Robert Cimrman

Cardiac function estimation from MRI using a heart model and data assimilation: advances and difficulties.

In this paper, we present a framework to estimate local ventricular myocardium contractility using clinical MRI, a heart model and data assimilation. First, we build a generic anatomical model of the ventricles including muscle fibre orientations and anatomical subdivisions. Then, this model is deformed to fit a clinical MRI, using a semi-automatic fuzzy segmentation, an affine registration method and a local deformable biomechanical model. An electromechanical model of the heart is then presented and simulated. Finally, a data assimilation procedure is described, and applied to this model. Data assimilation makes it possible to estimate local contractility from given displacements. Presented results on fitting to patient-specific anatomy and assimilation with simulated data are very promising. Current work on model calibration and estimation of patient parameters opens up possibilities to apply this framework in a clinical environment.

Cardiac function estimation from MRI using a heart model and data assimilation: advances and difficulties

In this paper, we present a framework to estimate local ventricular myocardium contractility using clinical MRI, a heart model and data assimilation. First, we build a generic anatomical model of the ventricles including muscle fibre orientations and anatomical subdivisions. Then, this model is deformed to fit a clinical MRI, using a semi-automatic fuzzy segmentation, an affine registration method and a local deformable biomechanical model. An electromechanical model of the heart is then presented and simulated. Finally, a data assimilation procedure is described, and applied to this model. Data assimilation makes it possible to estimate local contractility from given displacements. Presented results on fitting to patient-specific anatomy and assimilation with simulated data are very promising. Current work on model calibration and estimation of patient parameters opens up possibilities to apply this framework in a clinical environment.

The contribution of vascular smooth muscle, elastin and collagen on the passive mechanics of porcine carotid arteries

The main components responsible for the mechanical behavior of the arterial wall are collagen, elastin, and smooth muscle cells (SMCs) in the medial layer. We determined the structural and mechanical changes in porcine carotid arteries after administration of Triton® X-100, elastase, and collagenase using the inflation-deflation test. The arteries were intraluminarly pressurized from 0 to 200 mmHg, and the outer diameter of the artery was measured. The pressure-strain elastic modulus was determined based on the pressure/diameter ratio. The intima-media thickness, wall thickness, thickness of the tunica adventitia layer, and the area fractions of SMCs, elastin, and collagen within the arterial wall (A(A)(SMC/elastin/collagen, wall)) were measured using stereological methods. The relative changes in the relevant components of the treated samples were as follows: the decrease in A(A)(SMC, wall) after administration of Triton® X-100 was 11% ± 7%, the decrease in A(A)(elastin, wall) after administration of elastase was 40% ± 22%, and the decrease in A(A)(collagen, wall) after the application of collagenase was 51% ± 22%. The Triton® X-100 treatment led to a decrease in the SMC content that was associated with enlargement of the arterial wall (outer diameter) for pressures up to 120 mmHg, and with mechanical stiffening of the arterial wall at higher pressures. Elastase led to a decrease in the elastin content that was associated with enlargement of the arterial wall, but not with stiffening or softening. Collagenase led to a decrease in collagen content that was associated with a change in the stiffness of the arterial wall, although the exact contribution of mechanical loading and the duration of treatment (enlargement) could not be quantified.

Microcontinuum approach in biomechanical modeling

The living organs consist of tissues characterized by the hierarchical, very complex inner structure. One of theories taking this into account is the microcontinuum theory elaborated by Eringen [Microcontinuum Field Theories: Foundation and Solids, 1998]. The corresponding mathematical formulation is rather complicated, and therefore, the numerical application is still in progress. In this contribution, the boundary value problem for micropolar and microstretch linear continuum is defined. Using the authors formalism [ZAMM 65 (1985) 417; J. Computat. Appl. Math. 53 (1995) 307] which is based on Buffers work [Ingenieur-Arch. 45 (1976) 17] the corresponding variational principles are developed. These are used for the numerical implementation. The code for micropolar continuum is tested on some examples and used for the bone modeling.

On modelling the parallel diffusion flow in deforming porous media

We present a macroscopic model of the fluid diffusion in deformable porous media, motivated by diffusion-deformation phenomena influencing the heart muscle blood perfusion, or the mechanical properties of kidneys. The problems are described by the displacement field and by several fluid pressure fields associated with parallel porosities interpenetrating the material matrix and mutually separated by interface sectors. The model consists of the equilibrium equation, and a number of mass conservation equations, each incorporating the Darcy law of fluid diffusion. The steady state problem attains the form of the Barenblatt model of parallel flows, while, in the non-steady regime, the coupled diffusion and deformation phenomena induce the apparent viscoelastic behaviour of the bulk material. Numerical examples are given to illustrate some features of the finite element model.

