Ricardo L. Actis

An inverse approach to determining myocardial material properties

Passive myocardial material properties have been measured previously by subjecting test samples of myocardium to in vitro load-deformation analysis or, in the intact heart, by pressure-volume relationships. A new method for determining passive material properties, described in this paper, couples a p-version finite element model of the heart, a nonlinear optimization algorithm and a dense set of transmural measured strains that could be obtained in the intact heart by magnetic resonance imaging (MRI) radiofrequency tissue tagging. Unknown material parameters for a nonlinear, nonhomogeneous material law are determined by solving an inverse boundary value problem. An objective function relating the least-squares difference of model-predicted and measured strains is minimized with respect to the unknown material parameters using a novel optimization algorithm that utilizes forward finite element solutions to calculate derivatives of model-predicted strains with respect to the material parameters. Test cases incorporating several salient features of the inverse material identification problem for the heart are formulated to test the performance of the inverse algorithm in typical experimental conditions. Known true material parameters can be determined to within a small tolerance and random noise is shown not to affect the stability of the inverse solution appreciably. On the basis of these validation experiments, we conclude that the inverse material identification problem for the heart can be extended to solve for unknown material parameters that describe in vivo myocardial material behavior.

Hierarchic models for laminated plates and shells

The definition, essential properties and formulation of hierarchic models for laminated plates and shells are presented. The hierarchic models satisfy three essential requirements: approximability; asymptotic consistency, and optimality of convergence rate. Aspects of implementation are discussed and the performance characteristics are illustrated by examples.

Numerical simulation of the plantar pressure distribution in the diabetic foot during the push-off stance

The primary objective of conservative care for the diabetic foot is to protect the foot from excessive pressures. Pressure reduction and redistribution may be achieved by designing and fabricating orthotic devices based on foot structure, tissue mechanics, and external loads on the diabetic foot. The purpose of this paper is to describe the process used for the development of patient-specific mathematical models of the second and third rays of the foot, their solution by the finite element method, and their sensitivity to model parameters and assumptions. We hypothesized that the least complex model to capture the pressure distribution in the region of the metatarsal heads would include the bony structure segmented as toe, metatarsal and support, with cartilage between the bones, plantar fascia and soft tissue. To check the hypothesis, several models were constructed with different levels of details. The process of numerical simulation is comprised of three constituent parts: model definition, numerical solution and prediction. In this paper the main considerations relating model selection and computation of approximate solutions by the finite element method are considered. The fit of forefoot plantar pressures estimated using the FEA models and those explicitly tested were good as evidenced by high Pearson correlations (rxa0=xa00.70–0.98) and small bias and dispersion. We concluded that incorporating bone support, metatarsal and toes with linear material properties, tendon and fascia with linear material properties, soft tissue with nonlinear material properties, is sufficient for the determination of the pressure distribution in the metatarsal head region in the push-off position, both barefoot and with shoe and total contact insert. Patient-specific examples are presented.

Multi-plug insole design to reduce peak plantar pressure on the diabetic foot during walking

There is evidence that appropriate footwear is an important factor in the prevention of foot pain in otherwise healthy people or foot ulcers in people with diabetes and peripheral neuropathy. A standard care for reducing forefoot plantar pressure is the utilization of orthotic devices such as total contact inserts (TCI) with therapeutic footwear. Most neuropathic ulcers occur under the metatarsal heads, and foot deformity combined with high localized plantar pressure, appear to be the most significant factors contributing to these ulcers. In this study, patient-specific finite element models of the second ray of the foot were developed to study the influence of TCI design on peak plantar pressure (PPP) under the metatarsal heads. A typical full contact insert was modified based on the results of finite element analyses, by inserting 4xa0mm diameter cylindrical plugs of softer material in the regions of high pressure. Validation of the numerical model was addressed by comparing the numerical results obtained by the finite element method with measured pressure distribution in the region of the metatarsal heads for a shoe and TCI condition. Two subjects, one with a history of forefoot pain and one with diabetes and peripheral neuropathy, were tested in the laboratory while wearing therapeutic shoes and customized inserts. The study showed that customized inserts with softer plugs distributed throughout the regions of high plantar pressure reduced the PPP over that of the TCI alone. This supports the outcome as predicted by the numerical model, without causing edge effects as reported by other investigators using different plug designs, and provides a greater degree of flexibility for customizing orthotic devices than current practice allows.

Myocardial material property determination in the in vivo heart using magnetic resonance imaging

Objectives: To determine nonlinear material properties of passive, diastolic myocardium using magnetic resonance imaging (MRI) tissue-tagging, finite element analysis (FEA) and nonlinear optimization.Background: Alterations in the diastolic material properties of myocardium may pre-date the onset of or exist exclusive of systolic ventricular dysfunction in disease states such as hypertrophy and heart failure. Accordingly, significant effort has been expended recently to characterize the material properties of myocardium in diastole. The present study defines a new technique for determining material properties of passive myocardium using finite element (FE) models of the heart, MRI tissue-tagging and nonlinear optimization. This material parameter estimation algorithm is employed to estimate nonlinear material parameters in thein vivo canine heart and provides the necessary framework to study the full complexities of myocardial material behavior in health and disease.Methods and results: Material parameters for a proposed exponential strain energy function were determined by minimizing the least squares difference between FE model-predicted and MRI-measured diastolic strains. Six mongrel dogs underwent MRI imaging with radiofrequency (RF) tissue-tagging. Two-dimensional diastolic strains were measured from the deformations of the MRI tag lines. Finite element models were constructed from early diastolic images and were loaded with the mean early to late left ventricular and right ventricular diastolic change in pressure measured at the time of imaging. A nonlinear optimization algorithm was employed to solve the least squares objective function for the material parameters. Average material parameters for the six dogs wereE=28,722 ± 15,984 dynes/cm2 andc=0.00182 ± 0.00232 cm2/dyne.Conclusion: This parameter estimation algorithm provides the necessary framework for estimating the nonlinear, anisotropic and non-homogeneous material properties of passive myocardium in health and disease in thein vivo beating heart.

