Bio


Pinsky works in the theory and practice of computational mechanics with a particular interest in multiphysics problems in biomechanics. His work uses the close coupling of techniques for molecular, statistical and continuum mechanics with biology, chemistry and clinical science. Areas of current interest include the mechanics of human vision (ocular mechanics) and the mechanics of hearing. Topics in the mechanics of vision include the mechanics of transparency, which investigates the mechanisms by which corneal tissue self-organizes at the molecular scale using collagen-proteoglycan-ion interactions to explain the mechanical resilience and almost perfect transparency of the tissue and to provide a theoretical framework for engineered corneal tissue replacement. At the macroscopic scale, advanced imaging data is used to create detailed models of the 3-D organization of collagen fibrils and the results used to predict outcomes of clinical techniques for improving vision as well as how diseased tissue mechanically degrades. Theories for mass transport and reaction are being developed to model metabolic processes and swelling in tissue. Current topics in the hearing research arena include multiscale modeling of hair-cell mechanics in the inner ear including physical mechanisms for the activation of mechanically-gated ion channels. Supporting research addresses the mechanics of lipid bilayer cell membranes and their interaction with the cytoskeleton. Recent past research topics include computational acoustics for exterior, multifrequency and inverse problems; and multiscale modeling of transdermal drug delivery. Professor Pinsky currently serves as Chair of the Mechanics and Computation Group within the Department of Mechanical Engineering at Stanford.

Academic Appointments


Honors & Awards


  • Executive Committee Member, US Association for Computational Mechanics as Member-At-Large (2008-12)
  • Editorial Board, Engineering Computations & International Journal for Computer-Aided Engineering and Software (2002)
  • Editorial Board, Computer Methods in Applied Mechanics and Engineering (2003 -12)
  • Fellow, International Association of Computational Mechanics (2002)
  • Fellow, American Society of Mechanical Engineers (1998)

Professional Education


  • PhD, University of California, Berkeley, Civil Engineering (1981)
  • M.Sc, University of Toronto, Civil Engineering (1971)
  • B.Sc. (Hons), University of Wales, Swansea, Civil Engineering (1969)

2013-14 Courses


Journal Articles


  • The role of 3-D collagen organization in stromal elasticity: a model based on X-ray diffraction data and second harmonic-generated images BIOMECHANICS AND MODELING IN MECHANOBIOLOGY Petsche, S. J., Pinsky, P. M. 2013; 12 (6): 1101-1113

    Abstract

    Examining the cross-section of the human cornea with second harmonic-generated (SHG) imaging shows that many lamellae do not lie parallel to the cornea's anterior surface but have inclined trajectories that take them through the corneal thickness with a depth-dependent distribution. A continuum mechanics-based model of stromal elasticity is developed based on orientation information extracted and synthesized from both X-ray scattering studies and SHG imaging. The model describes the effects of inclined lamella orientation by introducing a probability function that varies with depth through the stroma, which characterizes the range and distribution of lamellae at inclined angles. When combined with the preferred lamellar orientations found from X-ray scattering experiments, a fully 3-D representation of lamella orientation is achieved. Stromal elasticity is calculated by a weighted average of individual lamella properties based on the spatially varying 3-D orientation distribution. The model is calibrated with in vitro torsional shear experiments and in vivo indentation data and then validated with an in vitro inflation study. A quantitative explanation of the experimentally measured depth dependence of mechanical properties emerges from the model. The significance of the 3-D lamella orientation in the mechanics of the human cornea is demonstrated by investigating and contrasting the effects of previous modeling assumptions made on lamella orientation.

    View details for DOI 10.1007/s10237-012-0466-8

    View details for Web of Science ID 000325815300003

    View details for PubMedID 23288406

  • The elusive hair cell gating spring, a potential role for the lipid membrane. journal of the Acoustical Society of America Kim, J., Pinsky, P. M., Steele, C. R., Puria, S., Ricci, A. J. 2013; 133 (5): 3509-?

    Abstract

    Deflection of auditory hair cell hair bundle results in a nonlinear (i.e., non Hookean) force-displacement relationships whose molecular mechanism remains elusive. A gating spring model posits that mechanosensitive channels are in series with a spring such that channel opening puts the activation gate in series with the spring, thus reducing spring extension until further stimulation is provided. Here we present a theoretical analysis of whether the lipid membrane might be the source of nonlinearity. A hair bundle kinematic model is coupled with a lipid membrane model that includes a diffusible compartment into which the tip-link embeds and a minimally diffusive reservoir pool. Using physiological parameters, this model was capable of reproducing nonlinear force-displacement plots, including a negative stiffness component but required a standing tip-link tension. In addition, this model suggests the mechanotransducer channel is most sensitive to curvature forces that are located within 2 nm of the tip-link. [Work supported in part by Grant Nos. R01-DC07910 and R01-DC03896 from the NIDCD of NIH and by The Timoshenko fund from Mechanical Engineering Department at Stanford University].

