Local Identifiability Analysis, Parameter Subset Selection and Verification for a Minimal Brain PBPK Model.

Physiologically-based pharmacokinetic (PBPK) modeling is important for studying drug delivery in the central nervous system, including determining antibody exposure, predicting chemical concentrations at target locations, and ensuring accurate dosages. The complexity of PBPK models, involving many variables and parameters, requires a consideration of parameter identifiability; i.e., which parameters can be uniquely determined from data for a specified set of concentrations. We introduce the use of a local sensitivity-based parameter subset selection algorithm in the context of a minimal PBPK (mPBPK) model of the brain for antibody therapeutics. This algorithm is augmented by verification techniques, based on response distributions and energy statistics, to provide a systematic and robust technique to determine identifiable parameter subsets in a PBPK model across a specified time domain of interest. The accuracy of our approach is evaluated for three key concentrations in the mPBPK model for plasma, brain interstitial fluid and brain cerebrospinal fluid. The determination of accurate identifiable parameter subsets is important for model reduction and uncertainty quantification for PBPK models.

Unsupervised learning methods for efficient geographic clustering and identification of disease disparities with applications to county-level colorectal cancer incidence in California.

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.

Modeling and Parameter Subset Selection for Fibrin Polymerization Kinetics with Applications to Wound Healing.

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.

Hidradenitis Suppurativa in Down Syndrome: A Case Series.

BACKGROUND/OBJECTIVES: Many dermatologic and systemic diseases have been reported in association with hidradenitis suppurativa, but its association with Down syndrome is rarely mentioned in the literature. The objective of the current study was to assess the frequency of hidradenitis suppurativa in patients with Down syndrome who visited our clinic over 4 years. METHODS: We recorded the presenting complaints and dermatologic problems of patients with Down syndrome who visited our clinic from January 2011 to December 2014. Medical photographs were taken. Patients with hidradenitis suppurativa were assessed according to severity and treated with topical and systemic medications. RESULTS: Twenty-nine new patients with Down syndrome visited our clinic during this period. Eleven had hidradenitis suppurativa. Disease severity included Hurley stages I and II. CONCLUSION: The presence of hidradenitis suppurativa in 38% of patients with Down syndrome is far higher than would be expected by chance alone.

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.

Pulmonary hypertension is a cardiovascular disorder manifested by elevated mean arterial blood pressure (>20 mmHg) together with vessel wall stiffening and thickening due to alterations in collagen, elastin, and smooth muscle cells. Hypoxia-induced (type 3) pulmonary hypertension can be studied in animals exposed to a low oxygen environment for prolonged time periods leading to biomechanical alterations in vessel wall structure. This study introduces a novel approach to formulating a reduced order nonlinear elastic structural wall model for a large pulmonary artery. The model relating blood pressure and area is calibrated using ex vivo measurements of vessel diameter and wall thickness changes, under controlled pressure conditions, in left pulmonary arteries isolated from control and hypertensive mice. A two-layer, hyperelastic, and anisotropic model incorporating residual stresses is formulated using the Holzapfel-Gasser-Ogden model. Complex relations predicting vessel area and wall thickness with increasing blood pressure are derived and calibrated using the data. Sensitivity analysis, parameter estimation, subset selection, and physical plausibility arguments are used to systematically reduce the 16-parameter model to one in which a much smaller subset of identifiable parameters is estimated via solution of an inverse problem. Our final reduced one layer model includes a single set of three elastic moduli. Estimated ranges of these parameters demonstrate that nonlinear stiffening is dominated by elastin in the control animals and by collagen in the hypertensive animals. The pressure-area relation developed in this novel manner has potential impact on one-dimensional fluids network models of vessel wall remodeling in the presence of cardiovascular disease.

Bulk and mosaic deletions of Egfr reveal regionally defined gliogenesis in the developing mouse forebrain.

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.

An axisymmetric boundary element model for determination of articular cartilage pericellular matrix properties in situ via inverse analysis of chondron deformation.

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 approximately 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.

Acquired cutis laxa type II (Marshall syndrome) in an 18-month-old child: a case report.

Cutis laxa is a rare disorder resulting from degradation and clumping of elastic fibers in dermis. Type II acquired cutis laxa, shows only cutaneous changes without any systemic involvement. We describe an infant with acquired cutis laxa type II following a generalized inflammatory dermatitis.

Clonal Analysis of Gliogenesis in the Cerebral Cortex Reveals Stochastic Expansion of Glia and Cell Autonomous Responses to Egfr Dosage.

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.

A computational reaction-diffusion model for biosynthesis and linking of cartilage extracellular matrix in cell-seeded scaffolds with varying porosity.

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.

Rituximab/IVIG in pemphigus - a 10-year study with a long follow-up.

BACKGROUND: Pemphigus is a chronic potentially life-threatening autoimmune blistering disease affecting the skin and/or mucous membranes. Rituximab is being increasingly used and found efficacious in the treatment of pemphigus. OBJECTIVE: To present the Middle-Eastern experience with the use of rituximab in pemphigus. METHODS: A retrospective analysis of patient files was conducted which revealed 23 patients of pemphigus who were treated with rituximab (either alone or with IVIG) in the dermatology department of a tertiary care hospital from July 2004 to December 2014. RESULTS: The mean time to disease control was 8 weeks (median 5 weeks and range 2-30 weeks). 90.9% attained early study end point with the first cycle of rituximab. The remaining 9.1% needed an additional course of rituximab + IVIG to attain disease control. 90.5% of our patients attained complete remission during the study period. The average time to attain complete remission on minimal treatment was 25.4 weeks and partial remission on minimal treatment was attained after a mean period of 18.3 weeks. Rituximab was well tolerated by our patients and the rate of adverse-effects in our cohort was comparable to the previous reports. CONCLUSIONS: Rituximab is an effective and safe treatment for pemphigus and should be considered earlier in the algorithm of pemphigus treatment.

Hemodynamic assessment of pulmonary hypertension in mice: a model-based analysis of the disease mechanism.

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.

Characteristic impedance: frequency or time domain approach?

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.

Application of a Three-Dimensional Poroelastic BEM to Modeling the Biphasic Mechanics of Cell-Matrix Interactions in Articular Cartilage (REVISION).

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.

The pericellular matrix as a transducer of biomechanical and biochemical signals in articular cartilage.

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.

A numerical method for the continuous spectrum biphasic poroviscoelastic model of articular cartilage.

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.

A mechano-chemical model for the passive swelling response of an isolated chondron under osmotic loading.

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.

Use of hybrid discrete cellular models for identification of macroscopic nutrient loss in reaction-diffusion models of tissues.

Macroscopic models accounting for cellular effects in natural or engineered tissues may involve unknown constitutive terms that are highly dependent on interactions at the scale of individual cells. Hybrid discrete models, which represent cells individually, were used to develop and apply techniques for modeling diffusive nutrient transport and cellular uptake to identify a nonlinear nutrient loss term in a macroscopic reaction-diffusion model of the system. Flexible and robust numerical methods were used, based on discontinuous Galerkin finite elements in space and a Crank-Nicolson temporal discretization. Scales were bridged via averaging operations over a complete set of subdomains yielding data for identification of a macroscopic nutrient loss term that was accurately captured via a fifth-order polynomial. Accuracy of the identified macroscopic model was demonstrated by direct, quantitative comparisons of the tissue and cellular scale models in terms of three error norms computed on a mesoscale mesh.