No full-text available
To read the full-text of this research,
you can request a copy directly from the authors.
Myocardial Stiffness Estimation: A Novel Cost Function for Unique Parameter Identification
Abstract
Myocardial stiffness is a clinical biomarker used to diagnose and stratify diseases such as heart failure. This biomechanical property can be inferred from the personalisation of computational cardiac models to clinical measures. Nevertheless, previous attempts have been unable to determine a unique set of material constitutive parameters. In this study we address this shortcoming by proposing a new cost function that allows us to uncouple key parameters and uniquely describe passive material properties in patients from available clinical data.
... These complex multi-physics and multi-scale cardiac simulations combine models that represent the distinct physiology of the material properties, cellular electrical activity and cellular contraction. When constructing multi-scale models of human function, there are currently many options for characterizing the cellular electrophysiology [19,52] or material properties [66,48]. Detailed biophysical models of cardiac contraction do exist for other species [56,8,36] and have been used to great effect in multi-scale computational models, particularly in the mouse [59,40] and rat [51,39]. ...
... Where W is the strain energy function and E ij are components of the Green-Lagrange strain tensor E in a fibre-based coordinate system [35]. We use parameters C 2 = 8, C 3 = 3, C 4 = 4 based on Nasopoulou et al. [48] and C 1 = 1 kPa to match end-diastolic volume. Meshes were 'deflated' to the reference configuration using the backward displacement method [6]. ...
Experimental data from human cardiac myocytes at body temperature is crucial for a quantitative understanding of clinically relevant cardiac function and development of whole-organ computational models. However, such experimental data is currently very limited. Specifically, important measurements to characterize changes in tension development in human cardiomyocytes that occur with perturbations in cell length are not available. To address this deficiency, in this study we present an experimental data set collected from skinned human cardiac myocytes, including the passive and viscoelastic properties of isolated myocytes, the steady-state force calcium relationship at different sarcomere lengths, and changes in tension following a rapid increase or decrease in length, and after constant velocity shortening. This data set is, to our knowledge, the first characterization of length and velocity-dependence of tension generation in human skinned cardiac myocytes at body temperature.
... where E is the Lagrangian strain tensor expressed relative to the muscle fiber and sheet directions and the parameters c 2 ¼ 8, c 3 ¼ 2, and c 4 ¼ 4 characterized the tissue anisotropy (69). Treating the prefactor c 1 as a phenomenological scaling factor for the overall passive tissue stiffness, we allowed it to vary to preserve the ratios between the different stiffness components. ...
Late-onset heart failure (HF) is a known side effect of doxorubicin chemotherapy. Typically, patients are diagnosed when already at an irreversible stage of HF, which allows few or no treatment options. Identifying the causes of compromised cardiac function in this patient group may improve early patient diagnosis and support treatment selection. To link doxorubicin-induced changes in cardiac cellular and tissue mechanical properties to overall cardiac function, we apply a multiscale biophysical biomechanics model of the heart to measure the plausibility of changes in model parameters representing the passive, active, or anatomical properties of the left ventricle for reproducing measured patient phenotypes. We create representative models of healthy controls (N = 10) and patients with HF induced by (N = 22) or unrelated to (N = 25) doxorubicin therapy. The model predicts that HF in the absence of doxorubicin is characterized by a 2- to 3-fold stiffness increase, decreased tension (0-20%), and ventricular dilation (of order 10-30%). HF due to doxorubicin was similar but showed stronger bias toward reduced active contraction (10-30%) and less dilation (0-20%). We find that changes in active, passive, and anatomical properties all play a role in doxorubicin-induced cardiotoxicity phenotypes. Differences in parameter changes between patient groups are consistent with doxorubicin cardiotoxicity having a greater dependence on reduced cellular contraction and less anatomical remodeling than HF not caused by doxorubicin.
