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Papers by David Rumschitzki

Journal of Theoretical Biology, Aug 1, 2020

Atherosclerosis starts with transmural (transwall) pressure-driven advective transport of blood-b... more Atherosclerosis starts with transmural (transwall) pressure-driven advective transport of blood-borne low-density lipoprotein (LDL) cholesterol across rare endothelial cell (EC) monolayer leaks into the arterial subendothelial intima (SI) wall layer where they can spread, bind to extracellular matrix and seed lesions. The local SI LDL concentration, which governs LDL's binding kinetics, depends on the overall diluting transmural liquid flow. Transmural pressures typically compress the SI at physiological pressures, which keeps this flow low. Nguyen et al. (2015) showed that aortic ECs express the water channel protein aquaporin-1 (AQP1) and the transEC (δP) portion of the transmural (P) pressure difference drives, in parallel, water across AQP1s and plasma across interEC junctions. Since the lumen is isotonic, selective AQP1-mediated water flow should quickly render the ECs' lumen side hypertonic and the SI hypotonic; resulting transEC oncotic pressure differences, δπ, should oppose δP and quickly halt transEC flow. Yet Nguyen et al.'s (2015) transAQP1 flows persist for hours. To resolve this paradox, we extend our fluid filtration theory Joshi et al. (2015) to include mass transfer for oncotically active solutes like albumin. This addition nonlinearly couples mass transfer, fluid flow and wall mechanics. We simultaneously solve these problems at steady state. Surprisingly it finds that media layer filtration causes steady SI to exceed EC glycocalyx albumin concentration. Thus δπ reinforces rather than opposes δP , i.e., it sucks water from, rather than pushing water into the lumen from the SI. Endothelial AQP1s raise the overall driving force for flow across the EC above δP , most significantly at pressures too low to compress the SI, and they increase the P needed for SI compression. This suggests the intriguing possibility that increasing EC AQP1 expression can raise this requisite compression pressure to physiological values. That is, increasing EC AQP1 may decompress the SI at physiological pressures, which would significantly increase SI thickness, flow and subsequently SI LDL dilution. This could retard LDL binding and delay preatherosclerotic lesion onset. The model also predicts that glycocalyx-degrading enzymes decrease overall transEC driving forces and thus lower, not raise, transmural water flux.

Physical Review E, Mar 5, 2014

One characteristic of multiphase lattice Boltzmann equation (LBE) methods is that the interfacial... more One characteristic of multiphase lattice Boltzmann equation (LBE) methods is that the interfacial region has a finite (i.e., noninfinitesimal) thickness known as a diffuse interface. In simulations of, e.g., bubble or drop dynamics, for problems involving nonideal gases, one frequently observes that the diffuse interface method produces a spontaneous, nonphysical shrinkage of the bubble or drop radius. In this paper, we analyze in detail a single-fluid two-phase model and use a LBE model for nonideal gases in order to explain this fundamental problem. For simplicity, we only investigate the static bubble or droplet problem. We find that the method indeed produces a density shift, bubble or droplet shrinkage, as well as a critical radius below which the bubble or droplet eventually vanishes. Assuming that the ratio between the interface thickness D and the initial bubble or droplet radius r 0 is small, we analytically show the existence of this density shift, bubble or droplet radius shrinkage, and critical bubble or droplet survival radius. Numerical results confirm our analysis. We also consider droplets on a solid surface with different curvatures, contact angles, and initial droplet volumes. Numerical results show that the curvature, contact angle, and the initial droplet volume have an effect on this spontaneous shrinkage process, consistent with the survival criterion.

Journal of Biomechanics, 2006

Atherosclerosis is a disease mainly of large, high pressure arteries and of valves, typically spa... more Atherosclerosis is a disease mainly of large, high pressure arteries and of valves, typically sparing veins and small, low pressure arteries. We investigate the resistances of the vena cava and the pulmonary artery to the flow of water and the infiltration of solutes into the vessel walls and compare them with similar processes in the aorta. The goal is to see if differences in macromolecular transport from the blood into the vessel wall amongst vessels can explain their different susceptibilities to atherosclerosis.