    View details for DOI 10.1121/1.4806258

    View details for PubMedID 23655592

  • Depth-Dependent Transverse Shear Properties of the Human Corneal Stroma INVESTIGATIVE OPHTHALMOLOGY & VISUAL SCIENCE Petsche, S. J., Chernyak, D., Martiz, J., Levenston, M. E., Pinsky, P. M. 2012; 53 (2): 873-880

    Abstract

    To measure the transverse shear modulus of the human corneal stroma and its profile through the depth by mechanical testing, and to assess the validity of the hypothesis that the shear modulus will be greater in the anterior third due to increased interweaving of lamellae.Torsional rheometry was used to measure the transverse shear properties of 6 mm diameter buttons of matched human cadaver cornea pairs. One cornea from each pair was cut into thirds through the thickness with a femtosecond laser and each stromal third was tested individually. The remaining intact corneas were tested to measure full stroma shear modulus. The shear modulus from a 1% shear strain oscillatory test was measured at various levels of axial compression for all samples.After controlling for axial compression, the transverse shear moduli of isolated anterior layers were significantly higher than central and posterior layers. Mean modulus values at 0% axial strain were 7.71 ± 6.34 kPa in the anterior, 1.99 ± 0.45 kPa in the center, 1.31 ± 1.01 kPa in the posterior, and 9.48 ± 2.92 kPa for full thickness samples. A mean equilibrium compressive modulus of 38.7 ± 8.6 kPa at 0% axial strain was calculated from axial compression measured during the shear tests.Transverse shear moduli are two to three orders of magnitude lower than tensile moduli reported in the literature. The profile of shear moduli through the depth displayed a significant increase from posterior to anterior. This gradient supports the hypothesis and corresponds to the gradient of interwoven lamellae seen in imaging of stromal cross-sections.

    View details for DOI 10.1167/iovs.11-8611

    View details for Web of Science ID 000302788600046

    View details for PubMedID 22205608

  • A nonlinear macroscopic multi-phasic model for describing interactions between solid, fluid and ionic species in biological tissue materials PHILOSOPHICAL MAGAZINE Li, L., Pinsky, P. M. 2011; 91 (2): 311-325
  • Matrix-Pade via Lanczos solutions for vibrations of fluid-structure interaction INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING Liew, H., Pinsky, P. M. 2010; 84 (10): 1183-1204

    View details for DOI 10.1002/nme.2936

    View details for Web of Science ID 000284204400003

  • DEPTH DEPENDENT IN-PLANE SHEAR PROPERTIES OF THE CORNEAL STROMA PROCEEDINGS OF THE ASME SUMMER BIOENGINEERING CONFERENCE, 2010 Petsche, S., Pinsky, P., Chernyak, D., Martiz, J. 2010: 397-398
  • Multiscale Modeling Framework of Transdermal Drug Delivery ANNALS OF BIOMEDICAL ENGINEERING Rim, J. E., Pinsky, P. M., van Osdol, W. W. 2009; 37 (6): 1217-1229

    Abstract

    This study addresses the modeling of transdermal diffusion of drugs to better understand the permeation of molecules through the skin, especially the stratum corneum, which forms the main permeation barrier to percutaneous permeation. In order to ensure reproducibility and predictability of drug permeation through the skin and into the body, a quantitative understanding of the permeation barrier properties of the stratum corneum (SC) is crucial. We propose a multiscale framework of modeling the multicomponent transdermal diffusion of molecules. The problem is divided into subproblems of increasing length scale: microscopic, mesoscopic, and macroscopic. First, the microscopic diffusion coefficient in the lipid bilayers of the SC is found through molecular dynamics (MD) simulations. Then, a homogenization procedure is performed over a model unit cell of the heterogeneous SC, resulting in effective diffusion parameters. These effective parameters are the macroscopic diffusion coefficients for the homogeneous medium that is "equivalent" to the heterogeneous SC, and thus can be used in finite element simulations of the macroscopic diffusion process. The resulting drug flux through the skin shows very reasonable agreement to experimental data.

    View details for DOI 10.1007/s10439-009-9678-1

    View details for Web of Science ID 000265787100015

    View details for PubMedID 19319682

  • Modeling electrostatic force microscopy for conductive and dielectric samples using the boundary element method ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS Shen, Y., Barnett, D. M., Pinsky, P. M. 2008; 32 (8): 682-691
  • Finite element modeling of acousto-mechanical coupling in the cat middle ear JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA Tuck-Lee, J. P., Pinsky, P. M., Steele, C. R., Puria, S. 2008; 124 (1): 348-362

    Abstract

    The function of the middle ear is to transfer acoustic energy from the ear canal to the cochlea. An essential component of this system is the tympanic membrane. In this paper, a new finite element model of the middle ear of the domestic cat is presented, generated in part from cadaver anatomy via microcomputed tomographic imaging. This model includes a layered composite model of the eardrum, fully coupled with the acoustics in the ear canal and middle-ear cavities. Obtaining the frequency response from 100 Hz to 20 kHz is a computationally challenging task, which has been accomplished by using a new adaptive implementation of the reduced-order matrix Padé-via-Lanczos algorithm. The results are compared to established physiological data. The fully coupled model is applied to study the role of the collagen fiber sublayers of the eardrum and to investigate the relationship between the structure of the middle-ear cavities and its function. Three applications of this model are presented, demonstrating the shift in the middle-ear resonance due to the presence of the septum that divides the middle-ear cavity space, the significance of the radial fiber layer on high frequency transmission, and the importance of the transverse shear modulus in the eardrum microstructure.