... 75 Research is also needed to uniquely identify material parameters, a problem that can be reduced by an adequate choice of the constitutive law. 26,52 Other methodologically critical aspects are the choice of a mechanical reference configuration, and the correct temporal alignment of pressure and deformation data. Since the seminal work where materials stiffness was estimated from clinical data, 70 computational models have been shown to be able to decouple active and passive mechanics, obtaining results that correlate with the disease status of subjects, 74 and to be more robust to offset errors in pressure recordings. ...
Computational modelling of the heart is rapidly advancing to the point of clinical utility. However, the difficulty of parameterizing and validating models from clinical data indicates that the routine application of truly predictive models remains a significant challenge. We argue there is significant value in an intermediate step towards prediction. This step is the use of biophysically based models to extract clinically useful information from existing patient data. Specifically in this paper we review methodologies for applying modelling frameworks for this goal in the areas of quantifying cardiac anatomy, estimating myocardial stiffness and optimizing measurements of coronary perfusion. Using these indicative examples of the general overarching approach, we finally discuss the value, ongoing challenges and future potential for applying biophysically based modelling in the clinical context.
An unresolved issue in patient–specific models of cardiac mechanics is the choice of an appropriate constitutive law, able to accurately capture the passive behavior of the myocardium, while still having uniquely identifiable parameters tunable from available clinical data. In this pa- per, we aim to facilitate this choice by examining the practical identifiability and model fidelity of constitutive laws often used in cardiac mechanics. Our analysis focuses on the use of novel 3D tagged MRI, providing detailed displacement information in three-dimensions. The practical identifiability of each law is examined by generating synthetic 3D tags from in silico simulations, allowing mapping of the objective function landscape over parame- ter space and comparison of minimizing parameter values with original ground truth values. Model fi- delity was tested by comparing these laws with the more complex transversely isotropic Guccione law, by characterising their passive end-diastolic pressure volume relation behavior, as well as by considering the in vivo case of a healthy volun- teer. These results show that a reduced form of the Holzapfel–Ogden law provides the best balance be- tween identifiability and model fidelity across the tests considered.
Computational cardiac physiology has great potential to improve the management of cardiovascular diseases. One of the main bottlenecks in this field is the customization of the computational model to the anatomical and physiological status of the patient. We present a fully automatic service for the geometrical personalization of cardiac ventricular meshes with high-order interpolation from segmented images. The method is versatile (able to work with different species and disease conditions) and robust (fully automatic results fulfilling accuracy and quality requirements in 87% of 255 cases). Results also illustrate the capability to minimize the impact of segmentation errors, to overcome the sparse resolution of dynamic studies and to remove the sometimes unnecessary anatomical detail of papillary and trabecular structures. The smooth meshes produced can be used to simulate cardiac function, and in particular mechanics, or can be used as diagnostic descriptors of anatomical shape by cardiologists. This fully automatic service is deployed in a cloud infrastructure, and has been made available and accessible to the scientific community.
The diastolic function (i.e., blood filling) of the left ventricle (LV) is determined by its capacity for relaxation, or the decay in residual active tension (AT) generated during systole, and its constitutive material properties, or myocardial stiffness. The clinical determination of these two factors (diastolic residual AT and stiffness) is thus essential for assessing LV diastolic function. To quantify these two factors, in our previous work, a novel model-based parameter estimation approach was proposed and successfully applied to multiple cases using clinically acquired motion and invasively measured ventricular pressure data. However, the need to invasively acquire LV pressure limits the wide application of this approach. In this study, we address this issue by analyzing the feasibility of using two kinds of non-invasively available pressure measurements for the purpose of inverse mechanical parameter estimation. The prescription of pressure based on a generic pressure-volume (P-V) relationship reported in literature is first evaluated in a set of 18 clinical cases (10 healthy and 8 diseased), finding reasonable results for stiffness but not for residual active tension. We then investigate the use of non-invasive pressure measures, now available through imaging techniques and limited by unknown or biased offset values. Specifically, three sets of physiologically realistic synthetic data with three levels of diastolic residual active tension (i.e., impaired relaxation capability) are designed to quantify the percentage error in the parameter estimation against the possible pressure offsets within the physiological limits. Maximum errors are quantified as 11 % for the magnitude of stiffness and 22 % for AT, with averaged 0.17 kPa error in pressure measurement offset using the state-of-the-art non-invasive pressure estimation method. The main cause for these errors is the limited temporal resolution of clinical imaging data currently available. These results demonstrate the potential feasibility of the estimation diastolic biomarkers with non-invasive assessment of pressure through medical imaging data.