American Journal of Physiology-heart and Circulatory Physiology, Jun 1, 2007

American Journal of Physiology-heart and Circulatory Physiology, Nov 1, 2017

Numerous studies have examined the role of aquaporins in osmotic water transport in various syste... more Numerous studies have examined the role of aquaporins in osmotic water transport in various systems, but virtually none have focused on the role of aquaporin in hydrostatically driven water transport involving mammalian cells save for our laboratory's recent study of aortic endothelial cells. Here, we investigated aquaporin-1 expression and function in the aortic endothelium in two high-renin rat models of hypertension, the spontaneously hypertensive genetically altered Wistar-Kyoto rat variant and Sprague-Dawley rats made hypertensive by two-kidney, one-clip Goldblatt surgery. We measured aquaporin-1 expression in aortic endothelial cells from whole rat aortas by quantitative immunohistochemistry and function by measuring the pressure-driven hydraulic conductivities of excised rat aortas with both intact and denuded endothelia on the same vessel. We used them to calculate the effective intimal hydraulic conductivity, which is a combination of endothelial and subendothelial components. We observed well-correlated enhancements in aquaporin-1 expression and function in both hypertensive rat models as well as in aortas from normotensive rats whose expression was upregulated by 2 h of forskolin treatment. Upregulated aquaporin-1 expression and function may be a response to hypertension that critically determines conduit artery vessel wall viability and long-term susceptibility to atherosclerosis. NEW & NOTEWORTHY The aortic endothelia of two high-renin hypertensive rat models express greater than two times the aquaporin-1 and, at low pressures, have greater than two times the endothelial hydraulic conductivity of normotensive rats. Data are consistent with theory predicting that higher endothelial aquaporin-1 expression raises the critical pressure for subendothelial intima compression and for artery wall hydraulic conductivity to drop.

Journal of Fluid Mechanics, Sep 10, 2002

A core-annular flow, the concurrent axial flow of two immiscible fluids in a circular tube or por... more A core-annular flow, the concurrent axial flow of two immiscible fluids in a circular tube or pore with one fluid in the core and the other in the wetting annular region, is frequently used to model technologically important flows, e.g. in liquid-liquid displacements in secondary oil recovery. Most of the existing literature assumes that the pores in which such flows occur are uniform circular cylinders, and examine the interfacial stability of such systems as a function of fluid and interfacial properties. Since real rock pores possess a more complex geometry, the companion paper examined the linear stability of core-annular flows in axisymmetric, corrugated pores in the limit of asymptotically weak corrugation. It found that shortwave disturbances that were stable in straight tubes could couple to the wall's periodicity to excite unstable long waves. In this paper, we follow the evolution of the axisymmetric, linearly unstable waves for fluids of equal densities in a corrugated tube into the weakly nonlinear regime. Here, we ask whether this continual generation of new disturbances by the coupling to the wall's periodicity can overcome the nonlinear saturation mechanism that relies on the nonlinear (kinematic-condition-derived) wave steepening of the Kuramoto-Sivashinsky (KS) equation. If it cannot, and the unstable waves still saturate, then do these additional excited waves make the KS solutions more likely to be chaotic, or does the dispersion introduced into the growth rate correction by capillarity serve to regularize otherwise chaotic motions? We find that in the usual strong surface tension limit, the saturation mechanism of the KS mechanism remains able to saturate all disturbances. Moreover, an additional capillary-derived nonlinear term seems to favour regular travelling waves over chaos, and corrugation adds a temporal periodicity to the waves associated with their periodical traversing of the wall's crests and troughs. For even larger surface tensions, capillarity dominates over convection and a weakly nonlinear version of Hammond's no-flow equation results; this equation, with or without corrugation, suggests further growth. Finally, for a weaker surface tension, the leading-order base flow interface follows the wall's shape. The corrugation-derived excited waves appear able to push an otherwise regular travelling wave solution to KS to become chaotic, whereas its dispersive properties in this limit seem insufficiently strong to regularize chaotic motions.

