@article{haider_pearce_chesler_hill_olufsen_2024, title={Application and reduction of a nonlinear hyperelastic wall model capturing ex vivo relationships between fluid pressure, area, and wall thickness in normal and hypertensive murine left pulmonary arteries}, volume={1}, ISSN={["2040-7947"]}, url={https://doi.org/10.1002/cnm.3798}, DOI={10.1002/cnm.3798}, abstractNote={Abstract}, journal={INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING}, author={Haider, Mansoor A. and Pearce, Katherine J. and Chesler, Naomi C. and Hill, Nicholas A. and Olufsen, Mette S.}, year={2024}, month={Jan} }
 @article{andrew_haider_2024, title={Bridging Continuous and Lattice-Based Models of Two-Dimensional Diffusion: A Systematic Approach for Estimating Transition Probabilities, Grid Size and Diffusivity}, url={https://doi.org/10.3390/app14135442}, DOI={10.3390/app14135442}, abstractNote={Lattice-based models have been broadly applied in mathematical and computational modeling of biological and biomedical systems for which spatial effects are important. These discrete models commonly include diffusion of mobile constituents as a key underlying mechanism. While the direct simulation of diffusion in continuous (off-lattice) domains is possible, it is computationally intensive, particularly when multiple coupled mechanisms are involved. This study presents a systematic approach for connecting continuous models of two-dimensional diffusion with internal obstacles to discrete, lattice-based (surrogate) models of diffusion. Results from continuous model simulations on a representative domain, and over many realizations, are used to develop accurate lattice-based surrogate models by exploiting internal symmetries. Probabilities determined for the lattice-based surrogate models are also connected to theoretical diffusivities for 2D random walks on a square lattice, necessitating the calibration of a spatial grid size. This approach can facilitate the inclusion of more accurate diffusive transport models of complex media within the general framework of lattice-based models that incorporate multiple coupled mechanisms.}, journal={Applied Sciences}, author={Andrew, Tricity M. and Haider, Mansoor A.}, year={2024}, month={Jun} }
 @article{dadashova_smith_haider_2024, title={Local Identifiability Analysis, Parameter Subset Selection and Verification for a Minimal Brain PBPK Model}, volume={86}, ISSN={["1522-9602"]}, url={https://doi.org/10.1007/s11538-023-01234-4}, DOI={10.1007/s11538-023-01234-4}, number={2}, journal={BULLETIN OF MATHEMATICAL BIOLOGY}, author={Dadashova, Kamala and Smith, Ralph C. and Haider, Mansoor A.}, year={2024}, month={Feb} }
 @article{zhang_xiao_johnson_cai_horowitz_mennicke_coffey_haider_threadgill_eliscu_et al._2023, title={Bulk and mosaic deletions of Egfr reveal regionally defined gliogenesis in the developing mouse forebrain}, volume={26}, ISSN={["2589-0042"]}, DOI={10.1016/j.isci.2023.106242}, abstractNote={The epidermal growth factor receptor (EGFR) plays a role in cell proliferation and differentiation during healthy development and tumor growth; however, its requirement for brain development remains unclear. Here we used a conditional mouse allele for Egfr to examine its contributions to perinatal forebrain development at the tissue level. Subtractive bulk ventral and dorsal forebrain deletions of Egfr uncovered significant and permanent decreases in oligodendrogenesis and myelination in the cortex and corpus callosum. Additionally, an increase in astrogenesis or reactive astrocytes in effected regions was evident in response to cortical scarring. Sparse deletion using mosaic analysis with double markers (MADM) surprisingly revealed a regional requirement for EGFR in rostrodorsal, but not ventrocaudal glial lineages including both astrocytes and oligodendrocytes. The EGFR-independent ventral glial progenitors may compensate for the missing EGFR-dependent dorsal glia in the bulk Egfr-deleted forebrain, potentially exposing a regenerative population of gliogenic progenitors in the mouse forebrain.}, number={3}, journal={ISCIENCE}, author={Zhang, Xuying and Xiao, Guanxi and Johnson, Caroline and Cai, Yuheng and Horowitz, Zachary K. and Mennicke, Christine and Coffey, Robert and Haider, Mansoor and Threadgill, David and Eliscu, Rebecca and et al.}, year={2023}, month={Mar} }
 @article{mcmahon_doroshenko_roostaei_cho_haider_2022, title={Unsupervised learning methods for efficient geographic clustering and identification of disease disparities with applications to county-level colorectal cancer incidence in California}, volume={6}, ISSN={["1572-9389"]}, url={https://doi.org/10.1007/s10729-022-09604-5}, DOI={10.1007/s10729-022-09604-5}, abstractNote={Many public health policymaking questions involve data subsets representing application-specific attributes and geographic location. We develop and evaluate standard and tailored techniques for clustering via unsupervised learning (UL) algorithms on such amalgamated (dual-domain) data sets. The aim of the associated algorithms is to identify geographically efficient clusters that also maximize the number of statistically significant differences in disease incidence and demographic variables across top clusters. Two standard UL approaches, k means with k++ initialization (k++) and the standard self-organizing map (SSOM), are considered along with a new, tailored version of the SOM (TSOM). The TSOM algorithm involves optimization of a customized objective function with terms promoting individual geographic cluster cohesion while also maximizing the number of differences across clusters, and two hyper-parameters controlling the relative weighting of geographic and attribute subspaces in a non-Euclidean distance measure within the clustering problem. The performance of these three techniques (k++, SSOM, TSOM) is compared and evaluated in the context of a data set for colorectal cancer incidence in the state of California, at the level of individual counties. Clusters are visualized via chloropleth maps and ordered graphs are also used to illustrate disparities in disease incidence among four identity groups. While all three approaches performed well, the TSOM identified the largest number of disease and demographic disparities while also yielding more geographically efficient top clusters. Techniques presented in this study are relevant to applications including the delivery of health care resources and identifying disparities among identity groups, and to questions involving coordination between county- and state-level policymakers.}, journal={HEALTH CARE MANAGEMENT SCIENCE}, author={McMahon, Mallory E. and Doroshenko, Lyubov and Roostaei, Javad and Cho, Hyunsoon and Haider, Mansoor A.}, year={2022}, month={Jun} }
 @article{pearce_nellenbach_smith_brown_haider_2021, title={Modeling and Parameter Subset Selection for Fibrin Polymerization Kinetics with Applications to Wound Healing}, volume={83}, ISSN={0092-8240 1522-9602}, url={http://dx.doi.org/10.1007/s11538-021-00876-6}, DOI={10.1007/s11538-021-00876-6}, abstractNote={During the hemostatic phase of wound healing, vascular injury leads to endothelial cell damage, initiation of a coagulation cascade involving platelets, and formation of a fibrin-rich clot. As this cascade culminates, activation of the protease thrombin occurs and soluble fibrinogen is converted into an insoluble polymerized fibrin network. Fibrin polymerization is critical for bleeding cessation and subsequent stages of wound healing. We develop a cooperative enzyme kinetics model for in vitro fibrin matrix polymerization capturing dynamic interactions among fibrinogen, thrombin, fibrin, and intermediate complexes. A tailored parameter subset selection technique is also developed to evaluate parameter identifiability for a representative data curve for fibrin accumulation in a short-duration in vitro polymerization experiment. Our approach is based on systematic analysis of eigenvalues and eigenvectors of the classical information matrix for simulations of accumulating fibrin matrix via optimization based on a least squares objective function. Results demonstrate robustness of our approach in that a significant reduction in objective function cost is achieved relative to a more ad hoc curve-fitting procedure. Capabilities of this approach to integrate non-overlapping subsets of the data to enhance the evaluation of parameter identifiability are also demonstrated. Unidentifiable reaction rate parameters are screened to determine whether individual reactions can be eliminated from the overall system while preserving the low objective cost. These findings demonstrate the high degree of information within a single fibrin accumulation curve, and a tailored model and parameter subset selection approach for improving optimization and reducing model complexity in the context of polymerization experiments.}, number={5}, journal={Bulletin of Mathematical Biology}, publisher={Springer Science and Business Media LLC}, author={Pearce, Katherine J. and Nellenbach, Kimberly and Smith, Ralph C. and Brown, Ashley C. and Haider, Mansoor A.}, year={2021}, month={Mar} }