In cardiovascular research, relaxation and stiffness are calculated from pressure-volume (PV) curves by separately fitting the data during the isovolumic and end-diastolic phases (EDPVR), respectively. This method is limited because it assumes uncoupled active and passive properties during these phases, it penalizes statistical power and cannot account for elastic restoring forces. We aimed to improve this analysis by implementing a method based on global optimization of all PV diastolic data. In 1000 Monte- Carlo experiments, the optimization algorithm recovered entered parameters of diastolic properties below and above the equilibrium volume (intraclass correlation coefficients [Ric]= 0.99). Inotropic modulation experiments in 26 pigs modified passive pressure generated by restoring forces due to changes in the operative and/or equilibrium volumes. Volume overload and coronary microembolization caused incomplete relaxation at end diastole (active pressure > 0.5 mm Hg), rendering the EDPVR method ill-posed. In 28 patients undergoing PV cardiac catheterization, the new algorithm reduced the confidence intervals of stiffness parameters by one fifth. The Jacobian matrix allowed visualizing the contribution of each property to instantaneous diastolic pressure on a per-patient basis. The algorithm allowed estimating stiffness from single-beat PV data (dP/dV at EDV Ric= 0.65, error= 0.07 ± 0.24 mm Hg/ml). Thus, in clinical and pre-clinical research, global optimization algorithms provide the most complete, accurate, and reproducible assessment of global LV diastolic chamber properties from PV data. Using global optimization we were able to fully uncouple relaxation and passive PV curves for the first time in the intact heart.
The quality of a computational mesh is an important characteristic for stable and accurate simulations. Quality depends on the regularity of the initial mesh, and in mechanical simulations it evolves in time, with deformations causing changes in volume and distortion of mesh elements. Mesh quality metrics are therefore relevant for both mesh personalization and the monitoring of the simulation process. This work evaluates the significance, in meshes with high order interpolation, of four quality metrics described in the literature, applying them to analyse the stability of the simulation of the heart beat. It also investigates how image registration and mesh warping parameters affect the quality and stability of meshes. Jacobianbased metrics outperformed or matched the results of coarse geometrical metrics of aspect ratio or orthogonality, although they are more expensive computationally. The stability of simulations of a complete heart cycle was best predicted with a specificity of 61%, sensitivity of 85%, and only nominal differences were found changing the intra-element and per-element combination of quality values. A compromise between fitting accuracy and mesh stability and quality was found. Generic geometrical quality metrics have a limited success predicting stability, and an analysis of the simulation problem may be required for an optimal definition of quality.
An unresolved issue in patients with diastolic dysfunction is that the estimation of myocardial stiffness cannot be decoupled from diastolic residual active tension (AT) because of the impaired ventricular relaxation during diastole. To address this problem, this paper presents a method for estimating diastolic mechanical parameters of the left ventricle (LV) from cine and tagged MRI measurements and LV cavity pressure recordings, separating the passive myocardial constitutive properties and diastolic residual AT. Dynamic C(1)-continuous meshes are automatically built from the anatomy and deformation captured from dynamic MRI sequences. Diastolic deformation is simulated using a mechanical model that combines passive and active material properties. The problem of non-uniqueness of constitutive parameter estimation using the well known Guccione law is characterized by reformulation of this law. Using this reformulated form, and by constraining the constitutive parameters to be constant across time points during diastole, we separate the effects of passive constitutive properties and the residual AT during diastolic relaxation. Finally, the method is applied to two clinical cases and one control, demonstrating that increased residual AT during diastole provides a potential novel index for delineating healthy and pathological cases.