Acta Applicandae Mathematicae, Feb 1, 1988

A connection between evolutionary mutation-selection dynamics on sequence space and linear repres... more A connection between evolutionary mutation-selection dynamics on sequence space and linear representations of the hyper-octahedral group (interpreted as the isometry group of the space of {0, 1-sequences relative to the Hamming distance metric) and other such wreath product groups is established and studied.

Journal of Fluid Mechanics, Oct 11, 2005

1999 Bioengineering Conference, Dec 1, 1999

Both linear and weakly nonlinear stability of a core annular flow in a corrugated tube in the lim... more Both linear and weakly nonlinear stability of a core annular flow in a corrugated tube in the limit of thin film and small corrugation are examined. Asymptotic techniques are used to derive the corrugated base flow and corresponding linear and weakly nonlinear stability equations. Interesting features show that the corrugation interaction can excite linear instability, but the nonlinearity still can suppress such instability in the weakly nonlinear regime.

Siam Journal on Applied Mathematics, 2013

ABSTRACT Prerequisite to atherogenesis is low-density lipoprotein (LDL) cholesterol transport fro... more ABSTRACT Prerequisite to atherogenesis is low-density lipoprotein (LDL) cholesterol transport from the blood into the artery wall across its endothelial cell (EC) lining. Whereas most EC junctions are tight enough to preclude LDL passage, some (approx1/2000−6000)(\approx 1/2000-6000)(approx1/2000−6000) rare ECs have temporarily-widened junctions (typically approx10−5\approx 10^{-5}approx10−5 of the problem’s radial scale) that allow passage of large molecular aggregates like LDL. In a purely diffusive transport model, Laplace's equation describes the steady tracer profile throughout the two major subendothelial wall layers, connected by matching conditions. In a diffusive and transmural-pressure-driven advective transport model, Laplace’s equation describes the steady pressure distribution in the wall, whose gradient is proportional to the advecting velocity. Both problems yield the same boundary value problem that has mixed Dirichlet/ Robin boundary conditions. We construct a linear system of integral equations that approximates the series expansion coefficients of the problem solution. We prove existence/convergence of this solution using the contraction mapping theorem and its uniqueness using Miranda's theorem. The analytical construction method yields a numerical calculation algorithm. Our analysis supports a surprising result that the series solution’s convergence rate increases as the ratio (approx10−5)(\approx 10^{-5})(approx10−5) of leaky junction width to mean half-distance between neighboring leaky cells increases. Numerical results agree well with previous ad hoc numerical methods. The subendothelial intima exhibits boundary layer scale separation. Calculations show the solution spike just beneath the leak is by far the region most sensitive to calculation accuracy. Since these models posit all LDL wall entry through these widened junctions, solution accuracy is particularly critical there.

American Journal of Physiology-heart and Circulatory Physiology, Apr 15, 2012

Zeng Z, Jan KM, Rumschitzki DS. A theory for water and macromolecular transport in the pulmonary ... more Zeng Z, Jan KM, Rumschitzki DS. A theory for water and macromolecular transport in the pulmonary artery wall with a detailed comparison to the aorta.

Studies in Surface Science and Catalysis, 1997

We propose an experimental protocol that can provide a diagnostic tool for probing the state of c... more We propose an experimental protocol that can provide a diagnostic tool for probing the state of catalyst coking and its influence on product composition in an operating reactor throughout the lifetime of the catalyst. The experimental equipment includes a vibrational microbalance, a multi-outlet fixed bed reactor, and a temperature-programmed oxidation appartus. We illustrates its use by applying it to n-heptane reformings on a commercial Pt-Re/Al 2 O 3 catalyst. The results idenfity five-memberee naphthenes (C5N) as the key source of coke and provide the data needed to develop kinetic models for both reforming and coking. From the measured or predicted C5N concentration, the models correctly predict the reactor coke profile and the reforming product composition as functions of on-stream time.