    View details for DOI 10.1121/1.2912438

    View details for Web of Science ID 000257768000034

    View details for PubMedID 18646982

  • Analytic perturbation solution to the capacitance system of a hyberboloidal tip and a rough surface APPLIED PHYSICS LETTERS Shen, Y., Barnett, D. M., Pinsky, P. M. 2008; 92 (13)

    View details for DOI 10.1063/1.2906487

    View details for Web of Science ID 000254669900117

  • Simulating and interpreting Kelvin probe force microscopy images on dielectrics with boundary integral equations REVIEW OF SCIENTIFIC INSTRUMENTS Shen, Y., Barnett, D. M., Pinsky, P. M. 2008; 79 (2)

    Abstract

    Kelvin probe force microscopy (KPFM) is designed for measuring the tip-sample contact potential differences by probing the sample surface, measuring the electrostatic interaction, and adjusting a feedback circuit. However, for the case of a dielectric (insulating) sample, the contact potential difference may be ill defined, and the KPFM probe may be sensing electrostatic interactions with a certain distribution of sample trapped charges or dipoles, leading to difficulty in interpreting the images. We have proposed a general framework based on boundary integral equations for simulating the KPFM image based on the knowledge about the sample charge distributions (forward problem) and a deconvolution algorithm solving for the trapped charges on the surface from an image (inverse problem). The forward problem is a classical potential problem, which can be efficiently solved using the boundary element method. Nevertheless, the inverse problem is ill posed due to data incompleteness. For some special cases, we have developed deconvolution algorithms based on the forward problem solution. As an example, this algorithm is applied to process the KPFM image of a gadolinia-doped ceria thin film to solve for its surface charge density, which is a more relevant quantity for samples of this kind than the contact potential difference (normally only defined for conductive samples) values contained in the raw image.

    View details for DOI 10.1063/1.2885679

    View details for Web of Science ID 000254194400034

    View details for PubMedID 18315309

  • Adaptive frequency windowing for multifrequency solutions in structural acoustics based on the matrix Pade-via-Lanczos algorithm INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING Tuck-Lee, J. P., Pinsky, P. M. 2008; 73 (5): 728-746

    View details for DOI 10.1002/nme.2102

    View details for Web of Science ID 000253694000007

  • A resolution study for electrostatic force microscopy on bimetallic samples using the boundary element method NANOTECHNOLOGY Shen, Y., Lee, M., Lee, W., Barnett, D. M., Pinsky, P., Prinz, F. B. 2008; 19 (3)

    Abstract

    Electrostatic force microscopy (EFM) is a special design of non-contact atomic force microscopy used for detecting electrostatic interactions between the probe tip and the sample. Its resolution is limited by the finite probe size and the long-range characteristics of electrostatic forces. Therefore, quantitative analysis is crucial to understanding the relationship between the actual local surface potential distribution and the quantities obtained from EFM measurements. To study EFM measurements on bimetallic samples with surface potential inhomogeneities as a special case, we have simulated such measurements using the boundary element method and calculated the force component and force gradient component that would be measured by amplitude modulation (AM) EFM and frequency modulation (FM) EFM, respectively. Such analyses have been performed for inhomogeneities of various shapes and sizes, for different tip-sample separations and tip geometries, for different applied voltages, and for different media (e.g., vacuum or water) in which the experiment is performed. For a sample with a surface potential discontinuity, the FM-EFM resolution expression agrees with the literature; however, the simulation for AM-EFM suggests the existence of an optimal tip radius of curvature in terms of resolution. On the other hand, for samples with strip- and disk-shaped surface potential inhomogeneities, we have obtained quantitative expressions for the detectability size requirements as a function of experimental conditions for both AM- and FM-EFMs, which suggest that a larger tip radius of curvature is moderately favored for detecting the presence of such inhomogeneities.

    View details for DOI 10.1088/0957-4484/19/03/035710

    View details for Web of Science ID 000252967700035

    View details for PubMedID 21817595

  • Using the method of homogenization to calculate the effective diffusivity of the stratum corneum with permeable corneocytes JOURNAL OF BIOMECHANICS Rim, J. E., Pinsky, P. M., van Osdol, W. W. 2008; 41 (4): 788-796

