Predicting Patient Status in Chronic Thromboembolic Pulmonary Hypertension Using a Biophysical Model.

Chronic thromboembolic pulmonary hypertension (CTEPH) involves abnormally high blood pressure in the pulmonary vessels and is associated with small vessel vasculopathy and pre-capillary proximal occlusions. Management of CTEPH disease is challenging, therefore accurate diagnosis is crucial in ensuring effective treatment and improved patient outcomes. The treatment of choice for CTEPH is pulmonary endarterectomy, which is an invasive surgical intervention to remove thrombi. Following PEA, a number of patients experience poor outcomes or worse-than-expected improvements, which may indicate that they have significant small vessel disease. A method that can predict the extent of distal remodelling may provide useful clinical information to plan appropriate CTEPH patient treatment. Here, a novel biophysical modelling approach has been developed to estimate and quantify the extent of distal remodelling. This method includes a combination of mathematical modelling and computed tomography pulmonary angiography to first model the geometry of the pulmonary arteries and to identify the under-perfused regions in CTEPH. The geometric model is then used alongside haemodynamic measurements from right heart catheterisation to predict distal remodelling. In this study, the method is tested and validated using synthetically generated remodelling data. Then, a preliminary application of this technique to patient data is shown to demonstrate the potential of the approach for use in the clinical setting.Clinical relevance- Patient-specific modelling can help provide useful information regarding the extent of distal vasculopathy on a per-patient basis, which remains challenging. Physicians can be unsure of outcomes following pulmonary endarterectomy. Therefore, the predictive aspect of the patient's response to surgery can help with clinical decision-making.

Probabilistic description of infant head kinematics in abusive head trauma.

Abusive head trauma (AHT) is a potentially fatal result of child abuse, but the mechanisms by which injury occur are often unclear. To investigate the contention that shaking alone can elicit the injuries observed, effective computational models are necessary. The aim of this study was to develop a probabilistic model describing infant head kinematics in AHT. A deterministic model incorporating an infant's mechanical properties, subjected to different shaking motions, was developed in OpenSim. A Monte Carlo analysis was used to simulate the range of infant kinematics produced as a result of varying both the mechanical properties and the type of shaking motions. By excluding physically unrealistic shaking motions, worst-case shaking scenarios were simulated and compared to existing injury criteria for a newborn, a 4.5 month-old, and a 12 month-old infant. In none of the three cases were head kinematics observed to exceed previously-estimated subdural haemorrhage injury thresholds. The results of this study provide no biomechanical evidence to demonstrate how shaking by a human alone can cause the injuries observed in AHT, suggesting either that additional factors, such as impact, are required, or that the current estimates of injury thresholds are incorrect.

Multidirectional In Vivo Characterization of Skin Using Wiener Nonlinear Stochastic System Identification Techniques.

A triaxial force-sensitive microrobot was developed to dynamically perturb skin in multiple deformation modes, in vivo. Wiener static nonlinear identification was used to extract the linear dynamics and static nonlinearity of the force-displacement behavior of skin. Stochastic input forces were applied to the volar forearm and thenar eminence of the hand, producing probe tip perturbations in indentation and tangential extension. Wiener static nonlinear approaches reproduced the resulting displacements with variances accounted for (VAF) ranging 94-97%, indicating a good fit to the data. These approaches provided VAF improvements of 0.1-3.4% over linear models. Thenar eminence stiffness measures were approximately twice those measured on the forearm. Damping was shown to be significantly higher on the palm, whereas the perturbed mass typically was lower. Coefficients of variation (CVs) for nonlinear parameters were assessed within and across individuals. Individual CVs ranged from 2% to 11% for indentation and from 2% to 19% for extension. Stochastic perturbations with incrementally increasing mean amplitudes were applied to the same test areas. Differences between full-scale and incremental reduced-scale perturbations were investigated. Different incremental preloading schemes were investigated. However, no significant difference in parameters was found between different incremental preloading schemes. Incremental schemes provided depth-dependent estimates of stiffness and damping, ranging from 300 N/m and 2 Ns/m, respectively, at the surface to 5 kN/m and 50 Ns/m at greater depths. The device and techniques used in this research have potential applications in areas, such as evaluating skincare products, assessing skin hydration, or analyzing wound healing.