 @article{zhang_mennicke_xiao_beattie_haider_hippenmeyer_ghashghaei_2020, title={Clonal Analysis of Gliogenesis in the Cerebral Cortex Reveals Stochastic Expansion of Glia and Cell Autonomous Responses to Egfr Dosage}, volume={9}, url={https://www.mdpi.com/2073-4409/9/12/2662}, DOI={10.3390/cells9122662}, abstractNote={Development of the nervous system undergoes important transitions, including one from neurogenesis to gliogenesis which occurs late during embryonic gestation. Here we report on clonal analysis of gliogenesis in mice using Mosaic Analysis with Double Markers (MADM) with quantitative and computational methods. Results reveal that developmental gliogenesis in the cerebral cortex occurs in a fraction of earlier neurogenic clones, accelerating around E16.5, and giving rise to both astrocytes and oligodendrocytes. Moreover, MADM-based genetic deletion of the epidermal growth factor receptor (Egfr) in gliogenic clones revealed that Egfr is cell autonomously required for gliogenesis in the mouse dorsolateral cortices. A broad range in the proliferation capacity, symmetry of clones, and competitive advantage of MADM cells was evident in clones that contained one cellular lineage with double dosage of Egfr relative to their environment, while their sibling Egfr-null cells failed to generate glia. Remarkably, the total numbers of glia in MADM clones balance out regardless of significant alterations in clonal symmetries. The variability in glial clones shows stochastic patterns that we define mathematically, which are different from the deterministic patterns in neuronal clones. This study sets a foundation for studying the biological significance of stochastic and deterministic clonal principles underlying tissue development, and identifying mechanisms that differentiate between neurogenesis and gliogenesis.}, number={12}, journal={Cells}, publisher={MDPI AG}, author={Zhang, Xuying and Mennicke, Christine V. and Xiao, Guanxi and Beattie, Robert and Haider, Mansoor A and Hippenmeyer, Simon and Ghashghaei, Troy}, year={2020}, month={Dec}, pages={2662} }
 @article{olson_haider_2019, title={A computational reaction–diffusion model for biosynthesis and linking of cartilage extracellular matrix in cell-seeded scaffolds with varying porosity}, volume={18}, ISSN={1617-7959 1617-7940}, url={http://dx.doi.org/10.1007/s10237-018-01110-4}, DOI={10.1007/s10237-018-01110-4}, abstractNote={Cartilage tissue engineering is commonly initiated by seeding cells in porous materials such as hydrogels or scaffolds. Under optimal conditions, the resulting engineered construct has the potential to fill regions where native cartilage has degraded or eroded. Within a cell-seeded scaffold supplied by nutrients and growth factors, extracellular matrix accumulation should occur concurrently with scaffold degradation. At present, the interplay between cell-mediated synthesis and linking of matrix constituents and the evolving scaffold properties is not well understood. We develop a computational model of extracellular matrix accumulation in a cell-seeded scaffold based on a continuum reaction-diffusion system with inhomogeneous inclusions representing individual cells. The effects of porosity on engineered tissue outcomes is accounted for via the use of mixture variables capturing the spatiotemporal dynamics of both bound and unbound system constituents. The unbound constituents are the nutrients and unlinked extracellular matrix, while the bound constituents are the scaffold and the linked extracellular matrix. The linking model delineates binding of matrix constituents to either existing bound extracellular matrix or to scaffold. Results on a representative domain exhibit bound matrix trapping (vs spreading) around cells in scaffolds with lower (vs higher) initial porosity, similar to experimental results obtained by Erickson et al. (Osteoarthr Cartil 17:1639-1648, 2009). Significant alterations in the spatiotemporal accumulation of bound matrix are observed when, among the set of all model parameters, only the initial scaffold porosity is varied. The model presented herein proposes a methodology to investigate coupling between cell-mediated biosynthesis and linking of extracellular matrix in porous, cell-seeded scaffolds that has the potential to aid in the design of optimal tissue-engineered cartilage constructs.}, number={3}, journal={Biomechanics and Modeling in Mechanobiology}, publisher={Springer Science and Business Media LLC}, author={Olson, Sarah D. and Haider, Mansoor A.}, year={2019}, month={Jan}, pages={701–716} }
 @article{qureshi_colebank_schreier_tabima_haider_chesler_olufsen_2018, title={Characteristic impedance: frequency or time domain approach?}, volume={39}, ISSN={1361-6579}, url={http://dx.doi.org/10.1088/1361-6579/aa9d60}, DOI={10.1088/1361-6579/aa9d60}, abstractNote={Objective: Characteristic impedance (Zc) is an important component in the theory of hemodynamics. It is a commonly used metric of proximal arterial stiffness and pulse wave velocity. Calculated using simultaneously measured dynamic pressure and flow data, estimates of characteristic impedance can be obtained using methods based on frequency or time domain analysis. Applications of these methods under different physiological and pathological conditions in species with different body sizes and heart rates show that the two approaches do not always agree. In this study, we have investigated the discrepancies between frequency and time domain estimates accounting for uncertainties associated with experimental processes and physiological conditions. Approach: We have used published data measured in different species including humans, dogs, and mice to investigate: (a) the effects of time delay and signal noise in the pressure-flow data, (b) uncertainties about the blood flow conditions, (c) periodicity of the cardiac cycle versus the breathing cycle, on the frequency and time domain estimates of Zc, and (d) if discrepancies observed under different hemodynamic conditions can be eliminated. Main results and Significance: We have shown that the frequency and time domain estimates are not equally sensitive to certain characteristics of hemodynamic signals including phase lag between pressure and flow, signal to noise ratio and the end of systole retrograde flow. The discrepancies between two types of estimates are inherent due to their intrinsically different mathematical expressions and therefore it is impossible to define a criterion to resolve such discrepancies. Considering the interpretation and role of Zc as an important hemodynamic parameter, we suggest that the frequency and time domain estimates should be further assessed as two different hemodynamic parameters in a future study.}, number={1}, journal={Physiological Measurement}, publisher={IOP Publishing}, author={Qureshi, M Umar and Colebank, Mitchel J and Schreier, David A and Tabima, Diana M and Haider, Mansoor A and Chesler, Naomi C and Olufsen, Mette S}, year={2018}, month={Jan}, pages={014004} }
 @article{qureshi_colebank_paun_ellwein fix_chesler_haider_hill_husmeier_olufsen_2018, title={Hemodynamic assessment of pulmonary hypertension in mice: a model-based analysis of the disease mechanism}, volume={18}, ISSN={1617-7959 1617-7940}, url={http://dx.doi.org/10.1007/s10237-018-1078-8}, DOI={10.1007/s10237-018-1078-8}, abstractNote={This study uses a one-dimensional fluid dynamics arterial network model to infer changes in hemodynamic quantities associated with pulmonary hypertension in mice. Data for this study include blood flow and pressure measurements from the main pulmonary artery for 7 control mice with normal pulmonary function and 5 mice with hypoxia-induced pulmonary hypertension. Arterial dimensions for a 21-vessel network are extracted from micro-CT images of lungs from a representative control and hypertensive mouse. Each vessel is represented by its length and radius. Fluid dynamic computations are done assuming that the flow is Newtonian, viscous, laminar, and has no swirl. The system of equations is closed by a constitutive equation relating pressure and area, using a linear model derived from stress–strain deformation in the circumferential direction assuming that the arterial walls are thin, and also an empirical nonlinear model. For each dataset, an inflow waveform is extracted from the data, and nominal parameters specifying the outflow boundary conditions are computed from mean values and characteristic timescales extracted from the data. The model is calibrated for each mouse by estimating parameters that minimize the least squares error between measured and computed waveforms. Optimized parameters are compared across the control and the hypertensive groups to characterize vascular remodeling with disease. Results show that pulmonary hypertension is associated with stiffer and less compliant proximal and distal vasculature with augmented wave reflections, and that elastic nonlinearities are insignificant in the hypertensive animal.}, number={1}, journal={Biomechanics and Modeling in Mechanobiology}, publisher={Springer Nature}, author={Qureshi, M. Umar and Colebank, Mitchel J. and Paun, L. Mihaela and Ellwein Fix, Laura and Chesler, Naomi and Haider, Mansoor A. and Hill, Nicholas A. and Husmeier, Dirk and Olufsen, Mette S.}, year={2018}, month={Oct}, pages={219–243} }
 @article{păun_qureshi_colebank_hill_olufsen_haider_husmeier_2018, title={MCMC methods for inference in a mathematical model of pulmonary circulation}, volume={72}, ISSN={0039-0402}, url={http://dx.doi.org/10.1111/stan.12132}, DOI={10.1111/stan.12132}, abstractNote={This study performs parameter inference in a partial differential equations system of pulmonary circulation. We use a fluid dynamics network model that takes selected parameter values and mimics the behaviour of the pulmonary haemodynamics under normal physiological and pathological conditions. This is of medical interest as it enables tracking the progression of pulmonary hypertension. We show how we make the fluids model tractable by reducing the parameter dimension from a 55D to a 5D problem. The Delayed Rejection Adaptive Metropolis algorithm, coupled with constraint non‐linear optimization, is successfully used to learn the parameter values and quantify the uncertainty in the parameter estimates. To accommodate for different magnitudes of the parameter values, we introduce an improved parameter scaling technique in the Delayed Rejection Adaptive Metropolis algorithm. Formal convergence diagnostics are employed to check for convergence of the Markov chains. Additionally, we perform model selection using different information criteria, including Watanabe Akaike Information Criteria.}, number={3}, journal={Statistica Neerlandica}, publisher={Wiley}, author={Păun, L. Mihaela and Qureshi, M. Umar and Colebank, Mitchel and Hill, Nicholas A. and Olufsen, Mette S. and Haider, Mansoor A. and Husmeier, Dirk}, year={2018}, month={Apr}, pages={306–338} }