In this paper, we first of all review the morphology and structure of the myocardium and discuss the main features of the mechanical response of passive myocardium tissue, which is an orthotropic material. Locally within the architecture of the myocardium three mutually orthogonal directions can be identified, forming planes with distinct material responses. We treat the left ventricular myocardium as a non-homogeneous, thick-walled, nonlinearly elastic and incompressible material and develop a general theoretical framework based on invariants associated with the three directions. Within this framework we review existing constitutive models and then develop a structurally based model that accounts for the muscle fibre direction and the myocyte sheet structure. The model is applied to simple shear and biaxial deformations and a specific form fitted to the existing (and somewhat limited) experimental data, emphasizing the orthotropy and the limitations of biaxial tests. The need for additional data is highlighted. A brief discussion of issues of convexity of the model and related matters concludes the paper.
Abnormal diastolic left ventricular function is an early marker for myocardial disease and may be impaired even when global systolic function is normal. Subendocardial function is affected early in ischaemic heart disease and by altering left ventricular long axis motion, may contribute to abnormal transmitral pressure gradients.
Regional myocardial long axis velocity in diastole measured by magnetic resonance was compared with left ventricular filling measured by Doppler echocardiography in 25 patients with coronary artery disease. Fifteen patients also underwent magnetic resonance assessment at the time of onset of early diastolic blood flow.
The onset of diastolic long axis velocity preceded flow across the mitral valve by a mean of 46 ms. Mean long axis myocardial velocity correlated with peak early filling velocity (E) (r=0·73, P<0·00l), early deceleration (r=−0·73, P<0·001 and the early to late filling ratio (E/A) ratio (r=06, P<0·01 Maximum myocardial long axis velocity also correlated with peak early filling velocity (r=0·56, P<0·01 early deceleration rate (r=0·53 P<0·001 and the E/A ratio (r=0·53, P<0·01). The variability of long axis velocity around the ventricle correlated inversely with peak early filling, (r−0·7, P<0·001), early deceleration (r=−0·56, P<0·01), and the E/A ratio (r=−0·48, P<0·02). Peak atrial filling velocity did not correlate with any measure of long axis myocardial velocity.
We conclude that early diastolic long axis myocardial velocity has a significant effect on left ventricular filling.
There is growing recognition that congestive heart failure (CHF) caused by a predominant abnormality in diastolic function (ie, diastolic heart failure) is both common and causes significant morbidity and mortality. However, there is continued controversy surrounding the definition of diastolic dysfunction and the diagnostic criteria for diastolic heart failure. As a result, clinical therapeutic trials have been slow to develop and difficult to design. Fortunately, these controversies are yielding to an emerging consensus. Recent clinical studies have provided sufficient data to develop standardized diagnostic criteria to define diastolic heart failure. 1– 4 Experimental studies have provided increased insight into the mechanisms that cause diastolic heart failure. 5–22 Together, these clinical and experimental studies are being used to design targeted clinical trials to test effective treatments for diastolic heart failure. The purpose of this 2-part article is to provide a perspective on these issues, highlight new research, and introduce emerging ideas. Part 1 will focus on the criteria used to diagnose diastolic heart failure, the effects of diastolic heart failure on prognosis, and measurements used to assess diastolic function. Part 2 will describe the mechanisms that cause diastolic heart failure and discuss approaches to treatment.