    Abstract

    The stratum corneum is the outermost layer of the skin, which acts as a barrier membrane against the penetration of molecules into and out of the body. It has a biphasic structure consisting of keratinized cells (corneocytes) that are embedded in a lipid matrix. The macroscopic transport properties of the stratum corneum are functions of its microstructure and the transport properties of the corneocytes and the lipid matrix, and are of considerable interest in the context of transdermal drug delivery and quantifying exposure to toxins, as well as for determining the relation of skin disorders to disruption of the stratum corneum barrier. Due to the complexity of the tissue and the difference in length scales involved in its microstructure, a direct analysis of the mass transport properties of the stratum corneum is not feasible. In this study, we undertake an approach where the macroscopic diffusion tensor of the stratum corneum is obtained through homogenization using the method of asymptotic expansions. The biphasic structure of the stratum corneum is fully accounted for by allowing the corneocytes to be permeable and considering the partitioning between the corneocytes and the lipid phases. By systematically exploring the effect of permeable corneocytes on the macroscopic transport properties of the stratum corneum, we show that solute properties such as lipophilicity and relative permeabilities in the two phases have large effects on its transdermal diffusion behavior.

    View details for DOI 10.1016/j.jbiomech.2007.11.011

    View details for Web of Science ID 000254677400008

    View details for PubMedID 18093598

  • Using the method of homogenization to calculate the effective diffusivity of the stratum corneum JOURNAL OF MEMBRANE SCIENCE Rim, J. E., Pinsky, P. M., van Osdol, W. W. 2007; 293 (1-2): 174-182
  • Finite element modeling of coupled diffusion with partitioning in transdermal drug delivery ANNALS OF BIOMEDICAL ENGINEERING Rim, J. E., PINSKY, P. M., van Osdol, W. W. 2005; 33 (10): 1422-1438

    Abstract

    The finite element method is employed to simulate two-dimensional (axisymmetric) drug diffusion from a finite drug reservoir into the skin. The numerical formulation is based on a general mathematical model for multicomponent nonlinear diffusion that takes into account the coupling effects between the different components. The presence of several diffusing components is crucial, as many transdermal drug delivery formulations contain one or more permeation enhancers in addition to the drug. The coupling between the drug and permeation enhancer(s) results in nonlinear diffusion with concentration-dependent diffusivities of the various components. The framework is suitable for modeling both linear and nonlinear, single- and multicomponent diffusions, however, as it reduces to the correct formulation simply by setting the relevant parameters to zero. In addition, we show that partitioning of the penetrants from the reservoir into the skin can be treated in a straightforward manner in this framework using the mixed method. Partitioning at interface boundaries poses some difficulty with the standard finite element method as it creates a discontinuity in the concentration variable at the interface. To our knowledge, nonlinear (concentration-dependent) partitioning in diffusion problems has not been treated numerically before, and we demonstrate that nonlinear partitioning may have an important role in the effect of permeation enhancers. The mixed method that we adopt includes the flux at the interface explicitly in the formulation, allowing the modeling of concentration-dependent partitioning of the permeants between the reservoir and the skin as well as constant (linear) partitioning. The result is a versatile finite element framework suitable for modeling both linear and nonlinear diffusions in heterogeneous media where the diffusivities and partition coefficients may vary in each subregion.

    View details for DOI 10.1007/s10439-005-5788-6

    View details for Web of Science ID 000232758300012

    View details for PubMedID 16240090

  • A 3D model of muscle reveals the causes of nonuniform strains in the biceps brachii JOURNAL OF BIOMECHANICS Blemker, S. S., PINSKY, P. M., Delp, S. L. 2005; 38 (4): 657-665

    Abstract

    Biomechanical models generally assume that muscle fascicles shorten uniformly. However, dynamic magnetic resonance (MR) images of the biceps brachii have recently shown nonuniform shortening along some muscle fascicles during low-load elbow flexion (J. Appl. Physiol. 92 (2002) 2381). The purpose of this study was to uncover the features of the biceps brachii architecture and material properties that could lead to nonuniform shortening. We created a three-dimensional finite-element model of the biceps brachii and compared the tissue strains predicted by the model with experimentally measured tissue strains. The finite-element model predicted strains that were within one standard deviation of the experimentally measured strains. Analysis of the model revealed that the variation in fascicle lengths within the muscle and the curvature of the fascicles were the primary factors contributing to nonuniform strains. Continuum representations of muscle, combined with in vivo image data, are needed to deepen our understanding of how complex geometric arrangements of muscle fibers affect muscle contraction mechanics.

    View details for DOI 10.1016/j.jbiomech.2004.04.009

    View details for Web of Science ID 000227590400002

    View details for PubMedID 15713285

  • Recovery of shear modulus in elastography using an ajoint method with B-spline representation FINITE ELEMENTS IN ANALYSIS AND DESIGN Liew, H. L., Pinsky, P. M. 2005; 41 (7-8): 778-799
  • Computational modeling of mechanical anisotropy in the cornea and sclera JOURNAL OF CATARACT AND REFRACTIVE SURGERY Pinsky, P. M., van der Heide, D., Chernyak, D. 2005; 31 (1): 136-145