 @article{battista_bia_germán_armentano_haider_olufsen_2016, title={Wave propagation in a 1D fluid dynamics model using pressure-area measurements from ovine arteries}, volume={16}, ISSN={0219-5194 1793-6810}, url={http://dx.doi.org/10.1142/S021951941650007X}, DOI={10.1142/S021951941650007X}, abstractNote={This study considers a 1D fluid dynamics arterial network model with 14 vessels developed to assimilate ex vivo 0D temporal data for pressure-area dynamics in individual vessel segments from 11 male Merino sheep. A 0D model was used to estimate vessel wall parameters in a two-parameter elastic model and a four-parameter Kelvin viscoelastic model. This was done using nonlinear optimization minimizing the least squares error between model predictions and measured cross-sectional areas. Subsequently, estimated values for elastic stiffness and unstressed area were related to construct a nonlinear relationship. This relation was used in the network model. A 1D single vessel model of the aorta was then developed and used to estimate the inflow profile and parameters for total resistance and compliance for the downstream network and to demonstrate effects of incorporating viscoelasticity in the arterial wall. Lastly, the extent to which vessel wall parameters estimated from ex vivo data can be used to realistically simulate pressure and area in a vessel network was evaluated. Elastic wall parameters in the network simulations were found to yield pressure-area relationships across all vessel locations and sheep that were in ranges comparable to those in the ex vivo data.}, number={02}, journal={Journal of Mechanics in Medicine and Biology}, publisher={World Scientific Pub Co Pte Lt}, author={Battista, Christina and Bia, Daniel and Germán, Yanina Zócalo and Armentano, Ricardo L. and Haider, Mansoor A. and Olufsen, Mette S.}, year={2016}, month={Mar}, pages={1650007} }
 @article{aristotelous_haider_2014, title={Evaluation of Diffusive Transport and Cellular Uptake of Nutrients in Tissue Engineered Constructs Using a Hybrid Discrete Mathematical Model}, volume={2}, ISSN={2227-9717}, url={http://dx.doi.org/10.3390/pr2020333}, DOI={10.3390/pr2020333}, abstractNote={Tissue engineering systems for orthopedic tissues, such as articular cartilage, are often based on the use of biomaterial scaffolds that are seeded with cells and supplied with nutrients or growth factors. In such systems, relationships between the functional outcomes of the engineered tissue construct and aspects of the initial system design are not well known, suggesting the use of mathematical models as an additional tool for optimal system design. This study develops a reaction-diffusion model that quantitatively describes the competing effects of nutrient diffusion and the cellular uptake of nutrients in a closed bioreactor system consisting of a cell-seeded scaffold adjacent to a nutrient-rich bath. An off-lattice hybrid discrete modeling framework is employed in which the diffusion equation incorporates a loss term that accounts for absorption due to nutrient uptake by cells that are modeled individually. Numerical solutions are developed based on a discontinuous Galerkin finite element method with high order quadrature to accurately resolve fine-scale cellular effects. The resulting model is applied to demonstrate that the ability of cells to absorb nutrients over time is highly dependent on both the normal distance to the nutrient bath, as well as the nutrient uptake rate for individual cells.}, number={2}, journal={Processes}, publisher={MDPI AG}, author={Aristotelous, Andreas and Haider, Mansoor}, year={2014}, month={Mar}, pages={333–344} }
 @article{aristotelous_haider_2014, title={Use of hybrid discrete cellular models for identification of macroscopic nutrient loss in reaction-diffusion models of tissues}, volume={30}, ISSN={["2040-7947"]}, DOI={10.1002/cnm.2628}, abstractNote={SUMMARY}, number={8}, journal={INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING}, author={Aristotelous, Andreas C. and Haider, Mansoor A.}, year={2014}, month={Aug}, pages={767–780} }
 @article{haider_olander_arnold_marous_mclamb_thompson_woodruff_haugh_2011, title={A phenomenological mixture model for biosynthesis and linking of cartilage extracellular matrix in scaffolds seeded with chondrocytes}, volume={10}, ISSN={1617-7959 1617-7940}, url={http://dx.doi.org/10.1007/s10237-010-0282-y}, DOI={10.1007/s10237-010-0282-y}, abstractNote={A phenomenological mixture model is presented for interactions between biosynthesis of extracellular matrix (ECM) constituents and ECM linking in a scaffold seeded with chondrocytes. A system of three ordinary differential equations for average apparent densities of unlinked ECM, linked ECM and scaffold is developed along with associated initial conditions for scaffold material properties. Equations for unlinked ECM synthesis and ECM linking include an inhibitory mechanism where associated rates decrease as unlinked ECM concentration in the interstitial fluid increases. Linking rates are proposed to depend on average porosity in the evolving tissue construct. The resulting initial value problem contains nine independent parameters that account for scaffold biomaterial properties and interacting mechanisms in the engineered system. Effects of parameter variations on model variables are analyzed relative to a baseline case with emphasis on the evolution of solid phase apparent density, which is often correlated with the compressive elastic modulus of the tissue construct. The new model provides an additional quantitative framework for assessing and optimizing the design of engineered cell-scaffold systems and guiding strategies for articular cartilage tissue engineering.}, number={6}, journal={Biomechanics and Modeling in Mechanobiology}, publisher={Springer Science and Business Media LLC}, author={Haider, Mansoor A. and Olander, Jeffrey E. and Arnold, Rachel F. and Marous, Daniel R. and McLamb, April J. and Thompson, Karmethia C. and Woodruff, William R. and Haugh, Janine M.}, year={2011}, month={Jan}, pages={915–924} }
 @article{hu_haider_2011, title={Algebraic Multigrid Preconditioning for Finite Element Solution of Inhomogeneous Elastic Inclusion Problems in Articular Cartilage}, volume={3}, ISSN={["2070-0733"]}, DOI={10.4208/aamm.10-m1070}, abstractNote={Abstract}, number={6}, journal={ADVANCES IN APPLIED MATHEMATICS AND MECHANICS}, author={Hu, Zhengzheng and Haider, Mansoor A.}, year={2011}, month={Dec}, pages={729–744} }
 @article{valdez-jasso_bia_zocalo_armentano_haider_olufsen_2011, title={Linear and Nonlinear Viscoelastic Modeling of Aorta and Carotid Pressure-Area Dynamics Under In Vivo and Ex Vivo Conditions}, volume={39}, ISSN={["1573-9686"]}, DOI={10.1007/s10439-010-0236-7}, abstractNote={A better understanding of the biomechanical properties of the arterial wall provides important insight into arterial vascular biology under normal (healthy) and pathological conditions. This insight has potential to improve tracking of disease progression and to aid in vascular graft design and implementation. In this study, we use linear and nonlinear viscoelastic models to predict biomechanical properties of the thoracic descending aorta and the carotid artery under ex vivo and in vivo conditions in ovine and human arteries. Models analyzed include a four-parameter (linear) Kelvin viscoelastic model and two five-parameter nonlinear viscoelastic models (an arctangent and a sigmoid model) that relate changes in arterial blood pressure to the vessel cross-sectional area (via estimation of vessel strain). These models were developed using the framework of Quasilinear Viscoelasticity (QLV) theory and were validated using measurements from the thoracic descending aorta and the carotid artery obtained from human and ovine arteries. In vivo measurements were obtained from 10 ovine aortas and 10 human carotid arteries. Ex vivo measurements (from both locations) were made in 11 male Merino sheep. Biomechanical properties were obtained through constrained estimation of model parameters. To further investigate the parameter estimates, we computed standard errors and confidence intervals and we used analysis of variance to compare results within and between groups. Overall, our results indicate that optimal model selection depends on the artery type. Results showed that for the thoracic descending aorta (under both experimental conditions), the best predictions were obtained with the nonlinear sigmoid model, while under healthy physiological pressure loading the carotid arteries nonlinear stiffening with increasing pressure is negligible, and consequently, the linear (Kelvin) viscoelastic model better describes the pressure–area dynamics in this vessel. Results comparing biomechanical properties show that the Kelvin and sigmoid models were able to predict the zero-pressure vessel radius; that under ex vivo conditions vessels are more rigid, and comparatively, that the carotid artery is stiffer than the thoracic descending aorta; and that the viscoelastic gain and relaxation parameters do not differ significantly between vessels or experimental conditions. In conclusion, our study demonstrates that the proposed models can predict pressure–area dynamics and that model parameters can be extracted for further interpretation of biomechanical properties.}, number={5}, journal={ANNALS OF BIOMEDICAL ENGINEERING}, author={Valdez-Jasso, Daniela and Bia, Daniel and Zocalo, Yanina and Armentano, Ricardo L. and Haider, Mansoor A. and Olufsen, Mette S.}, year={2011}, month={May}, pages={1438–1456} }