Multiscale FE simulation of diffusion-deformation processes in homogenized dual-porous media

AbstractThe paper deals with a model of the homogenized fluid saturated porous material which recently was obtained by the authors using the asymptotic analysis of the Biot type medium characterized by the double porosity. The homogenized macroscopic model is featured by the fading memory effects arising from the microflow in the dual porosity. We derive the steady state formulations and discuss several topics related to the numerical implementation of the model, namely the solution procedure of the discretized microscopic problems, evaluation of the homogenized coefficients and an approximation of the convolution integrals of the macroscopic model, so that the fading memory effects are computationally tractable. Numerical examples are presented to illustrate the approximation schemes discussed in the paper. All computations were performed using the in-house developed finite element code SfePy allowing the multiscale simulations. Besides various potential engineering applications, the present model is intended for simulations of compact bone poroelasticity.

How to asses, visualize and compare the anisotropy of linear structures reconstructed from optical sections—A study based on histopathological quantification of human brain microvessels

Three-dimensional analyses of the spatial arrangement, spatial orientation and preferential directions of systems of fibers are frequent tasks in many scientific fields, including the textile industry, plant biology and tissue modeling. In biology, systems of oriented and branching lines are often used to represent the three-dimensional directionality and topology of microscopic blood vessels supplying various organs. In our study, we present a novel p(χ²) (chi-square) method for evaluating the anisotropy of line systems that involves comparing the observed length densities of lines with the discrete uniform distribution of an isotropic line system with the χ²-test. Using this method in our open source software, we determined the rose of directions, preferential directions and level of anisotropy of linear systems representing the microscopic blood vessels in samples of various regions from human brains (cortex, subcortical gray matter and white matter). The novel method was compared with two other methods used for anisotropy quantification (ellipsoidal and fractional anisotropy). All three methods detected different levels of anisotropy of blood microvessels in human brain. The microvascular bed in the cortex was closer to an isotropic network, while the microvessels supplying the white matter appeared to be an anisotropic and direction-sensitive system. All three methods were able to determine the differences between various brain regions. The advantage of our p(χ²) method is its high correlation with the number of preferential directions of the line system. However, the software, named esofspy, is able to calculate all three of the measures of anisotropy compared and documented in this paper, thus making the methods freely available to the scientific community.

Modelling heart tissue using a composite muscle model with blood perfusion

Publisher Summary This chapter uses a macroscopic approach to model heart-muscle tissue. Muscle fibers of the heart have the same structure as those of striated muscles. Nevertheless, the bulk behavior of the tissue differs. During a single heartbeat, the volume of heart tissue varies because of the blood flow through numerous capillaries feeding the heart with oxygen and nutritives. Although, for a healthy myocardium, the volume variation is not substantial, its modelling may be of interest for more complex studies. Thus, for the myocardium the usual incompressibility assumption, which is generally accepted for both smooth and striated muscles, should be replaced by a model allowing for blood perfusion of the muscle. The chapter presents a simple model of blood perfusion coupled with the composite model of soft tissues. The model is evaluated using a numerical example simulating the perfusion through the deforming block of heart tissue under a periodic pressure loading and muscle activation.

On identification of the arterial model parameters from experiments applicable in vivo

We present a parameter identification procedure developed for a composite model of arterial wall which is characterized by collagen viscoelastic fibres embedded in hyperelastic incompressible matrix. The structure undergoes large deformation described using the total Lagrangian formulation. In the paper the identification procedure is tested numerically when applied to a simulated vessel dynamic inflation test, which can be performed in vivo. A stability test of the identification method is pursued as illustrated by two examples: the creep and relaxation tests.

A preliminary study into the correlation of stiffness of the laminar junction of the equine hoof with the length density of its secondary lamellae

REASON FOR PERFORMING STUDY The relationship between mechanical behaviour and microscopic structure of the laminar junction of equine hooves under testing conditions requires elucidation. OBJECTIVES To determine mechanical parameters and 2D length density of profiles of secondary lamellae of the laminar junction in the dermal region and to assess possible correlations. METHODS Specimens (25 samples in total) of the laminar junction were taken from front, quarter and heel parts from 3 equine hooves and exposed to a uniaxial tensile test until rupture to obtain Youngs moduli of elasticity, ultimate stress and strain. Neighbouring specimens to those used for the biomechanical experiment were processed histologically to assess the length density of laminar junction basement membrane using stereological grids. RESULTS The estimated median (interquartile range) length density of the laminar junction basement membrane was 0.024 (0.020-0.027)/µm. Youngs modulus of elasticity was 0.15 (0.11-0.35) MPa in the small deformation region, and 7.58 (6.14-8.68) MPa in the linear region was. The ultimate stress was 1.67 (1.41-2.67) MPa, and the ultimate strain was 0.50 (0.38-0.70). The Youngs modulus of elasticity in the region of small deformations has a moderate correlation with the length density of the laminar junction basement membrane. CONCLUSIONS As with most soft biological tissues, the laminar junction has a nonlinear mechanical behaviour. Within the range of small deformations, which correspond to physiological loading of the laminar junction, a higher length density of the laminar junction basement membrane is correlated with a higher resistance of the laminar junction against high stresses transmitted from the distal phalanx to the hoof wall. POTENTIAL RELEVANCE The condition of the laminar junction apparatus may be easily quantified as the length density of profiles of secondary dermal lamellae. This quantification provides a simple tool that could be used for comparing the proneness of the various parts of the laminar junction to initial stages of laminitis.