Understanding the need of ventricular pressure for the estimation of diastolic biomarkers

Robust and efficient fixed-point algorithm for the inverse elastostatic problem to identify myocardial passive material parameters and the unloaded reference configuration

Image-based computational models of the heart represent a powerful tool to shed new light on the mechanisms underlying physiological and pathological conditions in cardiac function and to improve diagnosis and therapy planning. However, in order to enable the clinical translation of such models, it is crucial to develop personalized models that are able to reproduce the physiological reality of a given patient. There have been numerous contributions in experimental and computational biomechanics to characterize the passive behavior of the myocardium. However, most of these studies suffer from severe limitations and are not applicable to high-resolution geometries. In this work, we present a novel methodology to perform an automated identification of in vivo properties of passive cardiac biomechanics. The highly-efficient algorithm fits material parameters against the shape of a patient-specific approximation of the end-diastolic pressure-volume relation (EDPVR). Simultaneously, an unloaded reference configuration is generated, where a novel line search strategy to improve convergence and robustness is implemented. Only clinical image data or previously generated meshes at one time point during diastole and one measured data point of the EDPVR are required as an input. The proposed method can be straightforwardly coupled to existing finite element (FE) software packages and is applicable to different constitutive laws and FE formulations. Sensitivity analysis demonstrates that the algorithm is robust with respect to initial input parameters.

Finite-element based optimization of left ventricular passive stiffness in normal volunteers and patients after myocardial infarction: Utility of an inverse deformation gradient calculation of regional diastolic strain

INTRODUCTION

Left ventricular (LV) diastolic dysfunction (DD) is common after myocardial infarction (MI). Whereas current clinical assessment of DD relies on indirect markers including LV filling, finite element (FE) -based computational modeling directly measures regional diastolic stiffness. We hypothesized that an inverse deformation gradient (DG) method calculation of diastolic strain (IDGDS) allows the FE model-based calculation of regional diastolic stiffness (material parameters; MP) in post-MI patients with DD.

METHODS

Cardiac magnetic resonance (CMR) with tags (CSPAMM) and late gadolinium enhancement (LGE) was performed in 10 patients with post-MI DD and 10 healthy volunteers. The 3-dimensional (3D) LV DG from end-diastole (ED) to early diastolic filling (EDF; DG_ED→EDF) was calculated from CSPAMM. Diastolic strain was calculated from DG_EDF→ED by inverting the DG_ED→EDF. FE models were created with MI and non-MI (remote; RM) regions determined by LGE. Guccione MPs C, and exponential fiber, b_f, and transverse, b_t , terms were optimized with IDGDS strain.

RESULTS

3D circumferential and longitudinal diastolic strain (E_cc;E_ll) calculated using IDGDS in CSPAMM obtained in volunteers and MI patients were [Formula: see text]  = 0.27 ± 0.01, [Formula: see text]  = 0.24 ± 0.03 and [Formula: see text]  = 0.21 ± 0.02, and [Formula: see text]  = 0.15 ± 0.02, respectively. MPs in the volunteer group were C_H = 0.013 [0.001, 0.235] kPa, [Formula: see text]  = 20.280 ± 4.994, and [Formula: see text]  = 7.460 ± 2.171 and C_RM = 0.0105 [0.010, 0.011] kPa, [Formula: see text]  = 50.786 ± 13.511 (p = 0.0846), and [Formula: see text]  = 17.355 ± 2.743 (p = 0.0208) in the remote myocardium of post-MI patients.

CONCLUSION

Diastolic strain, calculated from CSPAMM with IDGDS, enables calculation of FE model-based regional diastolic material parameters. Transverse stiffness of the remote myocardium, , may be a valuable new metric for determination of DD in patients after MI.

In vivo estimation of normal left ventricular stiffness and contractility based on routine cine MR acquisition

Post-myocardial infarction remodeling process is known to alter the mechanical properties of the heart. Biomechanical parameters, such as tissue stiffness and contractility, would be useful for clinicians to better assess the severity of the diseased heart. However, these parameters are difficult to obtain in the current clinical practice. In this paper, we estimated subject-specific in vivo myocardial stiffness and contractility from 21 healthy volunteers, based on left ventricle models constructed from data acquired from routine cardiac MR acquisition only. The subject-specific biomechanical parameters were quantified using an inverse finite-element modelling approach. The personalized models were evaluated against relevant clinical metrics extracted from the MR data, such as circumferential strain, wall thickness and fractional thickening. We obtained the ranges of healthy biomechanical indices of 1.60 ± 0.22 kPa for left ventricular stiffness and 95.13 ± 14.56 kPa for left ventricular contractility. These reference normal values can be used for future model-based investigation on the stiffness and contractility of ischemic myocardium.