We describe an experimental method and apparatus for the estimation of constitutive parameters of soft tissue using Magnetic Resonance Imaging (MRI), in particular for the estimation of passive myocardial material properties. MRI tissue tagged images were acquired with simultaneous pressure recordings, while the tissue was cyclically deformed using a custom built reciprocating pump actuator A continuous three-dimensional (3D) displacement field was reconstructed from the imaged tag motion. Cavity volume changes and local tissue microstructure were determined from phase contrast velocity and diffusion tensor MR images, respectively. The Finite Element Method (FEM) was used to solve the finite elasticity problem and obtain the displacement field that satisfied the applied boundary conditions and a given set of material parameters. The material parameters which best fit the FEM predicted displacements to the displacements reconstructed from the tagged images were found by nonlinear optimization. The equipment and method were validated using inflation of a deformable silicon gel phantom in the shape of a cylindrical annulus. The silicon gel was well described by a neo-Hookian material law with a single material parameter C1=8.71+/-0.06kPa, estimated independently using a rotational shear apparatus. The MRI derived parameter was allowed to vary regionally and was estimated as C1 =8.80+/-0.86kPa across the model. Preliminary results from the passive inflation of an isolated arrested pig heart are also presented, demonstrating the feasibility of the apparatus and method for isolated heart preparations. FEM based models can therefore estimate constitutive parameters accurately and reliably from MRI tagging data.
An accurate estimation of myocardial stiffness and decaying active tension is critical for the characterization of the diastolic function of the heart. Computational cardiac models can be used to analyse deformation and pressure data from the left ventricle in order to estimate these diastolic metrics. The results of this methodology depend on several model assumptions. In this work we reveal a nominal impact of the choice of myocardial fibre orientation between a rule-based description and personalised approach based on diffusion-tensor magnetic resonance imaging. This result suggests the viability of simplified clinical imaging protocols for the model-based estimation of diastolic biomarkers.
The Finite Element Method: Its Basis and Fundamentals offers a complete introduction to the basis of the finite element method, covering fundamental theory and worked examples in the detail required for readers to apply the knowledge to their own engineering problems and understand more advanced applications. This edition sees a significant rearrangement of the bookâ??s content to enable clearer development of the finite element method, with major new chapters and sections added to cover: Weak forms Variational forms Multi-dimensional field problems Automatic mesh generation Plate bending and shells Developments in meshless techniques Focusing on the core knowledge, mathematical and analytical tools needed for successful application, The Finite Element Method: Its Basis and Fundamentals is the authoritative resource of choice for graduate level students, researchers and professional engineers involved in finite element-based engineering analysis.
Recent morphological studies have demonstrated a laminar (sheet) organization of ventricular myofibers. Multiaxial measurements
of orthotropic myocardial constitutive properties have not been reported, but regional distributions of three-dimensional
diastolic and systolic strains relative to fiber and sheet axes have recently been measured in the dog heart by Takayama et
al. [30]. A three-dimensional finite-deformation, finite element model was used to investigate the effects of material orthotropy
on regional mechanics in the canine left ventricular wall at end-diastole and end-systole. The prolate spheroidal model incorporated
measured transmural distributions of fiber and sheet angles at the base and apex. Compared with transverse isotropy, the orthotropic
model of passive myocardial properties yielded improved agreement with measured end-diastolic strains when: (1) normal stiffness
transverse to the muscle fibers was increased tangent to the sheets and decreased normal to them; (2) shear coefficients were
increased within sheet planes and decreased transverse to them. For end-systole, orthotropic passive properties had little
effect, but three-dimensional systolic shear strain distributions were more accurately predicted by a model in which significant
active systolic stresses were developed in directions transverse to the mean fiber axis as well as axial to them. Thus the
ventricular laminar architecture may give rise to anisotropic material properties transverse to the fibers with greater resting
stiffness within than between myocardial laminae. There is also evidence that intact ventricular muscle develops significant
transverse stress during systole, though it remains to be seen if active stress is also orthotropic with respect to the laminar
architecture.