 @article{steele_valdez-jasso_haider_olufsen_2011, title={PREDICTING ARTERIAL FLOW AND PRESSURE DYNAMICS USING A 1D FLUID DYNAMICS MODEL WITH A VISCOELASTIC WALL}, volume={71}, ISSN={["1095-712X"]}, DOI={10.1137/100810186}, abstractNote={This paper combines a generalized viscoelastic model with a one-dimensional (1D) fluid dynamics model for the prediction of blood flow, pressure, and vessel area in systemic arteries. The 1D fluid dynamics model is derived from the Navier–Stokes equations for an incompressible Newtonian flow through a network of cylindrical vessels. This model predicts pressure and flow and is combined with a viscoelastic constitutive equation derived using the quasilinear viscoelasticity theory that relates pressure and vessel area. This formulation allows for inclusion of an elastic response as well as an appropriate creep function allowing for the description of the viscoelastic deformation of the arterial wall. Three constitutive models were investigated: a linear elastic model and two viscoelastic models. The Kelvin and sigmoidal viscoelastic models provide linear and nonlinear elastic responses, respectively. For the fluid domain, the model assumes that a given flow profile is prescribed at the inlet, that flow is c...}, number={4}, journal={SIAM JOURNAL ON APPLIED MATHEMATICS}, author={Steele, Brooke N. and Valdez-Jasso, Daniela and Haider, Mansoor A. and Olufsen, Mette S.}, year={2011}, pages={1123–1143} }
 @article{stuebner_haider_2010, title={A fast quadrature-based numerical method for the continuous spectrum biphasic poroviscoelastic model of articular cartilage}, volume={43}, ISSN={0021-9290}, url={http://dx.doi.org/10.1016/j.jbiomech.2010.02.023}, DOI={10.1016/j.jbiomech.2010.02.023}, abstractNote={A new and efficient method for numerical solution of the continuous spectrum biphasic poroviscoelastic (BPVE) model of articular cartilage is presented. Development of the method is based on a composite Gauss-Legendre quadrature approximation of the continuous spectrum relaxation function that leads to an exponential series representation. The separability property of the exponential terms in the series is exploited to develop a numerical scheme that can be reduced to an update rule requiring retention of the strain history at only the previous time step. The cost of the resulting temporal discretization scheme is O(N) for N time steps. Application and calibration of the method is illustrated in the context of a finite difference solution of the one-dimensional confined compression BPVE stress-relaxation problem. Accuracy of the numerical method is demonstrated by comparison to a theoretical Laplace transform solution for a range of viscoelastic relaxation times that are representative of articular cartilage.}, number={9}, journal={Journal of Biomechanics}, publisher={Elsevier BV}, author={Stuebner, Michael and Haider, Mansoor A.}, year={2010}, month={Jun}, pages={1835–1839} }
 @article{kim_guilak_haider_2010, title={An Axisymmetric Boundary Element Model for Determination of Articular Cartilage Pericellular Matrix Properties In Situ via Inverse Analysis of Chondron Deformation}, volume={132}, ISSN={0148-0731}, url={http://dx.doi.org/10.1115/1.4000938}, DOI={10.1115/1.4000938}, abstractNote={The pericellular matrix (PCM) is the narrow tissue region surrounding all chondrocytes in articular cartilage and, together, the chondrocyte(s) and surrounding PCM have been termed the chondron. Previous theoretical and experimental studies suggest that the structure and properties of the PCM significantly influence the biomechanical environment at the microscopic scale of the chondrocytes within cartilage. In the present study, an axisymmetric boundary element method (BEM) was developed for linear elastic domains with internal interfaces. The new BEM was employed in a multiscale continuum model to determine linear elastic properties of the PCM in situ, via inverse analysis of previously reported experimental data for the three-dimensional morphological changes of chondrons within a cartilage explant in equilibrium unconfined compression (Choi, et al., 2007, “Zonal Changes in the Three-Dimensional Morphology of the Chondron Under Compression: The Relationship Among Cellular, Pericellular, and Extracellular Deformation in Articular Cartilage,” J. Biomech., 40, pp. 2596–2603). The microscale geometry of the chondron (cell and PCM) within the cartilage extracellular matrix (ECM) was represented as a three-zone equilibrated biphasic region comprised of an ellipsoidal chondrocyte with encapsulating PCM that was embedded within a spherical ECM subjected to boundary conditions for unconfined compression at its outer boundary. Accuracy of the three-zone BEM model was evaluated and compared with analytical finite element solutions. The model was then integrated with a nonlinear optimization technique (Nelder–Mead) to determine PCM elastic properties within the cartilage explant by solving an inverse problem associated with the in situ experimental data for chondron deformation. Depending on the assumed material properties of the ECM and the choice of cost function in the optimization, estimates of the PCM Young's modulus ranged from ∼24 kPa to 59 kPa, consistent with previous measurements of PCM properties on extracted chondrons using micropipette aspiration. Taken together with previous experimental and theoretical studies of cell-matrix interactions in cartilage, these findings suggest an important role for the PCM in modulating the mechanical environment of the chondrocyte.}, number={3}, journal={Journal of Biomechanical Engineering}, publisher={ASME International}, author={Kim, Eunjung and Guilak, Farshid and Haider, Mansoor A.}, year={2010}, pages={031011} }
 @article{valdez-jasso_bia_haider_zocalo_armentano_olufsen_2010, title={Linear and Nonlinear Viscoelastic Modeling of Ovine Aortic Biomechanical Properties under in vivo and ex vivo Conditions}, ISSN={["1557-170X"]}, DOI={10.1109/iembs.2010.5626563}, abstractNote={This study uses linear and nonlinear viscoelastic models to describe the dynamic distention of the aorta induced by time-varying arterial blood pressure. We employ an inverse mathematical modeling approach on a four-parameter (linear) Kelvin viscoelastic model and two five-parameter nonlinear viscoelastic models (arctangent and sigmoid) to infer vascular biomechanical properties under in vivo and ex vivo experimental conditions in ten and eleven male Merino sheep, respectively. We used the Akaike Information Criterion (AIC) as a goodness-of-fit measure. Results show that under both experimental conditions, the nonlinear models generally outperform the linear Kelvin model, as judged by the AIC. Furthermore, the sigmoid nonlinear viscoelastic model consistently achieves the lowest AIC and also matches the zero-stress vessel radii measured ex vivo. Based on these observations, we conclude that the sigmoid nonlinear viscoelastic model best describes the biomechanical properties of ovine large arteries under both experimental conditions considered in this study.}, journal={2010 ANNUAL INTERNATIONAL CONFERENCE OF THE IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY (EMBC)}, author={Valdez-Jasso, D. and Bia, D. and Haider, M. A. and Zocalo, Y. and Armentano, R. L. and Olufsen, M. S.}, year={2010}, pages={2634–2637} }
 @article{nettles_haider_chilkoti_setton_2010, title={Neural Network Analysis Identifies Scaffold Properties Necessary for In Vitro Chondrogenesis in Elastin-like Polypeptide Biopolymer Scaffolds}, volume={16}, ISSN={1937-3341 1937-335X}, url={http://dx.doi.org/10.1089/ten.tea.2009.0134}, DOI={10.1089/ten.tea.2009.0134}, abstractNote={The successful design of biomaterial scaffolds for articular cartilage tissue engineering requires an understanding of the impact of combinations of material formulation parameters on diverse and competing functional outcomes of biomaterial performance. This study sought to explore the use of a type of unsupervised artificial network, a self-organizing map, to identify relationships between scaffold formulation parameters (crosslink density, molecular weight, and concentration) and 11 such outcomes (including mechanical properties, matrix accumulation, metabolite usage and production, and histological appearance) for scaffolds formed from crosslinked elastin-like polypeptide (ELP) hydrogels. The artificial neural network recognized patterns in functional outcomes and provided a set of relationships between ELP formulation parameters and measured outcomes. Mapping resulted in the best mean separation amongst neurons for mechanical properties and pointed to crosslink density as the strongest predictor of most outcomes, followed by ELP concentration. The map also grouped formulations together that simultaneously resulted in the highest values for matrix production, greatest changes in metabolite consumption or production, and highest histological scores, indicating that the network was able to recognize patterns amongst diverse measurement outcomes. These results demonstrated the utility of artificial neural network tools for recognizing relationships in systems with competing parameters, toward the goal of optimizing and accelerating the design of biomaterial scaffolds for articular cartilage tissue engineering.}, number={1}, journal={Tissue Engineering Part A}, publisher={Mary Ann Liebert Inc}, author={Nettles, Dana L. and Haider, Mansoor A. and Chilkoti, Ashutosh and Setton, Lori A.}, year={2010}, month={Jan}, pages={11–20} }
 @article{olson_haider_2009, title={A level set reaction-diffusion model for tissue regeneration in a cartilage-hydrogel aggregate}, volume={53}, journal={International Journal of Pure and Applied Mathematics}, author={Olson, S.D. and Haider, M.A.}, year={2009}, pages={333–353} }