Optimal Control of SonoVue Microbubbles to Estimate Hydrostatic Pressure

The measurement of cardiac and aortic pressures enables diagnostic insight into cardiac contractility and stiffness. However, these pressures are currently assessed invasively using pressure catheters. It may be possible to estimate these pressures less invasively by applying microbubble ultrasound contrast agents as pressure sensors. The aim of this study was to investigate the subharmonic response of the microbubble ultrasound contrast agent SonoVue (Bracco Spa, Milan, Italy) at physiological pressures using a static pressure phantom. A commercially available cell culture cassette with Luer connections was used as a static pressure chamber. SonoVue was added to the phantom, and radio frequency data were recorded on the ULtrasound Advanced Open Platform (ULA-OP). The mean subharmonic amplitude over a 40% bandwidth was extracted at 0-200-mmHg hydrostatic pressures, across 1.7-7.0-MHz transmit frequencies and 3.5%-100% maximum scanner acoustic output. The Rayleigh-Plesset equation for single-bubble oscillations and additional hysteresis experiments were used to provide insight into the mechanisms underlying the subharmonic pressure response of SonoVue. The subharmonic amplitude of SonoVue increased with hydrostatic pressure up to 50 mmHg across all transmit frequencies and decreased thereafter. A decreasing microbubble surface tension may drive the initial increase in the subharmonic amplitude of SonoVue with hydrostatic pressure, while shell buckling and microbubble destruction may contribute to the subsequent decrease above 125-mmHg pressure. In conclusion, a practical operating regime that may be applied to estimate cardiac and aortic blood pressures from the subharmonic signal of SonoVue has been identified.

Fast parameter inference in a biomechanical model of the left ventricle by using statistical emulation

A central problem in biomechanical studies of personalized human left ventricular modelling is estimating the material properties and biophysical parameters from in vivo clinical measurements in a timeframe that is suitable for use within a clinic. Understanding these properties can provide insight into heart function or dysfunction and help to inform personalized medicine. However, finding a solution to the differential equations which mathematically describe the kinematics and dynamics of the myocardium through numerical integration can be computationally expensive. To circumvent this issue, we use the concept of emulation to infer the myocardial properties of a healthy volunteer in a viable clinical timeframe by using in vivo magnetic resonance image data. Emulation methods avoid computationally expensive simulations from the left ventricular model by replacing the biomechanical model, which is defined in terms of explicit partial differential equations, with a surrogate model inferred from simulations generated before the arrival of a patient, vastly improving computational efficiency at the clinic. We compare and contrast two emulation strategies: emulation of the computational model outputs and emulation of the loss between the observed patient data and the computational model outputs. These strategies are tested with two interpolation methods, as well as two loss functions. The best combination of methods is found by comparing the accuracy of parameter inference on simulated data for each combination. This combination, using the output emulation method, with local Gaussian process interpolation and the Euclidean loss function, provides accurate parameter inference in both simulated and clinical data, with a reduction in the computational cost of about three orders of magnitude compared with numerical integration of the differential equations by using finite element discretization techniques.

Advances in computational modelling for personalised medicine after myocardial infarction

Myocardial infarction (MI) is a leading cause of premature morbidity and mortality worldwide. Determining which patients will experience heart failure and sudden cardiac death after an acute MI is notoriously difficult for clinicians. The extent of heart damage after an acute MI is informed by cardiac imaging, typically using echocardiography or sometimes, cardiac magnetic resonance (CMR). These scans provide complex data sets that are only partially exploited by clinicians in daily practice, implying potential for improved risk assessment. Computational modelling of left ventricular (LV) function can bridge the gap towards personalised medicine using cardiac imaging in patients with post-MI. Several novel biomechanical parameters have theoretical prognostic value and may be useful to reflect the biomechanical effects of novel preventive therapy for adverse remodelling post-MI. These parameters include myocardial contractility (regional and global), stiffness and stress. Further, the parameters can be delineated spatially to correspond with infarct pathology and the remote zone. While these parameters hold promise, there are challenges for translating MI modelling into clinical practice, including model uncertainty, validation and verification, as well as time-efficient processing. More research is needed to (1) simplify imaging with CMR in patients with post-MI, while preserving diagnostic accuracy and patient tolerance (2) to assess and validate novel biomechanical parameters against established prognostic biomarkers, such as LV ejection fraction and infarct size. Accessible software packages with minimal user interaction are also needed. Translating benefits to patients will be achieved through a multidisciplinary approach including clinicians, mathematicians, statisticians and industry partners.