Image-Based Predictive Modeling of Heart Mechanics.

Personalized biophysical modeling of the heart is a useful approach for noninvasively analyzing and predicting in vivo cardiac mechanics. Three main developments support this style of analysis: state-of-the-art cardiac imaging technologies, modern computational infrastructure, and advanced mathematical modeling techniques. In vivo measurements of cardiac structure and function can be integrated using sophisticated computational methods to investigate mechanisms of myocardial function and dysfunction, and can aid in clinical diagnosis and developing personalized treatment. In this article, we review the state-of-the-art in cardiac imaging modalities, model-based interpretation of 3D images of cardiac structure and function, and recent advances in modeling that allow personalized predictions of heart mechanics. We discuss how using such image-based modeling frameworks can increase the understanding of the fundamental biophysics behind cardiac mechanics, and assist with diagnosis, surgical guidance, and treatment planning. Addressing the challenges in this field will require a coordinated effort from both the clinical-imaging and modeling communities. We also discuss future directions that can be taken to bridge the gap between basic science and clinical translation.

Head kinematics during shaking associated with abusive head trauma.

Abusive head trauma (AHT) is a potentially fatal result of child abuse but the mechanisms of injury are controversial. To address the hypothesis that shaking alone is sufficient to elicit the injuries observed, effective computational and experimental models are necessary. This paper investigates the use of a coupled rigid-body computational modelling framework to reproduce in vivo shaking kinematics in AHT. A sagittal plane OpenSim computational model of a lamb was developed and used to interpret biomechanical data from in vivo shaking experiments. The acceleration of the head during shaking was used to provide in vivo validation of the associated computational model. Results of this study demonstrated that peak accelerations occurred when the head impacted the torso and produced acceleration magnitudes exceeding 200ms(-)(2). The computational model demonstrated good agreement with the experimental measurements and was shown to be able to reproduce the high accelerations that occur during impact. The biomechanical results obtained with the computational model demonstrate the utility of using a coupled rigid-body modelling framework to describe infant head kinematics in AHT.

Comparison of the Gibbs and Suga formulations of cardiac energetics: the demise of "isoefficiency".

Two very different sorts of experiments have characterized the field of cardiac energetics over the past three decades. In one of these, Gibbs and colleagues measured the heat production of isolated papillary muscles undergoing isometric contractions and afterloaded isotonic contractions. The former generated roughly linear heat vs. force relationships. The latter generated enthalpy-load relationships, the peak values of which occurred at or near peak isometric force, i.e., at a relative load of unity. Contractile efficiency showed a pronounced dependence on afterload. By contrast, Suga and coworkers measured the oxygen consumption (Vo(2)) while recording the pressure-volume-time work loops of blood-perfused isolated dog hearts. From the associated (linear) end-systolic pressure-volume relations they derived a quantity labeled pressure-volume area (PVA), consisting of the sum of pressure-volume work and unspent elastic energy and showed that this was linearly correlated with Vo(2) over a wide range of conditions. This linear dependence imposed isoefficiency: constant contractile efficiency independent of afterload. Neither these data nor those of Gibbs and colleagues are in dispute. Nevertheless, despite numerous attempts over the years, no demonstration of either compatibility or incompatibility of these disparate characterizations of cardiac energetics has been forthcoming. We demonstrate that compatibility between the two formulations is thwarted by the concept of isoefficiency, the thermodynamic basis of which we show to be untenable.

Relating components of pressure-volume area in Suga's formulation of cardiac energetics to components of the stress-time integral.

The concept of pressure-volume area (PVA) in whole heart studies is central to the phenomenological description of cardiac energetics proposed by Suga and colleagues (Physiol Rev 70: 247-277, 1990). PVA consists of two components: an approximately rectangular work loop (W) and an approximately triangular region of potential energy (U). In the case of isovolumic contractions, PVA consists entirely of U. The utility of Suga's description of cardiac energetics is the observation that the oxygen consumption of the heart (Vo(2)) is linearly dependent on PVA. By using isolated ventricular trabeculae, we found a basis on which to correlate the components of stress-length area (SLA; i.e., the 1-D equivalent of PVA) with specific regions of the stress-time integral (STI; i.e., the area under the force-time profile of a single twitch). In each case, proportionality obtains and is robust, independent of the type of twitch contraction (isometric or isotonic), and insensitive to changes of preload or afterload. We apply our results by examining retrospectively the interpretations reached in three independent studies published in the literature.