 @article{valdez-jasso_haider_banks_santana_german_armentano_olufsen_2009, title={Analysis of Viscoelastic Wall Properties in Ovine Arteries}, volume={56}, ISSN={["1558-2531"]}, DOI={10.1109/TBME.2008.2003093}, abstractNote={In this paper, we analyze how elastic and viscoelastic properties differ across seven locations along the large arteries in 11 sheep. We employ a two-parameter elastic model and a four-parameter Kelvin viscoelastic model to analyze experimental measurements of vessel diameter and blood pressure obtained in vitro at conditions mimicking in vivo dynamics. Elastic and viscoelastic wall properties were assessed via solutions to the associated inverse problem. We use sensitivity analysis to rank the model parameters from the most to the least sensitive, as well as to compute standard errors and confidence intervals. Results reveal that elastic properties in both models (including Young's modulus and the viscoelastic relaxation parameters) vary across locations (smaller arteries are stiffer than larger arteries). We also show that for all locations, the inclusion of viscoelastic behavior is important to capture pressure-area dynamics.}, number={2}, journal={IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING}, author={Valdez-Jasso, Daniela and Haider, Mansoor A. and Banks, H. T. and Santana, Daniel Bia and German, Yanina Zocalo and Armentano, Ricardo L. and Olufsen, Mette S.}, year={2009}, month={Feb}, pages={210–219} }
 @inbook{haider_benedict_kim_guilak_2009, title={Computational Modeling of Cell Mechanics in Articular Cartilage}, ISBN={9789048135745 9789048135752}, url={http://dx.doi.org/10.1007/978-90-481-3575-2_11}, DOI={10.1007/978-90-481-3575-2_11}, booktitle={Computational Modeling in Biomechanics}, publisher={Springer Netherlands}, author={Haider, Mansoor A. and Benedict, Brandy A. and Kim, Eunjung and Guilak, Farshid}, year={2009}, month={Nov}, pages={329–352} }
 @inbook{guilak_haider_setton_laursen_baaijens_2009, title={Multiphasic models of cell mechanics}, ISBN={9780511607318}, url={http://dx.doi.org/10.1017/cbo9780511607318.006}, DOI={10.1017/cbo9780511607318.006}, abstractNote={: Cells are highly complex structures whose physiology and biomechanical properties depend on the interactions among the varying concentrations of water, charged or uncharged macromolecules, ions, and other molecular components contained within the cytoplasm. To further investigate the mechanistic basis of the mechanical behaviors of cells, recent studies have developed models of single cells and cell–matrix interactions that use multiphasic constitutive laws to represent the interactions among solid, fluid, and in some cases, ionic phases of cells. The goals of such studies have been to characterize the relative contributions of different physical mechanisms responsible for empirically observed phenomena such as cell viscoelasticity or volume change under mechanical or osmotic loading, and to account for the coupling of mechanical, chemical, and electrical events within living cells. This chapter describes several two-phase (fluid-solid) or three-phase (fluid-solid-ion) models, originally developed for studying soft hydrated tissues, that have been extended to describe the biomechanical behavior of individual cells or cell–matrix interactions in various tissue systems. The application of such “biphasic” or “triphasic” continuum-based approaches can be combined with other structurally based models to study the interactions of the different constitutive phases in governing cell mechanical behavior.}, booktitle={Cytoskeletal Mechanics}, publisher={Cambridge University Press}, author={Guilak, Farshid and Haider, Mansoor A. and Setton, Lori A. and Laursen, Tod A. and Baaijens, Frank P. T.}, editor={Mofrad, Mohammad R. K. and Kamm, Roger D.Editors}, year={2009}, month={Dec}, pages={84–102} }
 @article{valdez-jasso_banks_haider_bia_zocalo_armentano_olufsen_2009, title={Viscoelastic models for passive arterial wall dynamics}, volume={1}, number={2}, journal={Advances in Applied Mathematics & Mechanics}, author={Valdez-Jasso, D. and Banks, H. T. and Haider, M. A. and Bia, D. and Zocalo, Y. and Armentano, R. L. and Olufsen, M. S.}, year={2009}, pages={151–165} }
 @article{mauldin_haider_loboa_behler_euliss_pfeiler_gallippi_2008, title={Monitored steady-state excitation and recovery (MSSR) radiation force imaging using viscoelastic models}, volume={55}, ISSN={0885-3010}, url={http://dx.doi.org/10.1109/tuffc.2008.836}, DOI={10.1109/tuffc.2008.836}, abstractNote={Acoustic radiation force imaging methods distinguish tissue structure and composition by monitoring tissue responses to applied radiation force excitations. Although these responses are a complex, multidimensional function of the geometric and viscoelastic nature of tissue, simplified discrete biomechanical models offer meaningful insight to the physical phenomena that govern induced tissue motion. Applying Voigt and standard linear viscoelastic tissue models, we present a new radiation force technique - monitored steady-state excitation and recovery (MSSER) imaging - that tracks both steady-state displacement during prolonged force application and transient response following force cessation to estimate tissue mechanical properties such as elasticity and viscosity. In concert with shear wave elasticity imaging (SWEI) estimates for Young's modulus, MSSER methods are useful for estimating tissue mechanical properties independent of the applied force magnitude. We test our methods in gelatin phantoms and excised pig muscle, with confirmation through mechanical property measurement. Our results measured 10.6 kPa, 14.7 kPa, and 17.1 kPa (gelatin) and 122.4 kPa (pig muscle) with less than 10% error. This work demonstrates the feasibility of MSSER imaging and merits further efforts to incorporate relevant mechanical tissue models into the development of novel radiation force imaging techniques.}, number={7}, journal={IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control}, publisher={Institute of Electrical and Electronics Engineers (IEEE)}, author={Mauldin, F.W. and Haider, M.A. and Loboa, E.G. and Behler, R.H. and Euliss, L.E. and Pfeiler, T.W. and Gallippi, C.M.}, year={2008}, month={Jul}, pages={1597–1610} }
 @article{kim_guilak_haider_2008, title={The Dynamic Mechanical Environment of the Chondrocyte: A Biphasic Finite Element Model of Cell-Matrix Interactions Under Cyclic Compressive Loading}, volume={130}, ISSN={0148-0731}, url={http://dx.doi.org/10.1115/1.2978991}, DOI={10.1115/1.2978991}, abstractNote={Cyclic mechanical loading of articular cartilage results in a complex biomechanical environment at the scale of the chondrocytes that strongly affects cellular metabolic activity. Under dynamic loading conditions, the quantitative relationships between macroscopic loading characteristics and solid and fluid mechanical variables in the local cellular environment are not well understood. In this study, an axisymmetric multiscale model of linear biphasic cell-matrix interactions in articular cartilage was developed to investigate the cellular microenvironment in an explant subjected to cyclic confined compressive loading. The model was based on the displacement-velocity-pressure (u-v-p) mixed-penalty weighted residual formulation of linear biphasic theory that was implemented in the COMSOL MULTIPHYSICS software package. The microscale cartilage environment was represented as a three-zone biphasic region consisting of a spherical chondrocyte with encapsulating pericellular matrix (PCM) that was embedded in a cylindrical extracellular matrix (ECM) subjected to cyclic confined compressive loading boundary conditions. Biphasic material properties for the chondrocyte and the PCM were chosen based on previous in vitro micropipette aspiration studies of cells or chondrons isolated from normal or osteoarthritic cartilage. Simulations performed at four loading frequencies in the range 0.01–1.0 Hz supported the hypothesized dual role of the PCM as both a protective layer for the cell and a mechanical transducer of strain. Time varying biphasic variables at the cellular scale were strongly dependent on relative magnitudes of the loading period, and the characteristic gel diffusion times for the ECM, the PCM, and the chondrocyte. The multiscale simulations also indicated that axial strain was significantly amplified in the range 0.01–1.0 Hz, with a decrease in amplification factor and frequency insensitivity at the higher frequencies. Simulations of matrix degradation due to osteoarthritis indicated that strain amplification factors were more significantly altered when loss of matrix stiffness was exclusive to the PCM. The findings of this study demonstrate the complex dependence of dynamic mechanics in the local cellular environment of cartilage on macroscopic loading features and material properties of the ECM and the chondron.}, number={6}, journal={Journal of Biomechanical Engineering}, publisher={ASME International}, author={Kim, Eunjung and Guilak, Farshid and Haider, Mansoor A.}, year={2008}, pages={061009} }
 @article{haider_guilak_2007, title={Application of a three-dimensional poroelastic BEM to modeling the biphasic mechanics of cell-matrix interactions in articular cartilage}, volume={196}, ISSN={["0045-7825"]}, DOI={10.1016/j.cma.2006.08.020}, abstractNote={Articular cartilage exhibits viscoelasticity in response to mechanical loading that is well described using biphasic or poroelastic continuum models. To date, boundary element methods (BEMs) have not been employed in modeling biphasic tissue mechanics. A three dimensional direct poroelastic BEM, formulated in the Laplace transform domain, is applied to modeling stress relaxation in cartilage. Macroscopic stress relaxation of a poroelastic cylinder in uni-axial confined compression is simulated and validated against a theoretical solution. Microscopic cell deformation due to poroelastic stress relaxation is also modeled. An extended Laplace inversion method is employed to accurately represent mechanical responses in the time domain.}, number={31-32}, journal={COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING}, author={Haider, Mansoor A. and Guilak, Farshid}, year={2007}, pages={2999–3010} }