    Abstract

    To determine the biomechanical deformation of the cornea resulting from tissue cutting and removal by use of a new computational model and to investigate the effect of mechanical anisotrophy resulting from the fibrillar architecture.Department of Mechanical Engineering, Stanford University, Stanford, California, USA.A mathematical model for a typical lamella that explicitly accounts for the strain energy of the collagen fibrils, extrafibrillar matrix, and proteoglycan cross-linking was developed. A stromal model was then obtained by generalized averaging of the lamella properties through the stromal thickness, taking into account the preferred orientations of the collagen fibrils, which were obtained from x-ray scattering data.The model was used to predict astigmatism induced by a tunnel incision in the sclera, such as is used for cataract extraction and intraocular lens implantation. The amount of induced cylinder was in good agreement with published clinical data. Results show it is important for the model to incorporate preexisting corneal physiological stress caused by intraocular pressure.The mathematical model described appears to provide a framework for further development, capturing the essential features of mechanical anisotropy of the cornea. The tunnel incision simulation indicated the importance of the anisotropy in this case.

    View details for DOI 10.1016/j.jcrs.2004.10.048

    View details for Web of Science ID 000227227000031

    View details for PubMedID 15721706

  • An application of shape optimization in the solution of inverse acoustic scattering problems INVERSE PROBLEMS Feijoo, G. R., Oberai, A. A., PINSKY, P. M. 2004; 20 (1): 199-228
  • Application of Pade via Lanczos approximations for efficient multifrequency solution of Helmholtz problems JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA Wagner, M. M., PINSKY, P. M., Malhotra, M. 2003; 113 (1): 313-319

    Abstract

    This paper addresses the efficient solution of acoustic problems in which the primary interest is obtaining the solution only on restricted portions of the domain but over a wide range of frequencies. The exterior acoustics boundary value problem is approximated using the finite element method in combination with the Dirichlet-to-Neumann (DtN) map. The restriction domain problem is formally posed in transfer function form based on the finite element solution. In order to obtain the solution over a range of frequencies, a matrix-valued Padé approximation of the transfer function is employed, using a two-sided block Lanczos algorithm. This approach provides a stable and efficient representation of the Padé approximation. In order to apply the algorithm, it is necessary to reformulate the transfer function due to the frequency dependency in the nonreflecting boundary condition. This is illustrated for the case of the DtN boundary condition, but there is no restriction on the approach which can also be applied to other radiation boundary conditions. Numerical tests confirm that the approach offers significant computational speed-up.