Myocardial twitch duration and the dependence of oxygen consumption on pressure-volume area: experiments and modelling.

We tested the proposition that linear length dependence of twitch duration underlies the well-characterised linear dependence of oxygen consumption (V(O(2)) ) on pressure­volume area (PVA) in the heart. By way of experimental simplification, we reduced the problem from three dimensions to one by substituting cardiac trabeculae for the classically investigated whole-heart. This allowed adoption of stress­length area (SLA) as a surrogate for PVA, and heat as a proxy for V(O(2)) . Heat and stress (force per cross-sectional area), at a range of muscle lengths and at both 1 mM and 2 mM [Ca(2+)](o), were recorded from continuously superfused rat right-ventricular trabeculae undergoing fixed-end contractions. The heat­SLA relations of trabeculae (reported here, for the first time) are linear. Twitch duration increases monotonically (but not strictly linearly) with muscle length. We probed the cellular mechanisms of this phenomenon by determining: (i) the length dependence of the duration of the Ca(2+) transient, (ii) the length dependence of the rate of force redevelopment following a length impulse (an index of Ca(2+) binding to troponin-C), (iii) the effect on the simulated time course of the twitch of progressive deletion of length and Ca(2+)-dependent mechanisms of crossbridge cooperativity, using a detailed mathematical model of the crossbridge cycle, and (iv) the conditions required to achieve these multiple length dependencies, using a greatly simplified model of twitch mechano-energetics. From the results of these four independent investigations, we infer that the linearity of the heat­SLA relation (and, by analogy, the V(O(2))­PVA relation) is remarkably robust in the face of departures from linearity of length-dependent twitch duration.

Experiment-model interaction for analysis of epicardial activation during human ventricular fibrillation with global myocardial ischaemia.

We describe a combined experiment-modelling framework to investigate the effects of ischaemia on the organisation of ventricular fibrillation in the human heart. In a series of experimental studies epicardial activity was recorded from 10 patients undergoing routine cardiac surgery. Ventricular fibrillation was induced by burst pacing, and recording continued during 2.5 min of global cardiac ischaemia followed by 30 s of coronary reflow. Modelling used a 2D description of human ventricular tissue. Global cardiac ischaemia was simulated by (i) decreased intracellular ATP concentration and subsequent activation of an ATP sensitive K⁺ current, (ii) elevated extracellular K⁺ concentration, and (iii) acidosis resulting in reduced magnitude of the L-type Ca²âº current I(Ca,L). Simulated ischaemia acted to shorten action potential duration, reduce conduction velocity, increase effective refractory period, and flatten restitution. In the model, these effects resulted in slower re-entrant activity that was qualitatively consistent with our observations in the human heart. However, the flattening of restitution also resulted in the collapse of many re-entrant waves to several stable re-entrant waves, which was different to the overall trend we observed in the experimental data. These findings highlight a potential role for other factors, such as structural or functional heterogeneity in sustaining wavebreak during human ventricular fibrillation with global myocardial ischaemia.

The effect of hoof angle variations on dorsal lamellar load in the equine hoof.