 @article{haider_schugart_setton_guilak_2006, title={A mechano-chemical model for the passive swelling response of an isolated chondron under osmotic loading}, volume={5}, ISSN={["1617-7959"]}, DOI={10.1007/s10237-006-0026-1}, abstractNote={The chondron is a distinct structure in articular cartilage that consists of the chondrocyte and its pericellular matrix (PCM), a narrow tissue region surrounding the cell that is distinguished by type VI collagen and a high glycosaminoglycan concentration relative to the extracellular matrix. We present a theoretical mechano-chemical model for the passive volumetric response of an isolated chondron under osmotic loading in a simple salt solution at equilibrium. The chondrocyte is modeled as an ideal osmometer and the PCM model is formulated using triphasic mixture theory. A mechano-chemical chondron model is obtained assuming that the chondron boundary is permeable to both water and ions, while the chondrocyte membrane is selectively permeable to only water. For the case of a neo-Hookean PCM constitutive law, the model is used to conduct a parametric analysis of cell and chondron deformation under hyper- and hypo-osmotic loading. In combination with osmotic loading experiments on isolated chondrons, model predictions will aid in determination of pericellular fixed charge density and its relative contribution to PCM mechanical properties.}, number={2-3}, journal={BIOMECHANICS AND MODELING IN MECHANOBIOLOGY}, author={Haider, MA and Schugart, RC and Setton, LA and Guilak, F}, year={2006}, month={Jun}, pages={160–171} }
 @article{haider_schugart_2006, title={A numerical method for the continuous spectrum biphasic poroviscoelastic model of articular cartilage}, volume={39}, ISSN={["0021-9290"]}, DOI={10.1016/j.jbiomech.2004.10.037}, abstractNote={A method for numerical solution of the continuous spectrum linear biphasic poroviscoelastic (BPVE) model of articular cartilage is presented. The method is based on an alternate formulation of the continuous spectrum stress-strain law that is implemented using Gaussian quadrature integration combined with quadratic interpolation of the strain history. For N time steps, the cost of the method is O(N). The method is applied to a finite difference solution of the one-dimensional confined compression BPVE stress-relaxation problem. For a range of relaxation times that are representative of articular cartilage, accuracy of the method is demonstrated by direct comparison to a theoretical Laplace transform solution.}, number={1}, journal={JOURNAL OF BIOMECHANICS}, author={Haider, MA and Schugart, RC}, year={2006}, pages={177–183} }
 @article{leddy_haider_guilak_2006, title={Diffusional anisotropy in collagenous tissues: Fluorescence imaging of continuous point photobleaching}, volume={91}, ISSN={["1542-0086"]}, DOI={10.1529/biophysj.105.075283}, abstractNote={Molecular transport in avascular collagenous tissues such as articular cartilage occurs primarily via diffusion. The presence of ordered structures in the extracellular matrix may influence the local transport of macromolecules, leading to anisotropic diffusion depending on the relative size of the molecule and that of extracellular matrix structures. Here we present what we believe is a novel photobleaching technique for measuring the anisotropic diffusivity of macromolecules in collagenous tissues. We hypothesized that macromolecular diffusion is anisotropic in collagenous tissues, depending on molecular size and the local organization of the collagen structure. A theoretical model and experimental protocol for fluorescence imaging of continuous point photobleaching was developed to measure diffusional anisotropy. Significant anisotropy was observed in highly ordered collagenous tissues such as ligament, with diffusivity ratios>2 along the fiber direction compared to the perpendicular direction. In less-ordered tissues such as articular cartilage, diffusional anisotropy was dependent on site in the tissue and size of the diffusing molecule. Anisotropic diffusion was also dependent on the size of the diffusing molecule, with greatest anisotropy observed for larger molecules. These findings suggest that diffusional transport of macromolecules is anisotropic in collagenous tissues, with higher rates of diffusion along primary orientation of collagen fibers.}, number={1}, journal={BIOPHYSICAL JOURNAL}, author={Leddy, Holly A. and Haider, Mansoor A. and Guilak, Farshid}, year={2006}, month={Jul}, pages={311–316} }
 @article{guilak_alexopoulos_upton_youn_choi_cao_setton_haider_2006, title={The pericellular matrix as a transducer of biomechanical and biochemical signals in articular cartilage}, volume={1068}, ISBN={["1-57331-583-4"]}, ISSN={["0077-8923"]}, DOI={10.1196/annals.1346.011}, abstractNote={Abstract:   The pericellular matrix (PCM) is a narrow tissue region surrounding chondrocytes in articular cartilage, which together with the enclosed cell(s) has been termed the “chondron.” While the function of this region is not fully understood, it is hypothesized to have important biological and biomechanical functions. In this article, we review a number of studies that have investigated the structure, composition, mechanical properties, and biomechanical role of the chondrocyte PCM. This region has been shown to be rich in proteoglycans (e.g., aggrecan, hyaluronan, and decorin), collagen (types II, VI, and IX), and fibronectin, but is defined primarily by the presence of type VI collagen as compared to the extracellular matrix (ECM). Direct measures of PCM properties via micropipette aspiration of isolated chondrons have shown that the PCM has distinct mechanical properties as compared to the cell or ECM. A number of theoretical and experimental studies suggest that the PCM plays an important role in regulating the microenvironment of the chondrocyte. Parametric studies of cell–matrix interactions suggest that the presence of the PCM significantly affects the micromechanical environment of the chondrocyte in a zone‐dependent manner. These findings provide support for a potential biomechanical function of the chondrocyte PCM, and furthermore, suggest that changes in the PCM and ECM properties that occur with osteoarthritis may significantly alter the stress‐strain and fluid environments of the chondrocytes. An improved understanding of the structure and function of the PCM may provide new insights into the mechanisms that regulate chondrocyte physiology in health and disease. }, number={1068}, journal={SKELETAL DEVELOPMENT AND REMODELING IN HEALTH, DISEASE, AND AGING}, publisher={New York: New York Academy of Sciences}, author={Guilak, Farshid and Alexopoulos, Leonidas G. and Upton, Maureen L. and Youn, Inchan and Choi, Jae Bong and Cao, Li and Setton, Lori A. and Haider, Mansoor A.}, year={2006}, pages={498–512} }
 @article{guilak_alexopoulos_haider_ting-beall_setton_2005, title={Zonal uniformity in mechanical properties of the chondrocyte pericellular matrix: Micropipette aspiration of canine chondrons isolated by cartilage homogenization}, volume={33}, ISSN={["0090-6964"]}, DOI={10.1007/s10439-005-4479-7}, abstractNote={The pericellular matrix (PCM) is a region of tissue that surrounds chondrocytes in articular cartilage and together with the enclosed cells is termed the chondron. Previous studies suggest that the mechanical properties of the PCM, relative to those of the chondrocyte and the extracellular matrix (ECM), may significantly influence the stress-strain, physicochemical, and fluid-flow environments of the cell. The aim of this study was to measure the biomechanical properties of the PCM of mechanically isolated chondrons and to test the hypothesis that the Young's modulus of the PCM varies with zone of origin in articular cartilage (surface vs. middle/deep). Chondrons were extracted from articular cartilage of the canine knee using mechanical homogenization, and the elastic properties of the PCM were determined using micropipette aspiration in combination with theoretical models of the chondron as an elastic incompressible half-space, an elastic compressible bilayer, or an elastic compressible shell. The Young's modulus of the PCM was significantly higher than that reported for isolated chondrocytes but over an order of magnitude lower than that of the cartilage ECM. No significant differences were observed in the Young's modulus of the PCM between surface zone (24.0 +/- 8.9 kPa) and middle/deep zone cartilage (23.2 +/- 7.1 kPa). In combination with previous theoretical biomechanical models of the chondron, these findings suggest that the PCM significantly influences the mechanical environment of the chondrocyte in articular cartilage and therefore may play a role in modulating cellular responses to micromechanical factors.}, number={10}, journal={ANNALS OF BIOMEDICAL ENGINEERING}, author={Guilak, F and Alexopoulos, LG and Haider, MA and Ting-Beall, HP and Setton, LA}, year={2005}, month={Oct}, pages={1312–1318} }
 @article{haider_2004, title={A radial biphasic model for local cell-matrix mechanics in articular cartilage}, volume={64}, ISSN={["0036-1399"]}, DOI={10.1137/S0036139902417700}, abstractNote={Analytical and numerical solutions are presented for an interface problem that models deformation in the local cell-matrix unit (chondron) of articular cartilage. The cell and its protective pericellular matrix layer are modeled as isotropic biphasic continua deforming in small strain. A spherical geometry with purely radial deformation is assumed. Enforcement of the boundary and interface conditions results in an eigenvalue problem that is self-adjoint when the permeabilities of the cell and the layer are the same. In this case, a series solution of the interface problem is presented for a time-varying displacement prescribed at the boundary of the pericellular layer. The case of nonuniform permeability is considered via a numerical finite difference solution. The analytical and numerical solutions are used to conduct a parametric analysis of mechanical signal transmission due to an applied sinusoidal displacement. The dual role of the pericellular matrix as a mechanical signal transmitter and a protecti...}, number={5}, journal={SIAM JOURNAL ON APPLIED MATHEMATICS}, author={Haider, MA}, year={2004}, pages={1588–1608} }