    View details for DOI 10.1121/1.1514932

    View details for Web of Science ID 000180485000032

    View details for PubMedID 12558270

  • A Krylov subspace projection method for simultaneous solution of Helmholtz problems at multiple frequencies COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING Wagner, M. M., PINSKY, P. M., Oberai, A. A., Malhotra, M. 2003; 192 (41-42): 4609-4640
  • Shape sensitivity calculations for exterior acoustics problems ENGINEERING COMPUTATIONS Feijoo, G. R., Malhotra, M., Oberai, A. A., PINSKY, P. M. 2001; 18 (3-4): 376-391
  • A residual-based finite element method for the Helmholtz equation INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING Oberai, A. A., PINSKY, P. M. 2000; 49 (3): 399-419
  • A numerical comparison of finite element methods for the Helmholtz equation JOURNAL OF COMPUTATIONAL ACOUSTICS Oberai, A. A., PINSKY, P. M. 2000; 8 (1): 211-221
  • Efficient computation of multi-frequency far-field solutions of the Helmholtz equation using Pade approximation JOURNAL OF COMPUTATIONAL ACOUSTICS Malhotra, M., PINSKY, P. M. 2000; 8 (1): 223-240
  • On the implementation of the Dirichlet-to-Neumann radiation condition for iterative solution of the Helmholtz equation APPLIED NUMERICAL MATHEMATICS Oberai, A. A., Malhotra, M., PINSKY, P. M. 1998; 27 (4): 443-464
  • Parallel preconditioning based on h-hierarchical finite elements with application to acoustics COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING Malhotra, M., PINSKY, P. M. 1998; 155 (1-2): 97-117
  • Galerkin Generalized Least Squares finite element methods for time-harmonic structural acoustics COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING Grosh, K., PINSKY, P. M. 1998; 154 (3-4): 299-318
  • A multiscale finite element method for the Helmholtz equation COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING Oberai, A. A., PINSKY, P. M. 1998; 154 (3-4): 281-297
  • Iterative solution of multiple radiation and scattering problems in structural acoustics using a block quasi-minimal residual algorithm COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING Malhotra, M., Freund, R. W., PINSKY, P. M. 1997; 146 (1-2): 173-196
  • A matrix-free interpretation of the non-local Dirichlet-to-Neumann radiation boundary condition INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING Malhotra, M., PINSKY, P. M. 1996; 39 (21): 3705-3713
  • Stabilized Element Residual Method (SERM): A posteriori error estimation for the advection-diffusion equation JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS Agarwal, A. N., PINSKY, P. M. 1996; 74 (1-2): 3-17
  • A space-time finite element method for structural acoustics in infinite domains .2. Exact time-dependent non-reflecting boundary conditions COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING Thompson, L. L., PINSKY, P. M. 1996; 132 (3-4): 229-258
  • A space-time finite element method for the exterior acoustics problem JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA Thompson, L. L., PINSKY, P. M. 1996; 99 (6): 3297-3311
  • A space-time finite element method for structural acoustics in infinite domains .1. Formulation, stability and convergence COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING Thompson, L. L., PINSKY, P. M. 1996; 132 (3-4): 195-227
  • A space-time finite element method for the exterior structural acoustics problem: Time-dependent radiation boundary conditions in two space dimensions INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING Thompson, L. L., PINSKY, P. M. 1996; 39 (10): 1635-?
  • Design of Galerkin Generalized Least Squares methods for Timoshenko beams COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING Grosh, K., PINSKY, P. M. 1996; 132 (1-2): 1-16
  • A Finite element method for the Helmholtz equation based on a subgrid scale model NUMERICAL METHODS IN ENGINEERING '96 Oberai, A. A., PINSKY, P. M. 1996: 79-85
  • NUMERICAL-SOLUTION OF 2-CARRIER HYDRODYNAMIC SEMICONDUCTOR-DEVICE EQUATIONS EMPLOYING A STABILIZED FINITE-ELEMENT METHOD COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING Aluru, N. R., Law, K. H., Raefsky, A., PINSKY, P. M., DUTTON, R. W. 1995; 125 (1-4): 187-220
  • An analysis of the hydrodynamic semiconductor device model - Boundary conditions and simulations COMPEL-THE INTERNATIONAL JOURNAL FOR COMPUTATION AND MATHEMATICS IN ELECTRICAL AND ELECTRONIC ENGINEERING Aluru, N. R., Law, K. H., PINSKY, P. M., DUTTON, R. W. 1995; 14 (2-3): 157-185
  • A GALERKIN LEAST-SQUARES FINITE-ELEMENT METHOD FOR THE 2-DIMENSIONAL HELMHOLTZ-EQUATION INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING Thompson, L. L., PINSKY, P. M. 1995; 38 (3): 371-397
  • SELECTED PAPERS FROM THE SYMPOSIUM ON COMPUTATIONAL STRUCTURAL ACOUSTICS, 2ND UNITED-STATES-NATIONAL-CONGRESS ON COMPUTATIONAL MECHANICS - PREFACE INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING PINSKY, P. M. 1994; 37 (17): 2891-2891
  • COMPLEX WAVE-NUMBER DISPERSION ANALYSIS OF GALERKIN AND GALERKIN LEAST-SQUARES METHODS FOR FLUID-LOADED PLATES COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING Grosh, K., PINSKY, P. M. 1994; 113 (1-2): 67-98
  • GALERKIN GENERALIZED LEAST SQUARES METHODS FOR INVACUO AND FLUID-LOADED TIMOSHENKO BEAMS RECENT DEVELOPMENTS IN FINITE ELEMENT ANALYSIS PINSKY, P. M., Grosh, K. 1994: 47-61
  • COMPLEX WAVE-NUMBER FOURIER-ANALYSIS OF THE P-VERSION FINITE-ELEMENT METHOD COMPUTATIONAL MECHANICS Thompson, L. L., PINSKY, P. M. 1994; 13 (4): 255-275
  • A FINITE-ELEMENT FORMULATION FOR THE HYDRODYNAMIC SEMICONDUCTOR-DEVICE EQUATIONS COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING Aluru, N. R., Raefsky, A., PINSKY, P. M., Law, K. H., GOOSSENS, R. J., DUTTON, R. W. 1993; 107 (1-2): 269-298
  • NEW GENERALIZED GALERKIN LEAST-SQUARES FINITE-ELEMENT METHODS FOR WAVE-PROPAGATION IN TIMOSHENKO BEAMS SECOND INTERNATIONAL CONFERENCE ON MATHEMATICAL AND NUMERICAL ASPECTS OF WAVE PROPAGATION Grosh, K., PINSKY, P. M. 1993: 237-245
  • FINITE-ELEMENT DISPERSION ANALYSIS FOR THE 3-DIMENSIONAL 2ND-ORDER SCALAR WAVE-EQUATION INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING ABBOUD, N. N., PINSKY, P. M. 1992; 35 (6): 1183-1218
  • Numerical modeling of radial, astigmatic, and hexagonal keratotomy. Refractive and corneal surgery PINSKY, P. M., DATYE, D. V. 1992; 8 (2): 164-172

    Abstract

    A mechanical model of the human cornea is proposed and employed in a finite element formulation for simulating the effects of keratotomy on the cornea.The formulation assumes that the structural behavior of the cornea is governed by the properties of the stroma which is modeled as a thick membrane. The tensile forces in the cornea are resisted by the collagen fibrils embedded in the ground substance of the stromal lamellae. When the stromal lamellae are cut, as in keratotomy, it is assumed that they no longer carry any tensile forces, and the forces in the cornea are then resisted only by the remaining uncut lamellae. A constitutive model, which represents the anisotropy and inhomogeneity in the membrane rigidity induced by the incisions, has been employed in a geometrically nonlinear finite element membrane formulation for small strains with moderate rotations. This preliminary model is restricted to linear material behavior with no time dependency.A number of numerical examples are presented to illustrate the effectiveness of the proposed constitutive model and the finite element formulation for computing the immediate postoperative shift in corneal power resulting from radial, astigmatic, and hexagonal keratotomy. Surgical changes computed using the proposed model compare well with surgical corrections predicted by expert surgeons.The proposed computational model of the cornea and the effects of surgical procedures on it is based on a number of important simplifying assumptions regarding the mechanical properties and structure of the corneal tissue at the ultrastructure level. The encouraging results found with present model suggest that further development and refinement will be useful.