Industrial & Engineering Chemistry Research, Nov 27, 2002

ABSTRACT We reported previously that coke can indiscriminately deposit on the metal, acid, and al... more ABSTRACT We reported previously that coke can indiscriminately deposit on the metal, acid, and already-coked sites on a Pt−Re/Al2O3 reforming catalyst. Here we show that the thus-deposited coke, when still in a freshly formed state, can be indiscriminately gasified by hydrogen at temperatures as low as 477 °C. Once the freshly formed coke transforms into a more refractory form, it cannot be gasified by hydrogen. The kinetics of coke hydrogasification is first order with respect to both the concentration of the freshly formed coke and hydrogen partial pressure, with an apparent activation energy of 9.2 kcal/mol. A random coke deposition model offers a theoretical basis for correlating the decoking data.

American Journal of Physiology-heart and Circulatory Physiology, Jun 1, 2007

The heart valve leaflets of 29-day cholesterol-fed rabbits were examined by ultrarapid freezing w... more The heart valve leaflets of 29-day cholesterol-fed rabbits were examined by ultrarapid freezing without conventional chemical fixation/processing, followed by rotary shadow freeze-etching. This procedure images the leaflets' subendothelial extracellular matrix in extraordinary detail, and extracellular lipid liposomes, from 23 to 220 nm in diameter, clearly appear there. These liposomes are linked to matrix filaments and appear in clusters. Their size distribution shows 60.7% with diameters 23-69 nm, 31.7% between 70 and 119 nm, 7.3% between 120 and 169 nm, and 0.3% between 170 and 220 nm (superlarge) and suggests that smaller liposomes can fuse into larger ones. We couple our model from Part II of this series (Zeng Z, Yin Y, Jan KM, Rumschitzki DS.

American Journal of Physiology-heart and Circulatory Physiology, Jun 1, 2007

This paper proposes a new, two-dimensional convection-diffusion model for macromolecular transpor... more This paper proposes a new, two-dimensional convection-diffusion model for macromolecular transport in heart valves based on horseradish peroxidase (HRP) experiments on rats presented in the first of the papers in this series (

Chemical Engineering Science, 1988

In two recent articles, connections were drawn between reaction network structure and the possibi... more In two recent articles, connections were drawn between reaction network structure and the possibility of multiple steady states in complex isothermal reactors. The particular applicability of these results to continuous flow stirred tank reactors is studied. It is shown that CFSTRs involving heterogeneous catalysis will often be good candidates for application of existing theory. On the other hand, it is also shown that homogeneous CFSTRs will generally require different ideas. This last observation provides motivation for a companion paper. f. INTRODUCTION In two recent articles (Feinberg, 1987, 1988) connections were drawn between the behavior of complex isothermal reactors and the structure of the underlying reaction network. Special emphasis was placed on the relationship between reaction network structure and the possibility of multiple steady states. The results permit one to determine for each reaction network within a certain large class whether multiple steady states can be admitted by the corresponding differential equations. Although continuous flow stirred tank reactors (CFSTRs) were considered in some examples, the theory was intended to be sufficiently general as to be applicable to wide varieties of reactors and to CFSTRs only incidentally. This is the first in a series of articles dedicated speczficaily to questions about steady state multiplicity in isothermal CFSTRs. Here we will show that for CFSTRs involving heterogeneous catalysis the theory given by Feinberg (1988) can often provide the basis for an incisive analysis of multiplicity questions. On the other hand, we will also show why the situation is not nearly as satisfactory for homogeneous CFSTRs. This last observation will provide motivation for a companion article that contains theory constructed especially for homogeneous CFSTRs. Readers of this article should already have some understanding of how CFSTRs are described in terms 'The research described here was done while D. Rumschitzki was a visitor from the University of California, Berkeley, where he was a Ph.D. candidate.

Aiche Journal, Oct 1, 1989

This paper focuses on the problem of scale-up of two-phase (e.g., solid-fluid) reactors. It outli... more This paper focuses on the problem of scale-up of two-phase (e.g., solid-fluid) reactors. It outlines a class of such reactors which, for firstorder reactions, scale in the familiar single-phase manner via an analog of the usual residence time distribution formula. The differences lie in the fact that the appropriate tracer experiment entering the formalism for this reactor class refers to a nonadsorbing tracer, and the analog of the plug flow solution is the solution for a fixed bed with fluid-phase plug flow. Surprisingly, unlike single-phase systems, there exist two-phase reactors, outside of the class defined, that do not scale in this manner, even when, say, the true catalyst surface chemistry is purely first-order. The paper discusses a few examples and implications for the design of two-phase reactors, including fluidized beds.