In-silico continuum simulations of organ and tissue scale physiology often require a discretisation or mesh of the solution domain. Cubic Hermite meshes provide a smooth representation of anatomy that is well-suited for simulating large deformation mechanics. Models of organ mechanics and deformation have demonstrated significant potential for clinical application. However, the production of a personalised mesh from patient's anatomy using medical images remains a major bottleneck in simulation workflows. To address this issue, we have developed an accurate, fast and automatic method for deriving patient-specific cubic Hermite meshes. The proposed solution customises a predefined template with a fast binary image registration step and a novel cubic Hermite mesh warping constructed using a variational technique. Image registration is used to retrieve the mapping field between the template mesh and the patient images. The variational warping technique then finds a smooth and accurate projection of this field into the basis functions of the mesh. Applying this methodology, cubic Hermite meshes are fitted to the binary description of shape with sub-voxel accuracy and within a few minutes, which is a significant advance over the existing state of the art methods. To demonstrate its clinical utility, a generic cubic Hermite heart biventricular model is personalised to the anatomy of four patients, and the resulting mechanical stability of these customised meshes is successfully demonstrated.
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.
The majority of patients with clinically diagnosed heart failure have normal systolic pump function and are commonly categorized as suffering from diastolic heart failure. The left ventricle (LV) remodels its structure and function to adapt to pathophysiological changes in geometry and loading conditions, which in turn can alter the passive ventricular mechanics. In order to better understand passive ventricular mechanics, a LV finite element (FE) model was customized to geometric data segmented from in vivo tagged magnetic resonance images (MRI) data and myofibre orientation derived from ex vivo diffusion tensor MRI (DTMRI) of a canine heart using nonlinear finite element fitting techniques. MRI tissue tagging enables quantitative evaluation of cardiac mechanical function with high spatial and temporal resolution, whilst the direction of maximum water diffusion in each voxel of a DTMRI directly corresponds to the local myocardial fibre orientation. Due to differences in myocardial geometry between in vivo and ex vivo imaging, myofibre orientations were mapped into the geometric FE model using host mesh fitting (a free form deformation technique). Pressure recordings, temporally synchronized to the tagging data, were used as the loading constraints to simulate the LV deformation during diastole. Simulation of diastolic LV mechanics allowed us to estimate the stiffness of the passive LV myocardium based on kinematic data obtained from tagged MRI. Integrated physiological modelling of this kind will allow more insight into mechanics of the LV on an individualized basis, thereby improving our understanding of the underlying structural basis of mechanical dysfunction under pathological conditions.
The equatorial region of the canine left ventricle was modeled as a thick-walled cylinder consisting of an incompressible hyperelastic material with homogeneous exponential properties. The anisotropic properties of the passive myocardium were assumed to be locally transversely isotropic with respect to a fiber axis whose orientation varied linearly across the wall. Simultaneous inflation, extension, and torsion were applied to the cylinder to produce epicardial strains that were measured previously in the potassium-arrested dog heart. Residual stress in the unloaded state was included by considering the stress-free configuration to be a warped cylindrical arc. In the special case of isotropic material properties, torsion and residual stress both significantly reduced the high circumferential stress peaks predicted at the endocardium by previous models. However, a resultant axial force and moment were necessary to cause the observed epicardial deformations. Therefore, the anisotropic material parameters were found that minimized these resultants and allowed the prescribed displacements to occur subject to the known ventricular pressure loads. The global minimum solution of this parameter optimization problem indicated that the stiffness of passive myocardium (defined for a 20 percent equibiaxial extension) would be 2.4 to 6.6 times greater in the fiber direction than in the transverse plane for a broad range of assumed fiber angle distributions and residual stresses. This agrees with the results of biaxial tissue testing. The predicted transmural distributions of fiber stress were relatively flat with slight peaks in the subepicardium, and the fiber strain profiles agreed closely with experimentally observed sarcomere length distributions. The results indicate that torsion, residual stress and material anisotropy associated with the fiber architecture all can act to reduce endocardial stress gradients in the passive left ventricle.
Left ventricular remodeling is the process by which ventricular size, shape, and function are regulated by mechanical, neurohormonal, and genetic factors.1 2 Remodeling may be physiological and adaptive during normal growth or pathological due to myocardial infarction, cardiomyopathy, hypertension, or valvular heart disease (Figure 1⇓). This article will review postinfarction remodeling, pathophysiological mechanisms, and therapeutic intervention.