    View details for PubMedID 1591212

  • LOCAL HIGH-ORDER RADIATION BOUNDARY-CONDITIONS FOR THE 2-DIMENSIONAL TIME-DEPENDENT STRUCTURAL ACOUSTICS PROBLEM JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA PINSKY, P. M., Thompson, L. L., ABBOUD, N. N. 1992; 91 (3): 1320-1335
  • FINITE-ELEMENT SOLUTION OF THE TRANSIENT EXTERIOR STRUCTURAL ACOUSTICS PROBLEM BASED ON THE USE OF RADIALLY ASYMPTOTIC BOUNDARY OPERATORS COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING PINSKY, P. M., ABBOUD, N. N. 1991; 85 (3): 311-348
  • A MICROSTRUCTURALLY-BASED FINITE-ELEMENT MODEL OF THE INCISED HUMAN CORNEA JOURNAL OF BIOMECHANICS PINSKY, P. M., DATYE, D. V. 1991; 24 (10): 907-922

    Abstract

    A mechanical model of the human cornea is proposed and employed in a finite element formulation for simulating the effects of surgical procedures, such as radial keratotomy, on the cornea. The model assumes that the structural behavior of the cornea is governed by the properties of the stroma. Arguments based on the microstructural organization and properties of the stroma lead to the conclusion that the human cornea exhibits flexural and shear rigidities which are negligible compared to its membrane rigidity. Accordingly, it is proposed that to a first approximation, the structural behavior of the cornea is that of a thick membrane shell. The tensile forces in the cornea are resisted by very fine collagen fibrils embedded in the ground substance of the stromal lamellae. When the collagen fibrils are cut, as in radial keratotomy, it is argued that they become relaxed since there is negligible transfer of load between adjacent fibrils due to the low shear modulus of the ground substance. The forces in the cornea are then resisted only by the remaining uncut fibrils. The cutting of fibrils induces an anisotropy and inhomogeneity in the membrane rigidity. By assuming a uniform angular distribution of stromal lamellae through the corneal thickness, geometric arguments lead to a quantitative representation for the anisotropy and inhomogeneity. All material behavior is assumed to be in the linear elastic regime and with no time-dependency. The resulting constitutive model for the incised cornea has been employed in a geometrically non-linear finite element membrane shell formulation for small strains with moderate rotations. A number of numerical examples are presented to illustrate the effectiveness of the proposed constitutive model and finite element formulation. The dependence of the outcome of radial keratotomy, measured in terms of the immediate postoperative shift in corneal power, on a number of important factors is investigated. These factors include the value of the elastic moduli of the stromal lamellae (dependent on the patient's age), the incision depth, the optic zone size, the number of incisions and their positions, and the intraocular pressure. Results have also been compared with expected surgical corrections predicted by three expert surgeons and show an excellent correspondence.