REASONS FOR PERFORMING STUDY: In the treatment of laminitis it is believed that reducing tension in the deep digital flexor tendon by raising the palmar angle of the hoof can reduce the load on the dorsal lamellae, allowing them to heal or prevent further damage. OBJECTIVE: To determine the effect of alterations in hoof angle on the load in the dorsal laminar junction. METHODS: Biomechanical finite element models of equine hooves were created with palmar angles of the distal phalanx varying from 0-15°. Tissue material relations accounting for anisotropy and the effect of moisture were used. Loading conditions simulating the stages in the stance where the vertical ground reaction force, midstance joint moment and breakover joint moment were maximal, were applied to the models. The loads were adjusted to account for the reduction in joint moment caused by increasing the palmar angle. Models were compared using the stored elastic energy, an indication of load, which was sampled in the dorsal laminar junction. RESULTS: For all loading cases, increasing the palmar angle increased the stored elastic energy in the dorsal laminar junction. The stored elastic energy near the proximal laminar junction border for a palmar angle of 15° was between 1.3 and 3.8 times that for a palmar angle of 0°. Stored elastic energy at the distal laminar junction border was small in all cases. For the breakover case, stored elastic energy at the proximal border also increased with increasing palmar angle. CONCLUSIONS AND POTENTIAL RELEVANCE: The models in this study predict that raising the palmar angle increases the load on the dorsal laminar junction. Therefore, hoof care interventions that raise the palmar angle in order to reduce the dorsal lamellae load may not achieve this outcome.

Coupling multi-physics models to cardiac mechanics.

We outline and review the mathematical framework for representing mechanical deformation and contraction of the cardiac ventricles, and how this behaviour integrates with other processes crucial for understanding and modelling heart function. Building on general conservation principles of space, mass and momentum, we introduce an arbitrary Eulerian-Lagrangian framework governing the behaviour of both fluid and solid components. Exploiting the natural alignment of cardiac mechanical properties with the tissue microstructure, finite deformation measures and myocardial constitutive relations are referred to embedded structural axes. Coupling approaches for solving this large deformation mechanics framework with three dimensional fluid flow, coronary hemodynamics and electrical activation are described. We also discuss the potential of cardiac mechanics modelling for clinical applications.

Electromechanical wavebreak in a model of the human left ventricle.

In the present report, we introduce an integrative three-dimensional electromechanical model of the left ventricle of the human heart. Electrical activity is represented by the ionic TP06 model for human cardiac cells, and mechanical activity is represented by the Niederer-Hunter-Smith active contractile tension model and the exponential Guccione passive elasticity model. These models were embedded into an anatomic model of the left ventricle that contains a detailed description of cardiac geometry and the fiber orientation field. We demonstrated that fiber shortening and wall thickening during normal excitation were qualitatively similar to experimental recordings. We used this model to study the effect of mechanoelectrical feedback via stretch-activated channels on the stability of reentrant wave excitation. We found that mechanoelectrical feedback can induce the deterioration of an otherwise stable spiral wave into turbulent wave patterns similar to that of ventricular fibrillation. We identified the mechanisms of this transition and studied the three-dimensional organization of this mechanically induced ventricular fibrillation.

A finite element study of invariant-based orthotropic constitutive equations in the context of myocardial material parameter estimation.

A previous study investigated a number of invariant-based orthotropic and transversely isotropic constitutive equations for their suitability to fit three-dimensional simple shear mechanics data of passive myocardial tissue. The study was based on the assumption of a homogeneous deformation. Here, we extend the previous study by performing an inverse finite element material parameter estimation. This ensures a more realistic deformation state and material parameter estimates. The constitutive relations were compared on the basis of (i) 'goodness of fit': how well they fit a set of six shear deformation tests and (ii) 'variability': how well determined the material parameters are over the range of experiments. These criteria were utilised to discuss the advantages and disadvantages of the constitutive relations. It was found that a specific form of the polyconvex type as well as the exponential Fung-type equations were most suitable for modelling the orthotropic behaviour of myocardium under simple shear.

Modeling of the mechanical function of the human gastroesophageal junction using an anatomically realistic three-dimensional model.

The aim of this study was to combine the anatomy and physiology of the human gastroesophageal junction (the junction between the esophagus and the stomach) into a unified computer model. A three-dimensional (3D) computer model of the gastroesophageal junction was created using cross-sectional images from a human cadaver. The governing equations of finite deformation elasticity were incorporated into the 3D model. The model was used to predict the intraluminal pressure values (pressure inside the junction) due to the muscle contraction of the gastroesophageal junction and the effects of the surrounding structures. The intraluminal pressure results obtained from the 3D model were consistent with experimental values available in the literature. The model was also used to examine the independent roles of each muscle layer (circular and longitudinal) of the gastroesophageal junction by contracting them separately. Results showed that the intraluminal pressure values predicted by the model were primarily due to the contraction of the circular muscle layer. If the circular muscle layer was quiescent, the contraction of the longitudinal muscle layer resulted in an expansion of the junction. In conclusion, the model provided reliable predictions of the intraluminal pressure values during the contraction of a normal gastroesophageal junction. The model also provided a framework to examine the role of each muscle layer during the contraction of the gastroesophageal junction.

