical experiments, the tissue after myocardial infarction shows significantly stiffer behaviour than in the healthy case, and the stiffness correlates with the amount of fibrosis. A similar relationship is observed in the computational simulation of the end-diastolic filling. We conclude that our new proposed material model can capture the behaviour of two kinds of tissues - healthy and infarcted rat myocardium, and its calibration with the fitted parameters represents the experimental data well.

Evaluation of Optical and Radar Based Motion Capturing Technologies for Characterizing Hand Movement in Rheumatoid Arthritis-A Pilot Study.

In light of the state-of-the-art treatment options for patients with rheumatoid arthritis (RA), a detailed and early quantification and detection of impaired hand function is desirable to allow personalized treatment regiments and amend currently used subjective patient reported outcome measures. This is the motivation to apply and adapt modern measurement technologies to quantify, assess and analyze human hand movement using a marker-based optoelectronic measurement system (OMS), which has been widely used to measure human motion. We complement these recordings with data from markerless (Doppler radar) sensors and data from both sensor technologies are integrated with clinical outcomes of hand function. The technologies are leveraged to identify hand movement characteristics in RA affected patients in comparison to healthy control subjects, while performing functional tests, such as the Moberg-Picking-Up Test. The results presented discuss the experimental framework and present the limiting factors imposed by the use of marker-based measurements on hand function. The comparison of simple finger motion data, collected by the OMS, to data recorded by a simple continuous wave radar suggests that radar is a promising option for the objective assessment of hand function. Overall, the broad scope of integrating two measurement technologies with traditional clinical tests shows promising potential for developing new pathways in understanding of the role of functional outcomes for the RA pathology.

Towards the simulation of active cardiac mechanics using a smoothed finite element method.

In the last decades, various computational models have been developed to simulate cardiac electromechanics. The most common numerical tool is the finite element method (FEM). However, this method crucially depends on the mesh quality. For complex geometries such as cardiac structures, it is convenient to use tetrahedral discretisations which can be generated automatically. On the other hand, such automatic meshing with tetrahedrons together with large deformations often lead to elements distortion and volumetric locking. To overcome these difficulties, different smoothed finite element methods (S-FEMs) have been proposed in the recent years. They are known to be volumetric locking free, less sensitive to mesh distortion and so far have been used e.g. in simulation of passive cardiac mechanics. In this work, we extend for the first time node-based S-FEM (NS-FEM) towards active cardiac mechanics. Firstly, the sensitivity to mesh distortion is tested and compared to that of FEM. Secondly, an active contraction in circumferentially aligned fibre direction is modelled in the healthy and the infarcted case. We show, that the proposed method is more robust with respect to mesh distortion and computationally more efficient than standard FEM. Being furthermore free of volumetric locking problems makes S-FEM a promising alternative in modelling of active cardiac mechanics, respectively electromechanics.

Interaction of the Mechano-Electrical Feedback With Passive Mechanical Models on a 3D Rat Left Ventricle: A Computational Study.

In this paper, we are investigating the interaction between different passive material models and the mechano-electrical feedback (MEF) in cardiac modeling. Various types of passive mechanical laws (nearly incompressible/compressible, polynomial/exponential-type, transversally isotropic/orthotropic material models) are integrated in a fully coupled electromechanical model in order to study their specific influence on the overall MEF behavior. Our computational model is based on a three-dimensional (3D) geometry of a healthy rat left ventricle reconstructed from magnetic resonance imaging (MRI). The electromechanically coupled problem is solved using a fully implicit finite element-based approach. The effects of different passive material models on the MEF are studied with the help of numerical examples. It turns out that there is a significant difference between the behavior of the MEF for compressible and incompressible material models. Numerical results for the incompressible models exhibit that a change in the electrophysiology can be observed such that the transmembrane potential (TP) is unable to reach the resting state in the repolarization phase, and this leads to non-zero relaxation deformations. The most significant and strongest effects of the MEF on the rat cardiac muscle response are observed for the exponential passive material law.

Kinematic Flexibility Analysis: Hydrogen Bonding Patterns Impart a Spatial Hierarchy of Protein Motion.

Elastic network models (ENMs) and constraint-based, topological rigidity analysis are two distinct, coarse-grained approaches to study conformational flexibility of macromolecules. In the two decades since their introduction, both have contributed significantly to insights into protein molecular mechanisms and function. However, despite a shared purpose of these approaches, the topological nature of rigidity analysis, and thereby the absence of motion modes, has impeded a direct comparison. Here, we present an alternative, kinematic approach to rigidity analysis, which circumvents these drawbacks. We introduce a novel protein hydrogen bond network spectral decomposition, which provides an orthonormal basis for collective motions modulated by noncovalent interactions, analogous to the eigenspectrum of normal modes. The zero modes decompose proteins into rigid clusters identical to those from topological rigidity, while nonzero modes rank protein motions by their hydrogen bond collective energy penalty. Our kinematic flexibility analysis bridges topological rigidity theory and ENM, enabling a detailed analysis of motion modes obtained from both approaches. Analysis of a large, structurally diverse data set revealed that collectivity of protein motions, reported by the Shannon entropy, is significantly reduced for rigidity theory compared to normal mode approaches. Strikingly, kinematic flexibility analysis suggests that the hydrogen bonding network encodes a protein-fold specific, spatial hierarchy of motions, which goes nearly undetected in ENM. This hierarchy reveals distinct motion regimes that rationalize experimental and simulated protein stiffness variations. Kinematic motion modes highly correlate with reported crystallographic B factors and molecular dynamics simulations of adenylate kinase. A formal expression for changes in free energy derived from the spectral decomposition indicates that motions across nearly 40% of modes obey enthalpy-entropy compensation. Taken together, our results suggest that hydrogen bond networks have evolved to modulate protein structure and dynamics, which can be efficiently probed by kinematic flexibility analysis.

Frustration-guided motion planning reveals conformational transitions in proteins.

Proteins exist as conformational ensembles, exchanging between substates to perform their function. Advances in experimental techniques yield unprecedented access to structural snapshots of their conformational landscape. However, computationally modeling how proteins use collective motions to transition between substates is challenging owing to a rugged landscape and large energy barriers. Here, we present a new, robotics-inspired motion planning procedure called dCC-RRT that navigates the rugged landscape between substates by introducing dynamic, interatomic constraints to modulate frustration. The constraints balance non-native contacts and flexibility, and instantaneously redirect the motion towards sterically favorable conformations. On a test set of eight proteins determined in two conformations separated by, on average, 7.5 Å root mean square deviation (RMSD), our pathways reduced the Cα atom RMSD to the goal conformation by 78%, outperforming peer methods. We then applied dCC-RRT to examine how collective, small-scale motions of four side-chains in the active site of cyclophilin A propagate through the protein. dCC-RRT uncovered a spatially contiguous network of residues linked by steric interactions and collective motion connecting the active site to a recently proposed, non-canonical capsid binding site 25 Å away, rationalizing NMR and multi-temperature crystallography experiments. In all, dCC-RRT can reveal detailed, all-atom molecular mechanisms for small and large amplitude motions. Source code and binaries are freely available at https://github.com/ExcitedStates/KGS/.