    View details for Web of Science ID A1991GK60000004

    View details for PubMedID 1744149

  • ON THE USE OF LAGRANGE MULTIPLIER COMPATIBLE MODES FOR CONTROLLING ACCURACY AND STABILITY OF MIXED SHELL FINITE-ELEMENTS COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING PINSKY, P. M., JASTI, R. V. 1991; 85 (2): 151-182
  • TRANSIENT FINITE-ELEMENT ANALYSIS OF THE EXTERIOR STRUCTURAL ACOUSTICS PROBLEM JOURNAL OF VIBRATION AND ACOUSTICS-TRANSACTIONS OF THE ASME PINSKY, P. M., ABBOUD, N. N. 1990; 112 (2): 245-256
  • A MIXED FINITE-ELEMENT FORMULATION FOR REISSNER-MINDLIN PLATES BASED ON THE USE OF BUBBLE FUNCTIONS INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING PINSKY, P. M., JASTI, R. V. 1989; 28 (7): 1677-1702
  • 2 MIXED VARIATIONAL-PRINCIPLES FOR EXTERIOR FLUID STRUCTURE INTERACTION PROBLEMS COMPUTERS & STRUCTURES PINSKY, P. M., ABBOUD, N. N. 1989; 33 (3): 621-635
  • ELASTOPLASTIC SHELL ELEMENT BASED ON ASSUMED COVARIANT STRAIN INTERPOLATIONS JOURNAL OF ENGINEERING MECHANICS-ASCE PINSKY, P. M., Jang, J. 1988; 114 (6): 1045-1062
  • CONVERGENCE OF CURVED SHELL ELEMENTS BASED ON ASSUMED COVARIANT STRAIN INTERPOLATIONS INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING Jang, J. H., PINSKY, P. M. 1988; 26 (2): 329-347
  • AN ASSUMED COVARIANT STRAIN BASED 9-NODE SHELL ELEMENT INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING Jang, J. H., PINSKY, P. M. 1987; 24 (12): 2389-2411
  • A FINITE-ELEMENT FORMULATION FOR ELASTOPLASTICITY BASED ON A 3-FIELD VARIATIONAL EQUATION COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING PINSKY, P. M. 1987; 61 (1): 41-60
  • A MULTI-DIRECTOR FORMULATION FOR ELASTIC VISCOELASTIC LAYERED SHELLS INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING PINSKY, P. M., Kim, K. O. 1986; 23 (12): 2213-2244
  • A MULTI-DIRECTOR FORMULATION FOR NONLINEAR ELASTIC VISCOELASTIC LAYERED SHELLS COMPUTERS & STRUCTURES PINSKY, P. M., Kim, K. O. 1986; 24 (6): 901-913
  • COMPUTER ASSISTED TEST CONSTRUCTION - EFFORT BASED ON AN EVALUATION METHODOLOGY EDUCATIONAL TECHNOLOGY OREILLY, R. P., GORTH, W. P., Pinsky, P. 1973; 13 (3): 32-34

Conference Proceedings


  • A molecular dynamics study of the diffusion of fentanyl in DPPC bilayers Rim, J. E., PINSKY, P. M., van Osdol, W. W. CELL PRESS. 2005: 148A-148A
  • Computational investigation of the biomechanical response of the cornea to lamellar procedures. Guarnieri, F. A., PINSKY, P. M., Shimmick, J. ASSOC RESEARCH VISION OPHTHALMOLOGY INC. 2001: S603-S603
  • Numerical simulation of glucose diffusion in the cornea with an ICR(R) (intrastromal corneal ring) Silvestrini, T. A., PINSKY, P. M., DATYE, D. V. ASSOC RESEARCH VISION OPHTHALMOLOGY INC. 1996: 311-311
  • Finite element modelling of intravitreous drug kinetics PINSKY, P. M., Maurice, D. M., DATYE, D. V. ASSOC RESEARCH VISION OPHTHALMOLOGY INC. 1996: 3200-3200
  • Numerical prediction of astigmatic corrections in the human cornea after insertion of intrastromal corneal ring arcs DATYE, D. V., PINSKY, P. M., Silvestrini, T. A. ASSOC RESEARCH VISION OPHTHALMOLOGY INC. 1996: 310-310
  • NUMERICAL-SIMULATION OF SURGICAL-PROCEDURES ON THE HUMAN CORNEA USING MECHANICAL MODELS BASED ON CORNEAL ULTRA-STRUCTURE DATYE, D. V., PINSKY, P. M. ASSOC RESEARCH VISION OPHTHALMOLOGY INC. 1995: S38-S38
  • NUMERICAL-SIMULATION OF TOPOGRAPHICAL ALTERATIONS IN THE CORNEA AFTER ICR(R) (INTRASTROMAL CORNEAL RING) PINSKY, P. M., DATYE, D. V., Silvestrini, T. A. ASSOC RESEARCH VISION OPHTHALMOLOGY INC. 1995: S309-S309
  • FINITE-ELEMENT FORMULATION FOR A BAFFLED, FLUID-LOADED, FINITE CYLINDRICAL-SHELL Grosh, K., PINSKY, P. M., Malhotra, M., Rao, V. S. JOHN WILEY & SONS LTD. 1994: 2971-2985
  • DETERMINATION OF MECHANICAL-PROPERTIES OF CORNEA IN-VIVO BY INDENTATION Chang, S. S., Maurice, D. M., PINSKY, P. M., DATYE, D. V. ASSOC RESEARCH VISION OPHTHALMOLOGY INC. 1994: 1357-1357
  • A MICROSTRUCTURALLY-BASED MECHANICAL MODEL OF THE HUMAN CORNEA WITH APPLICATION TO KERATOTOMY PINSKY, P. M., DATYE, D. V. ASSOC RESEARCH VISION OPHTHALMOLOGY INC. 1994: 1296-1296
  • SPACE-TIME GALERKIN LEAST-SQUARES FINITE-ELEMENT FORMULATION FOR THE HYDRODYNAMIC DEVICE EQUATIONS Aluru, N. R., Law, K. H., PINSKY, P. M., Raefsky, A., GOOSSENS, R. J., DUTTON, R. W. IEICE-INST ELECTRON INFO COMMUN ENG. 1994: 227-235
  • CORNEAL DEFORMATION BY INDENTATION AND APPLANATION FORCES Chang, S. S., Hjortdal, J. O., Maurice, D. M., PINSKY, P. M. ASSOC RESEARCH VISION OPHTHALMOLOGY INC. 1993: 1241-1241