Organization of ventricular fibrillation in the human heart: experiments and models.

Sudden cardiac death is a major health problem in the industrialized world. The lethal event is typically ventricular fibrillation (VF), during which the co-ordinated regular contraction of the heart is overthrown by a state of mechanical and electrical anarchy. Understanding the excitation patterns that sustain VF is important in order to identify potential therapeutic targets. In this paper, we studied the organization of human VF by combining clinical recordings of electrical excitation patterns on the epicardial surface during in vivo human VF with simulations of VF in an anatomically and electrophysiologically detailed computational model of the human ventricles. We find both in the computational studies and in the clinical recordings that epicardial surface excitation patterns during VF contain around six rotors. Based on results from the simulated three-dimensional excitation patterns during VF, which show that the total number of electrical sources is 1.4 +/- 0.12 times greater than the number of epicardial rotors, we estimate that the total number of sources present during clinically recorded VF is 9.0 +/- 2.6. This number is approximately fivefold fewer compared with that observed during VF in dog and pig hearts, which are of comparable size to human hearts. We explain this difference by considering differences in action potential duration dynamics across these species. The simpler spatial organization of human VF has important implications for treatment and prevention of this dangerous arrhythmia. Moreover, our findings underline the need for integrated research, in which human-based clinical and computational studies complement animal research.

A computational study of mother rotor VF in the human ventricles.

Sudden cardiac death is one of the major causes of death in the industrialized world. It is most often caused by a cardiac arrhythmia called ventricular fibrillation (VF). Despite its large social and economical impact, the mechanisms for VF in the human heart yet remain to be identified. Two of the most frequently discussed mechanisms observed in experiments with animal hearts are the multiple wavelet and mother rotor hypotheses. Most recordings of VF in animal hearts are consistent with the multiple wavelet mechanism. However, in animal hearts, mother rotor fibrillation has also been observed. For both multiple wavelet and mother rotor VF, cardiac heterogeneity plays an important role. Clinical data of action potential restitution measured from the surface of human hearts have been recently published. These in vivo data show a substantial degree of spatial heterogeneity. Using these clinical restitution data, we studied the dynamics of VF in the human heart using a heterogeneous computational model of human ventricles. We hypothesized that this observed heterogeneity can serve as a substrate for mother rotor fibrillation. We found that, based on these data, mother rotor VF can occur in the human heart and that ablation of the mother rotor terminates VF. Furthermore, we found that both mother rotor and multiple wavelet VF can occur in the same heart depending on the initial conditions at the onset of VF. We studied the organization of these two types of VF in terms of filament numbers, excitation periods, and frequency domains. We conclude that mother rotor fibrillation is a possible mechanism in the human heart.

Myocardial material parameter estimation: a comparison of invariant based orthotropic constitutive equations.

This study investigated a number of invariant based orthotropic and transversely isotropic constitutive equations for their suitability to fit three-dimensional simple shear mechanics data of passive myocardial tissue. A number of orthotropic laws based on Green strain components and one microstructurally based law have previously been investigated to fit experimental measurements of stress-strain behaviour. Here we extend this investigation to include several recently proposed functional forms, i.e. invariant based orthotropic and transversely isotropic constitutive relations. These laws were compared on the basis of (i) 'goodness of fit': how well they fit a set of six shear deformation tests, (ii) 'variability': how well determined the material parameters are over the range of experiments. These criteria were utilised to discuss the advantages and disadvantages of the constitutive laws. It was found that a specific form of the polyconvex type as well as the exponential Fung-type law from the previous study were most suitable for modelling the orthotropic behaviour of myocardium under simple shear.