 @article{haider_mehta_fouque_2004, title={Time-reversal simulations for detection in randomly layered media}, volume={14}, ISSN={["0959-7174"]}, DOI={10.1088/0959-7174/14/2/007}, abstractNote={Abstract A time-reversal mirror is, roughly speaking, a device which is capable of receiving an acoustic signal in time, keeping it in memory and sending it back into the medium in the reversed direction of time. In this paper, we employ an accurate numerical method for simulating waves propagating in complex one-dimensional media. We use numerical simulations to reproduce the time-reversal self-averaging effect which takes place in randomly layered media. This is done in the regime where the inhomogeneities are smaller than the pulse, which propagates over long distances compared to its width. We show numerical evidence for possible use of an expanding window time-reversal technique for detecting anomalies buried in the medium.}, number={2}, journal={WAVES IN RANDOM MEDIA}, author={Haider, MA and Mehta, KJ and Fouque, JP}, year={2004}, month={Apr}, pages={185–198} }
 @article{alexopoulos_haider_vail_guilak_2003, title={Alterations in the mechanical properties of the human chondrocyte pericellular matrix with osteoarthritis}, volume={125}, ISSN={["0148-0731"]}, DOI={10.1115/1.1579047}, abstractNote={In articular cartilage, chondrocytes are surrounded by a pericellular matrix (PCM), which together with the chondrocyte have been termed the “chondron.” While the precise function of the PCM is not known there has been considerable speculation that it plays a role in regulating the biomechanical environment of the chondrocyte. In this study, we measured the Young’s modulus of the PCM from normal and osteoarthritic cartilage using the micropipette aspiration technique, coupled with a newly developed axisymmetric elastic layered half-space model of the experimental configuration. Viable, intact chondrons were extracted from human articular cartilage using a new microaspiration-based isolation technique. In normal cartilage, the Young’s modulus of the PCM was similar in chondrons isolated from the surface zone (68.9±18.9 kPa) as compared to the middle and deep layers (62.0±30.5 kPa). However, the mean Young’s modulus of the PCM (pooled for the two zones) was significantly decreased in osteoarthritic cartilage (66.5±23.3 kPa versus 41.3±21.1 kPa, p<0.001). In combination with previous theoretical models of cell-matrix interactions in cartilage, these findings suggest that the PCM has an important influence on the stress-strain environment of the chondrocyte that potentially varies with depth from the cartilage surface. Furthermore, the significant loss of PCM stiffness that was observed in osteoarthritic cartilage may affect the magnitude and distribution of biomechanical signals perceived by the chondrocytes.}, number={3}, journal={JOURNAL OF BIOMECHANICAL ENGINEERING-TRANSACTIONS OF THE ASME}, author={Alexopoulos, LG and Haider, MA and Vail, TP and Guilak, F}, year={2003}, month={Jun}, pages={323–333} }
 @article{haider_guilak_2002, title={An axisymmetric boundary integral model for assessing elastic cell properties in the micropipette aspiration contact problem}, volume={124}, ISSN={["0148-0731"]}, DOI={10.1115/1.1504444}, abstractNote={The micropipette aspiration technique has been used extensively in recent years to measure the mechanical properties of living cells. In the present study, a boundary integral formulation with quadratic elements is used to predict the elastic equilibrium response in the micropipette aspiration contact problem for a three-dimensional incompressible spherical continuum cell model (Young’s modulus E). In contrast to the halfspace model [19], the spherical cell model accounts for nonlinearities in the cell response which result from a consideration of geometric factors including the finite cell dimension (radius R), curvature of the cell boundary, evolution of the cell-micropipette contact region and curvature of the edges of the micropipette (inner radius a, edge curvature radius ε). The efficiency of the boundary element method facilitates the quantification of cell response as a function of the scaled pressure p/E, for the range of parameters a/R=0.4-0.7,ε/a=0.02-0.08, in terms of two measures that can be quantified using video microscopy. These are the aspiration length, which measures projection of the cell into the micropipette, and a characteristic strain, which measures stretching along the symmetry axis. For both measures of cell response, the resistance to aspiration is found to decrease with increasing values of the aspect ratio a/R and curvature parameter ε/a, and the nonlinearities in the cell response are most pronounced in the earlier portion of the aspiration test. The aspiration length is found to exhibit less sensitivity to the aspect ratio a/R than to the curvature parameter ε/a, whereas the characteristic strain, which provides a more realistic measure of overall cell stiffness, exhibits sensitivity to the aspect ratio a/R. The resistance to aspiration in the spherical cell model is initially less than that of the half space model but eventually exceeds the halfspace prediction and the deviation between the two models increases as the parameter ε/a decreases. Adjustment factors for the Young’s modulus E, as predicted by the halfspace model, are presented and the deviation from the spherical cell model is found to be as large as 35%, when measured locally on the response curve. In practice, the deviation will be less than the maximum figure but its precise value will depend on the number of data points available in the experiment and the specific curve-fitting procedure. The spherical cell model allows for efficient and more realistic simulations of the micropipette aspiration contact problem and quantifies two observable measures of cell response that, using video microscopy, can facilitate the determination of Young’s modulus for various cell populations while, simultaneously, providing a means of evaluating the validity of continuum cell models. Furthermore, this numerical model may be readily extended to account for more complex geometries, inhomogeneities in cellular properties, or more complex constitutive descriptions of the cell.}, number={5}, journal={JOURNAL OF BIOMECHANICAL ENGINEERING-TRANSACTIONS OF THE ASME}, author={Haider, MA and Guilak, F}, year={2002}, month={Oct}, pages={586–595} }
 @article{haider_shipman_venakides_2002, title={Boundary-integral calculations of two-dimensional electromagnetic scattering in infinite photonic crystal slabs: Channel defects and resonances}, volume={62}, ISSN={["1095-712X"]}, DOI={10.1137/S003613990138531X}, abstractNote={We compute the transmission of two-dimensional (2D) electromagnetic waves through a square lattice of lossless dielectric rods with a channel defect. The lattice is finite in the direction of propagation of the incident wave and periodic in a transverse direction. We revisit a boundary-integral formulation of 2D electromagnetic scattering [Venakides, Haider, and Papanicolaou, SIAM J. Appl. Math., 60 (2000), pp. 1686--1706] that is Fredholm of the first kind and develop a second-kind formulation. We refine the numerical implementation in the above paper by exploiting separability in the Green's function to evaluate the far-field influence more efficiently. The resulting cost savings in computing and solving the discretized linear system leads to an accelerated method. We use it to analyze E-polarized electromagnetic scattering of normally incident waves on a structure with a periodic channel defect. We find three categories of resonances: waveguide modes in the channel, high-amplitude fields in the crystal...}, number={6}, journal={SIAM JOURNAL ON APPLIED MATHEMATICS}, author={Haider, MA and Shipman, SP and Venakides, S}, year={2002}, month={Aug}, pages={2129–2148} }
 @article{haider_guilak_2000, title={An axisymmetric boundary integral model for incompressible linear viscoelasticity: Application to the micropipette aspiration contact problem}, volume={122}, ISSN={["0148-0731"]}, DOI={10.1115/1.429654}, abstractNote={The micropipette aspiration test has been used extensively in recent years as a means of quantifying cellular mechanics and molecular interactions at the microscopic scale. However, previous studies have generally modeled the cell as an infinite half-space in order to develop an analytical solution for a viscoelastic solid cell. In this study, an axisymmetric boundary integral formulation of the governing equations of incompressible linear viscoelasticity is presented and used to simulate the micropipette aspiration contact problem. The cell is idealized as a homogenous and isotropic continuum with constitutive equation given by three-parameter E,τ1,τ2 standard linear viscoelasticity. The formulation is used to develop a computational model via a “correspondence principle” in which the solution is written as the sum of a homogeneous (elastic) part and a nonhomogeneous part, which depends only on past values of the solution. Via a time-marching scheme, the solution of the viscoelastic problem is obtained by employing an elastic boundary element method with modified boundary conditions. The accuracy and convergence of the time-marching scheme are verified using an analytical solution. An incremental reformulation of the scheme is presented to facilitate the simulation of micropipette aspiration, a nonlinear contact problem. In contrast to the halfspace model (Sato et al., 1990), this computational model accounts for nonlinearities in the cell response that result from a consideration of geometric factors including the finite cell dimension (radius R), curvature of the cell boundary, evolution of the cell–micropipette contact region, and curvature of the edges of the micropipette (inner radius a, edge curvature radius ε). Using 60 quadratic boundary elements, a micropipette aspiration creep test with ramp time t*=0.1 s and ramp pressure p*/E=0.8 is simulated for the cases a/R=0.3, 0.4, 0.5 using mean parameter values for primary chondrocytes. Comparisons to the half-space model indicate that the computational model predicts an aspiration length that is less stiff during the initial ramp response t=0-1 s but more stiff at equilibrium t=200 s. Overall, the ramp and equilibrium predictions of aspiration length by the computational model are fairly insensitive to aspect ratio a/R but can differ from the half-space model by up to 20 percent. This computational approach may be readily extended to account for more complex geometries or inhomogeneities in cellular properties. [S0148-0731(00)00503-3]}, number={3}, journal={JOURNAL OF BIOMECHANICAL ENGINEERING-TRANSACTIONS OF THE ASME}, author={Haider, MA and Guilak, F}, year={2000}, month={Jun}, pages={236–244} }