American Journal of Physiology-heart and Circulatory Physiology, Apr 1, 1997

Journal of Theoretical Biology, Aug 1, 2020

Atherosclerosis starts with transmural (transwall) pressure-driven advective transport of blood-b... more Atherosclerosis starts with transmural (transwall) pressure-driven advective transport of blood-borne low-density lipoprotein (LDL) cholesterol across rare endothelial cell (EC) monolayer leaks into the arterial subendothelial intima (SI) wall layer where they can spread, bind to extracellular matrix and seed lesions. The local SI LDL concentration, which governs LDL's binding kinetics, depends on the overall diluting transmural liquid flow. Transmural pressures typically compress the SI at physiological pressures, which keeps this flow low. Nguyen et al. (2015) showed that aortic ECs express the water channel protein aquaporin-1 (AQP1) and the transEC (δP) portion of the transmural (P) pressure difference drives, in parallel, water across AQP1s and plasma across interEC junctions. Since the lumen is isotonic, selective AQP1-mediated water flow should quickly render the ECs' lumen side hypertonic and the SI hypotonic; resulting transEC oncotic pressure differences, δπ, should oppose δP and quickly halt transEC flow. Yet Nguyen et al.'s (2015) transAQP1 flows persist for hours. To resolve this paradox, we extend our fluid filtration theory Joshi et al. (2015) to include mass transfer for oncotically active solutes like albumin. This addition nonlinearly couples mass transfer, fluid flow and wall mechanics. We simultaneously solve these problems at steady state. Surprisingly it finds that media layer filtration causes steady SI to exceed EC glycocalyx albumin concentration. Thus δπ reinforces rather than opposes δP , i.e., it sucks water from, rather than pushing water into the lumen from the SI. Endothelial AQP1s raise the overall driving force for flow across the EC above δP , most significantly at pressures too low to compress the SI, and they increase the P needed for SI compression. This suggests the intriguing possibility that increasing EC AQP1 expression can raise this requisite compression pressure to physiological values. That is, increasing EC AQP1 may decompress the SI at physiological pressures, which would significantly increase SI thickness, flow and subsequently SI LDL dilution. This could retard LDL binding and delay preatherosclerotic lesion onset. The model also predicts that glycocalyx-degrading enzymes decrease overall transEC driving forces and thus lower, not raise, transmural water flux.

Physical Review E, Mar 5, 2014

One characteristic of multiphase lattice Boltzmann equation (LBE) methods is that the interfacial... more One characteristic of multiphase lattice Boltzmann equation (LBE) methods is that the interfacial region has a finite (i.e., noninfinitesimal) thickness known as a diffuse interface. In simulations of, e.g., bubble or drop dynamics, for problems involving nonideal gases, one frequently observes that the diffuse interface method produces a spontaneous, nonphysical shrinkage of the bubble or drop radius. In this paper, we analyze in detail a single-fluid two-phase model and use a LBE model for nonideal gases in order to explain this fundamental problem. For simplicity, we only investigate the static bubble or droplet problem. We find that the method indeed produces a density shift, bubble or droplet shrinkage, as well as a critical radius below which the bubble or droplet eventually vanishes. Assuming that the ratio between the interface thickness D and the initial bubble or droplet radius r 0 is small, we analytically show the existence of this density shift, bubble or droplet radius shrinkage, and critical bubble or droplet survival radius. Numerical results confirm our analysis. We also consider droplets on a solid surface with different curvatures, contact angles, and initial droplet volumes. Numerical results show that the curvature, contact angle, and the initial droplet volume have an effect on this spontaneous shrinkage process, consistent with the survival criterion.