Improved identifiability of myocardial material parameters by an energy-based cost function

Myocardial stiffness is a valuable clinical biomarker for the monitoring and stratification of heart failure (HF). Cardiac finite element models provide a biomechanical framework for the assessment of stiffness through the determination of the myocardial constitutive model parameters. The reported parameter intercorrelations in popular constitutive relations, however, obstruct the unique estimation of material parameters and limit the reliable translation of this stiffness metric to clinical practice. Focusing on the role of the cost function (CF) in parameter identifiability, we investigate the performance of a set of geometric indices (based on displacements, strains, cavity volume, wall thickness and apicobasal dimension of the ventricle) and a novel CF derived from energy conservation. Our results, with a commonly used transversely isotropic material model (proposed by Guccione et al.), demonstrate that a single geometry-based CF is unable to uniquely constrain the parameter space. The energy-based CF, conversely, isolates one of the parameters and in conjunction with one of the geometric metrics provides a unique estimation of the parameter set. This gives rise to a new methodology for estimating myocardial material parameters based on the combination of deformation and energetics analysis. The accuracy of the pipeline is demonstrated in silico, and its robustness in vivo, in a total of 8 clinical data sets (7 HF and one control). The mean identified parameters of the Guccione material law were [Formula: see text] and [Formula: see text] ([Formula: see text], [Formula: see text], [Formula: see text]) for the HF cases and [Formula: see text] and [Formula: see text] ([Formula: see text], [Formula: see text], [Formula: see text]) for the healthy case.

Improved identifiability of myocardial material parameters by an energy-based cost function

Myocardial stiffness is a valuable clinical biomarker for the monitoring and stratification of heart failure (HF). Cardiac finite element models provide a biomechanical framework for the assessment of stiffness through the determination of the myocardial constitutive model parameters. The reported parameter intercorrelations in popular constitutive relations, however, obstruct the unique estimation of material parameters and limit the reliable translation of this stiffness metric to clinical practice. Focusing on the role of the cost function (CF) in parameter identifiability, we investigate the performance of a set of geometric indices (based on displacements, strains, cavity volume, wall thickness and apicobasal dimension of the ventricle) and a novel CF derived from energy conservation. Our results, with a commonly used transversely isotropic material model (proposed by Guccione et al.), demonstrate that a single geometry-based CF is unable to uniquely constrain the parameter space. The energy-based CF, conversely, isolates one of the parameters and in conjunction with one of the geometric metrics provides a unique estimation of the parameter set. This gives rise to a new methodology for estimating myocardial material parameters based on the combination of deformation and energetics analysis. The accuracy of the pipeline is demonstrated in silico, and its robustness in vivo, in a total of 8 clinical data sets (7 HF and one control). The mean identified parameters of the Guccione material law were [Formula: see text] and [Formula: see text] ([Formula: see text], [Formula: see text], [Formula: see text]) for the HF cases and [Formula: see text] and [Formula: see text] ([Formula: see text], [Formula: see text], [Formula: see text]) for the healthy case.

Estimation of passive and active properties in the human heart using 3D tagged MRI

Advances in medical imaging and image processing are paving the way for personalised cardiac biomechanical modelling. Models provide the capacity to relate kinematics to dynamics and-through patient-specific modelling-derived material parameters to underlying cardiac muscle pathologies. However, for clinical utility to be achieved, model-based analyses mandate robust model selection and parameterisation. In this paper, we introduce a patient-specific biomechanical model for the left ventricle aiming to balance model fidelity with parameter identifiability. Using non-invasive data and common clinical surrogates, we illustrate unique identifiability of passive and active parameters over the full cardiac cycle. Identifiability and accuracy of the estimates in the presence of controlled noise are verified with a number of in silico datasets. Unique parametrisation is then obtained for three datasets acquired in vivo. The model predictions show good agreement with the data extracted from the images providing a pipeline for personalised biomechanical analysis.

Estimation of passive and active properties in the human heart using 3D tagged MRI

Advances in medical imaging and image processing are paving the way for personalised cardiac biomechanical modelling. Models provide the capacity to relate kinematics to dynamics and-through patient-specific modelling-derived material parameters to underlying cardiac muscle pathologies. However, for clinical utility to be achieved, model-based analyses mandate robust model selection and parameterisation. In this paper, we introduce a patient-specific biomechanical model for the left ventricle aiming to balance model fidelity with parameter identifiability. Using non-invasive data and common clinical surrogates, we illustrate unique identifiability of passive and active parameters over the full cardiac cycle. Identifiability and accuracy of the estimates in the presence of controlled noise are verified with a number of in silico datasets. Unique parametrisation is then obtained for three datasets acquired in vivo. The model predictions show good agreement with the data extracted from the images providing a pipeline for personalised biomechanical analysis.

Clinical Diagnostic Biomarkers from the Personalization of Computational Models of Cardiac Physiology

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.

Images as drivers of progress in cardiac computational modelling

Computational models have become a fundamental tool in cardiac research. Models are evolving to cover multiple scales and physical mechanisms. They are moving towards mechanistic descriptions of personalised structure and function, including effects of natural variability. These developments are underpinned to a large extent by advances in imaging technologies. This article reviews how novel imaging technologies, or the innovative use and extension of established ones, integrate with computational models and drive novel insights into cardiac biophysics. In terms of structural characterization, we discuss how imaging is allowing a wide range of scales to be considered, from cellular levels to whole organs. We analyse how the evolution from structural to functional imaging is opening new avenues for computational models, and in this respect we review methods for measurement of electrical activity, mechanics and flow. Finally, we consider ways in which combined imaging and modelling research is likely to continue advancing cardiac research, and identify some of the main challenges that remain to be solved.