Figure 1.
Diagrammatic representation of the many factors involved in the pathophysiology of ventricular remodeling. ECM indicates extracellular matrix; RAAS, renin-angiotensin-aldosterone system; CO, cardiac output; SVR, systemic vascular resistance; LV, left ventricular; and AII, angiotensin II.
### Postinfarction Left Ventricular Remodeling
The acute loss of myocardium results in an abrupt increase in loading conditions that induces a unique pattern of remodeling involving the infarcted border zone and remote noninfarcted myocardium. Myocyte necrosis and the resultant increase in load trigger a cascade of biochemical intracellular signaling processes that initiates and subsequently modulates reparative changes, which include dilatation, hypertrophy, and the formation of a discrete collagen scar. Ventricular remodeling may continue for weeks or months until the distending forces are counterbalanced by the tensile strength of the collagen scar. This balance is determined by the size, location, and transmurality of the infarct, the extent of myocardial stunning, the patency of the infarct-related artery, and local tropic factors.1 3
The myocardium consists of 3 integrated components: myocytes, extracellular matrix, and the capillary microcirculation that services the contractile unit assembly. Consideration of all 3 components provides important insights into the remodeling process and a rationale for future therapeutic strategies. The cardiomyocyte is terminally differentiated and develops tension by shortening. The extracellular matrix provides a stress-tolerant, viscoelastic scaffold consisting of type I and type III collagen that couples myocytes and maintains the spatial relations between the myofilaments and their capillary microcirculation.4 5 The collagen framework couples adjacent myocytes by intercellular struts that …
The numerical solution of the coupled system of partial differential and ordinary differential equations that model the whole heart in three dimensions is a considerable computational challenge. As a consequence, it is not computationally practical--either in terms of memory or time--to repeat simulations on a finer computational mesh to ensure that convergence of the solution has been attained. In an attempt to avoid this problem while retaining mathematical rigour, we derive a one dimensional model of a cardiac fibre that takes account of elasticity properties in three structurally defined axes within the myocardial tissue. This model of a cardiac fibre is then coupled with an electrophysiological cell model and a model of cellular electromechanics to allow us to simulate the coupling of the electrical and mechanical activity of the heart. We demonstrate that currently used numerical methods for coupling electrical and mechanical activity do not work in this case, and identify appropriate numerical techniques that may be used when solving the governing equations. This allows us to perform a series of simulations that: (i) investigate the effect of some of the assumptions inherent in other models; and (ii) reproduce qualitatively some experimental observations.
Increased left ventricular stiffness is a distinct finding in patients who have heart failure with normal ejection fraction (HFNEF). To elucidate how diastolic dysfunction contributes to heart failure symptomatology during exercise, we conducted a study using an invasive pressure-volume loop approach and measured cardiac function at rest and during atrial pacing and handgrip exercise.
Patients with HFNEF (n=70) and patients without heart failure symptoms (n=20) were enrolled. Pressure-volume loops were measured with a conductance catheter during basal conditions, handgrip exercise, and atrial pacing with 120 bpm to analyze diastolic and systolic left ventricular function. During transient preload reduction, the diastolic stiffness constant was measured directly. Diastolic function with increased stiffness was significantly impaired in patients with HFNEF during basal conditions. This was associated with increased end-diastolic pressures during handgrip exercise and with decreased stroke volume and a leftward shift of pressure-volume loops during atrial pacing.
Increased left ventricular stiffness contributed to increased end-diastolic pressure during handgrip exercise and decreased stroke volume during atrial pacing in patients with HFNEF. These data suggest that left ventricular stiffness modulates cardiac function in HFNEF patients and suggests that diastolic dysfunction with increased stiffness is a target for treating HFNEF.
Estimation of diastolic biomarkers: sensitiviy to fibre orientation
- S Land
- S Niederer
- P Lamata
- O Camara
- T Mansi
- M Pop
- K Rhode
- M Sermesant