Passive ventricular mechanics modelling using MRI of structure and function.

Patients suffering from dilated cardiomyopathy or myocardial infarction can develop left ventricular (LV) diastolic impairment. The LV remodels its structure and function to adapt to pathophysiological changes in geometry and loading conditions and this remodeling process can alter the passive ventricular mechanics. In order to better understand passive ventricular mechanics, a LV finite element model was developed to incorporate physiological and mechanical information derived from in vivo magnetic resonance imaging (MRI) tissue tagging, in vivo LV cavity pressure recording and ex vivo diffusion tensor MRI (DTMRI) of a canine heart. MRI tissue tagging enables quantitative evaluation of cardiac mechanical function with high spatial and temporal resolution, whilst the direction of maximum water diffusion (the primary eigenvector) in each voxel of a DTMRI directly correlates with the myocardial fibre orientation. This model was customized to the geometry of the canine LV during diastasis by fitting the segmented epicardial and endocardial surface data from tagged MRI using nonlinear finite element fitting techniques. Myofibre orientations, extracted from DTMRI of the same heart, were incorporated into this geometric model using a free form deformation methodology. Pressure recordings, temporally synchronized to the tissue tagging MRI data, were used to simulate the LV deformation during diastole. Simulation of the diastolic LV mechanics allowed us to estimate the stiffness of the passive LV myocardium based on kinematic data obtained from tagged MRI. This integrated physiological model will allow more insight into the regional passive diastolic mechanics of the LV on an individualized basis, thereby improving our understanding of the underlying structural basis of mechanical dysfunction in pathological conditions.

A biomechanical model of mammographic compressions.

A number of biomechanical models have been proposed to improve nonrigid registration techniques for multimodal breast image alignment. A deformable breast model may also be useful for overcoming difficulties in interpreting 2D X-ray projections (mammograms) of 3D volumes (breast tissues). If a deformable model could accurately predict the shape changes that breasts undergo during mammography, then the model could serve to localize suspicious masses (visible in mammograms) in the unloaded state, or in any other deformed state required for further investigations (such as biopsy or other medical imaging modalities). In this paper, we present a validation study that was conducted in order to develop a biomechanical model based on the well-established theory of continuum mechanics (finite elasticity theory with contact mechanics) and demonstrate its use for this application. Experimental studies using gel phantoms were conducted to test the accuracy in predicting mammographic-like deformations. The material properties of the gel phantom were estimated using a nonlinear optimization process, which minimized the errors between the experimental and the model-predicted surface data by adjusting the parameter associated with the neo-Hookean constitutive relation. Two compressions (the equivalent of cranio-caudal and medio-lateral mammograms) were performed on the phantom, and the corresponding deformations were recorded using a MRI scanner. Finite element simulations were performed to mimic the experiments using the estimated material properties with appropriate boundary conditions. The simulation results matched the experimental recordings of the deformed phantom, with a sub-millimeter root-mean-square error for each compression state. Having now validated our finite element model of breast compression, the next stage is to apply the model to clinical images.

Myocardial material parameter estimation: a non-homogeneous finite element study from simple shear tests.

The passive material properties of myocardium play a major role in diastolic performance of the heart. In particular, the shear behaviour is thought to play an important mechanical role due to the laminar architecture of myocardium. We have previously compared a number of myocardial constitutive relations with the aim to extract their suitability for inverse material parameter estimation. The previous study assumed a homogeneous deformation. In the present study we relaxed the homogeneous assumption by implementing these laws into a finite element environment in order to obtain more realistic measures for the suitability of these laws in both their ability to fit a given set of experimental data, as well as their stability in the finite element environment. In particular, we examined five constitutive laws and compare them on the basis of (i) "goodness of fit": how well they fit a set of six shear deformation tests, (ii) "determinability": how well determined the objective function is at the optimal parameter fit, and (iii) "variability": how well determined the material parameters are over the range of experiments. Furthermore, we compared the FE results with those from the previous study.It was found that the same material law as in the previous study, the orthotropic Fung-type "Costa-Law", was the most suitable for inverse material parameter estimation for myocardium in simple shear.