Alan D. Freed

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We investigate a method for the numerical solution of the nonlinear fractional differential equation D * α y(t)=f(t,y(t)), equipped with initial conditions y (k)(0)=y 0 (k), k=0,1,...,⌈α⌉−1. Here α may be an arbitrary positive real number, and the differential operator is the Caputo derivative. The numerical method can be seen as a generalization of the(More)
We present a mathematical model for the description of the behavior of viscoplastic materials. The model is based on a nonlinear diierential equation of order , where is a material constant typically in the range 0 < < 1. This equation is coupled with a rst-order diierential equation. For the numerical solution of these equations, we have developed an(More)
A physiologic constitutive expression is presented in algorithmic format for the nonlinear elastic response of wavy collagen fibrils found in soft connective tissues. The model is based on the observation that crimped fibrils in a fascicle have a three-dimensional structure at the micron scale that we approximate as a helical spring. The symmetry of this(More)
BACKGROUND Left ventricular (LV) torsional deformation, based in part on the helical myocardial fiber architecture, is an important component of LV systolic and diastolic performance. However, there is no comprehensive study describing its normal development during childhood and adult life. METHODS AND RESULTS Forty-five normal subjects (25 children and(More)
A viscoelastic model of the K-BKZ (Kaye, Technical Report 134, College of Aeronautics, Cranfield 1962; Bernstein et al., Trans Soc Rheol 7: 391-410, 1963) type is developed for isotropic biological tissues and applied to the fat pad of the human heel. To facilitate this pursuit, a class of elastic solids is introduced through a novel strain-energy function(More)
Most soft tissues possess an oriented architecture of collagen fiber bundles, conferring both anisotropy and nonlinearity to their elastic behavior. Transverse isotropy has often been assumed for a subset of these tissues that have a single macroscopically-identifiable preferred fiber direction. Micro-structural studies, however, suggest that, in some(More)
The airways and parenchyma of lung experience large deformations during normal respiration. Spatially accurate predictions of airflow patterns and aerosol transport therefore require respiration to be modeled as a fluid-structure interaction problem. Such computational models in turn require constitutive models for the parencyhma that are both accurate and(More)
In Part I, a novel hypoelastic framework for soft-tissues was presented. One of the hallmarks of this new theory is that the well-known exponential behavior of soft-tissues arises consistently and spontaneously from the integration of a rate based formulation. In Part II, we examine the application of this framework to the problem of biaxial kinematics,(More)
BACKGROUND Quasilinear viscoelasticity (QLV) theory has been widely and successfully used to describe the time-dependent response of connective tissues. Difficulties remain, however, particularly in material parameter estimation and sensitivities. In this study, we introduce a new alternative: the fractional order viscoelasticity (FOV) theory, which uses a(More)
In this paper, we present the application of a semi-global inverse method for determining material parameters of biological tissues. The approach is based on the successive response surface method, and is illustrated by fitting constitutive parameters to two nonlinear anisotropic constitutive equations, one for aortic sinus and aortic wall, the other for(More)