Finite element modeling and experimental verification of lower extremity shape change under load

Prediction and measurement of residuum shape change inside the prosthesis under various loading conditions is important for prosthesis design and evaluation. Residual limb surface measurements with the prosthesis in situ were used for construction of a finite element model (FEM). These surface measurements were obtained from volumetric computed tomography. A new experimental method for modeling the shape of the in situ lower residual limb was developed based on spiral X-ray computed tomography (SXCT) imaging. The p-version of the finite element method was used for estimating the material properties from known load and displacement data. A homogeneous, isotropic, linear constitutive model with accommodation of the constitutive soft and hard tissues of the residuum was evaluated with static axial loading applied to the in situ prosthesis and compared with experimental results obtained in a human volunteer. Two FEMs were created for similar coronal cross sections of the below knee residuum under two loading conditions. Agreement between observed (from SXCT) and predicted (from FEA) residual limb shape changes inside the prosthesis were maximized with a single modulus of elasticity for the residuum soft tissue of 0.06 MPa, consistent with previously published results. This methodology provides a framework to predict and objectively evaluate FEMs and determine residuum material properties by inverse methods.

MRI-Radiofrequency Tissue Tagging in Patients With Aortic Insufficiency Before and After Operation

BACKGROUNDnMagnetic resonance imaging tissue tagging is a relatively recent methodology that describes ventricular systolic function in terms of intramyocardial ventricular deformation. Because the analysis involves the use of many intramyocardial points to describe systolic deformation, it is theoretically more sensitive at describing subtle differences in regional myocardial fiber shortening when compared with conventional measures of ventricular function such as wall thickening. The objectives of this study were (1) to define sensitive indices of ventricular systolic deformation to assist the clinician in the surgical evaluation of patients with aortic insufficiency, and (2) to quantify differences in regional systolic deformation before and after surgery for aortic insufficiency.nnnMETHODSnMagnetic resonance imaging with tissue tagging was performed on 10 normal volunteers and 8 patients with chronic severe aortic insufficiency. Follow-up postoperative studies (5.4+/-1.1 months) were obtained in 6 patients who underwent Ross procedure (1 patient), David procedure (1), and St. Jude aortic valve replacement (4).nnnRESULTSnThere was no significant difference in fractional area change, overall circumferential shortening, or overall radial thickening among the normal group, the preoperative aortic insufficiency group, or the postoperative aortic insufficiency group. However, on a regional basis, there was a decrease in posterior wall circumferential strains in the postoperative aortic insufficiency group (29%+/-13% preoperative aortic insufficiency (n=6) versus 24%+/-12% postoperative aortic insufficiency (n=6), p=0.02).nnnCONCLUSIONSnOn regional analysis, there was a small but significant decrease in posterior wall circumferential shortening after operation. Magnetic resonance imaging tissue tagging is a sensitive and clinically applicable method of quantifying regional ventricular wall function before and after intervention for aortic insufficiency.

Solution of elastic-plastic stress analysis problems by the p-version of the finite element method

The solution of small-strain elastic-plastic stress analysis problems by the p-version of the finite element method is discussed. The formulation is based on the deformation theory of plasticity and the displacement method. Practical realization of controlling discretization errors for elastic-plastic problems is the main focus of the paper. Numerical examples, whicii include comparisons between the deformation and incremental theories of plasticity under tight control of discretization errors, are presented.

Finite element analysis in professional practice

Abstract The use of finite element analysis (FEA) software products in mechanical and structural design are examined. It is found that current FEA software products are being under-utilized because they do not satisfy the requirements of the design process well. Specifications for future FEA software products are outlined.

Ventricular interaction in the pathologic heart: A model based study

The effects of direct ventricular interaction and interaction mediated by the pericardium on the diastolic left ventricle (LV) were quantified using idealized models of five pathologic conditions. Two-dimensional (2D) mathematical models were constructed in long and short axis views of four pathologic LV conditions and the normal heart (NL): dilated cardiomyopathy (DCM), concentric LV hypertrophy (HYP), chronic anterior-apical infarction in a normal shaped LV (CAINL), and CAI in a dilated LV (CAID). To assess the effects of RV pressure increase on the LV mechanical state, RV pressure was systematically increased for several LV pressures and changes in the LV diastolic pressure-area relationships, and LV free wall and septal principal stresses and strains were quantified. At higher RV pressures, with pericardial effects included in the models, the pressure-area relationship was similar for all models, indicating that, at these higher pressures, the effects of RV and pericardial pressures are more important than global LV shape, wall thickness, or material properties in determining the pressure-area relationship. There were significant differences among models in the changes in LV free wall and septal stress and strain after an increase in RV pressure. These models may be of use in predicting interaction in the corresponding clinical state.