 @article{venakides_haider_papanicolaou_2000, title={Boundary integral calculations of two-dimensional electromagnetic scattering by photonic crystal Fabry-Perot structures}, volume={60}, DOI={10.1137/s0036139999350779}, abstractNote={We compute the transmission properties of two-dimensional (2-D) electromagnetic transverse magnetic (TM) waves that are normally incident on a Fabry--Perot structure with mirrors consisting of photonic crystals. We use a boundary integral formulation with quadratic boundary elements and utilize the Ewald representation for Green's functions. We trace the frequencies of the Fabry--Perot cavity modes traversing the photonic bandgap as the cavity length increases and calculate corresponding Q-values.}, number={5}, journal={SIAM Journal on Applied Mathematics}, author={Venakides, S. and Haider, Mansoor A and Papanicolaou, V.}, year={2000}, pages={1686–1706} }
 @inproceedings{venakides_haider_papanicolaou_2000, place={River Edge, New Jersey}, title={Wave propagation in photonic crystal models}, ISBN={9789810243913 9789812792327}, url={http://dx.doi.org/10.1142/9789812792327_0013}, DOI={10.1142/9789812792327_0013}, abstractNote={Abstract : We compute the transmission properties of 2-D electromagnetic TM waves that are normally incident on a Fabry-Perot structure with mirrors consisting of photonic crystals. We use a boundary integral formulation with quadratic boundary elements and utilize the Ewald representation for the Green's functions. We trace the frequencies of the Fabry-Perot cavity modes traversing the photon bandgap as the cavity length increases and calculate corresponding Q-values. For the case of lossy dielectrics, we compare bandgap frequencies and Q-values to experimental results obtained by H. Everitt and his group at Duke University.}, booktitle={Scattering Theory and Biomedical Engineering Modelling and Applications}, publisher={World Scientific}, author={Venakides, S. and Haider, M. A. and Papanicolaou, V.}, editor={Dassios, G. and Fotiadis, D. I. and Massalas, C. V. and Kiriaki, K.Editors}, year={2000}, month={Oct}, pages={120–134} }
 @article{beaky_burk_everitt_haider_venakides_1999, title={Two-dimensional photonic crystal Fabry-Perot resonators with lossy dielectrics}, volume={47}, ISSN={["1557-9670"]}, DOI={10.1109/22.798003}, abstractNote={Square and triangular lattice two-dimensional (2D) photonic crystals (PCs) composed of lossy dielectric rods in air were constructed with a microwave bandgap between 4-8 GHz. Fabry-Perot resonators of varying length were constructed from two of these PCs of adjustable thickness and reflectivity. The quality factor of cavity modes supported in the resonators was found to increase with increasing PC mirror thickness, but only to a point dictated by the lossiness of the dielectric rods. A 2-D periodic Green's function simulation was found to model the data accurately and quickly using physical parameters obtained in separate measurements. Simple rules are developed for designing optimal resonators in the presence of dielectric loss.}, number={11}, journal={IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES}, author={Beaky, MM and Burk, JB and Everitt, HO and Haider, MA and Venakides, S}, year={1999}, month={Nov}, pages={2085–2091} }
 @inbook{haider_holmes_1998, title={Three dimensional viscoelasticity in finite strain: Formulation of a rate-type constitutive law consistent with dissipation}, DOI={10.1007/978-1-4684-7109-0_4}, abstractNote={Viscoelastic constitutive models can predict transient phenomena like creep and stress relaxation. Among the materials that can exhibit such effects in finite strain are biological soft tissues which are commonly modeled using a multiphasic continuum theory. Under infinitesimal strain, the classical 1-D Standard Linear Model (1-D SLM) is a simple law containing a stress rate and exhibiting the desired transient and equilibrium behavior observable in many soft tissues. The derivation of a rate-type constitutive law appropriate for modeling the non-linear viscoelasticity of soft tissues is the focus of this study. Well-posed laws should be objective and consistent with thermodynamic considerations of dissipation and energy. Infinitesimal models are not objective, while many non-linear analogies to the 1-D SLM fail to address dissipation. In the current study, internal variables are introduced, and employed in the derivation of a 3-D non-linear rate-type viscoelastic constitutive law. Evolution of the internal variables is assumed to involve first order rates. Properties of the 1-D SLM as well as existing non-linear models of soft tissues are used to motivate the constitutive assumptions and additional requirements. These requirements include symmetry of the stress, isotropy, reduction to hyperelasticity (via material parameters) and the existence of a hyperelastic equilibrium state. A class of objective rate-type constitutive laws satisfying dissipation and the additional requirements is derived. As an illustration, a compressible finite linear model is formulated. In infinitesimal strain, this model provides a 3-D analogy to the 1-D SLM with a set of constraints on the material parameters. The finite linear model is analyzed under simple time-dependent compression, extension and shear and shown to be consistent with expected behavior.}, booktitle={Particulate flows: Processing and rheology (The IMA volumes in mathematics and its applications ;  v. 98)}, publisher={New York: Springer}, author={Haider, Mansoor A and Holmes, M. H.}, editor={D. A. Drew, D. D. Joseph and Passman, S. L.Editors}, year={1998}, pages={67–88} }
 @article{haider_holmes_1997, title={A mathematical approximation for the solution of a static indentation test}, volume={30}, ISSN={["1873-2380"]}, DOI={10.1016/S0021-9290(97)00024-9}, abstractNote={The classical contact problem of the indentation of a thin compressible linear elastic layer bonded to a rigid substrate is considered. Closed-form mathematical approximations of the deformation are presented for the cases of plane indentation by a rectangular block and three dimensional indentation by a plane-ended (axisymmetric) cylinder. The approximations are analyzed in the context of a static indentation test by comparison of applied load values to those obtained using a classical integral transform solution. In the case of plane indentation, the mathematical and classical predictions agree to within 2% relative error for aspect ratios between 0.1 and 1.0 and apparent Poisson ratio between 0.0 and 0.3. Comparisons for the axisymmetric case indicate a similar pattern. The main advantage of the new approach is that it yields closed-form approximations of the static indentation solution which can also capture the essential singular behavior.}, number={7}, journal={JOURNAL OF BIOMECHANICS}, author={Haider, MA and Holmes, MH}, year={1997}, month={Jul}, pages={747–751} }
 @inbook{haider_holmes_1997, title={Analytic approximations to the deformation of a thin compressible elastic layer by a rigid indenter}, booktitle={Applied Mathematics: Methods and Applications}, publisher={Nova Science}, author={Haider, M.A. and Holmes, M.H.}, editor={Oyibo, G.Editor}, year={1997}, pages={257–288} }
 @phdthesis{haider_1996, place={Troy, NY}, title={Analytic Appoximations for the Indentation of a Thin Linear Elastic Layer and a Viscoelastic Formulation in Finite Strain with Applications to the Mechanics of Biological Soft Tissues}, school={Rensselaer Polytechnic Institute}, author={Haider, M.A.}, year={1996} }
 @article{haider_holmes_1996, title={Analytic approximations to the deformation of a thin compressible elastic layer by a rigid flat indenter}, volume={5}, journal={International Journal of Mathematics, Game Theory and Algebra}, publisher={Nova Science Publishers}, author={Haider, M.A. and Holmes, M.H.}, year={1996}, pages={1–32} }
 @article{haider_holmes_1995, title={Indentation of a thin compressible elastic layer: Approximate analytic and numerical solutions for rigid flat indenters}, volume={43}, ISSN={0022-5096}, url={http://dx.doi.org/10.1016/0022-5096(95)00032-e}, DOI={10.1016/0022-5096(95)00032-e}, abstractNote={Abstract Indentation of a thin compressible linearly elastic layer in bonded or frictionless contact with a rigid foundation is considered. Using the small parameter e = h a , an asymptotic analysis of the deformation for thin layers in plane strain is conducted. For flat indenters, the existence of an outer solution and interior layers near the edges of the indenter are demonstrated. In the interior layers, an analytic approximation is developed and closed form expressions for the vertical deformation and normal stress are obtained. The equilibrium equations and all but one (frictionless case) or two (bonded case) of the boundary conditions are satisfied. The approximation incorporates a large portion of the singular deformation gradients near the edge of the indenter and is in close agreement with known asymptotic results. A numerical study of the plane strain case shows that incorporation of the approximation into a numerical scheme greatly increases convergence rate, in that accurate results may be obtained on coarse meshes.}, number={8}, journal={Journal of the Mechanics and Physics of Solids}, publisher={Elsevier BV}, author={Haider, M.A. and Holmes, M.H.}, year={1995}, month={Aug}, pages={1199–1219} }