Journal of Biomechanics, 2006

Atherosclerosis is a disease mainly of large, high pressure arteries and of valves, typically spa... more Atherosclerosis is a disease mainly of large, high pressure arteries and of valves, typically sparing veins and small, low pressure arteries. We investigate the resistances of the vena cava and the pulmonary artery to the flow of water and the infiltration of solutes into the vessel walls and compare them with similar processes in the aorta. The goal is to see if differences in macromolecular transport from the blood into the vessel wall amongst vessels can explain their different susceptibilities to atherosclerosis.

American Journal of Physiology-heart and Circulatory Physiology, Jun 1, 2007

American Journal of Physiology-heart and Circulatory Physiology, Nov 1, 2017

Numerous studies have examined the role of aquaporins in osmotic water transport in various syste... more Numerous studies have examined the role of aquaporins in osmotic water transport in various systems, but virtually none have focused on the role of aquaporin in hydrostatically driven water transport involving mammalian cells save for our laboratory's recent study of aortic endothelial cells. Here, we investigated aquaporin-1 expression and function in the aortic endothelium in two high-renin rat models of hypertension, the spontaneously hypertensive genetically altered Wistar-Kyoto rat variant and Sprague-Dawley rats made hypertensive by two-kidney, one-clip Goldblatt surgery. We measured aquaporin-1 expression in aortic endothelial cells from whole rat aortas by quantitative immunohistochemistry and function by measuring the pressure-driven hydraulic conductivities of excised rat aortas with both intact and denuded endothelia on the same vessel. We used them to calculate the effective intimal hydraulic conductivity, which is a combination of endothelial and subendothelial components. We observed well-correlated enhancements in aquaporin-1 expression and function in both hypertensive rat models as well as in aortas from normotensive rats whose expression was upregulated by 2 h of forskolin treatment. Upregulated aquaporin-1 expression and function may be a response to hypertension that critically determines conduit artery vessel wall viability and long-term susceptibility to atherosclerosis. NEW & NOTEWORTHY The aortic endothelia of two high-renin hypertensive rat models express greater than two times the aquaporin-1 and, at low pressures, have greater than two times the endothelial hydraulic conductivity of normotensive rats. Data are consistent with theory predicting that higher endothelial aquaporin-1 expression raises the critical pressure for subendothelial intima compression and for artery wall hydraulic conductivity to drop.

Journal of Fluid Mechanics, Sep 10, 2002

A core-annular flow, the concurrent axial flow of two immiscible fluids in a circular tube or por... more A core-annular flow, the concurrent axial flow of two immiscible fluids in a circular tube or pore with one fluid in the core and the other in the wetting annular region, is frequently used to model technologically important flows, e.g. in liquid-liquid displacements in secondary oil recovery. Most of the existing literature assumes that the pores in which such flows occur are uniform circular cylinders, and examine the interfacial stability of such systems as a function of fluid and interfacial properties. Since real rock pores possess a more complex geometry, the companion paper examined the linear stability of core-annular flows in axisymmetric, corrugated pores in the limit of asymptotically weak corrugation. It found that shortwave disturbances that were stable in straight tubes could couple to the wall's periodicity to excite unstable long waves. In this paper, we follow the evolution of the axisymmetric, linearly unstable waves for fluids of equal densities in a corrugated tube into the weakly nonlinear regime. Here, we ask whether this continual generation of new disturbances by the coupling to the wall's periodicity can overcome the nonlinear saturation mechanism that relies on the nonlinear (kinematic-condition-derived) wave steepening of the Kuramoto-Sivashinsky (KS) equation. If it cannot, and the unstable waves still saturate, then do these additional excited waves make the KS solutions more likely to be chaotic, or does the dispersion introduced into the growth rate correction by capillarity serve to regularize otherwise chaotic motions? We find that in the usual strong surface tension limit, the saturation mechanism of the KS mechanism remains able to saturate all disturbances. Moreover, an additional capillary-derived nonlinear term seems to favour regular travelling waves over chaos, and corrugation adds a temporal periodicity to the waves associated with their periodical traversing of the wall's crests and troughs. For even larger surface tensions, capillarity dominates over convection and a weakly nonlinear version of Hammond's no-flow equation results; this equation, with or without corrugation, suggests further growth. Finally, for a weaker surface tension, the leading-order base flow interface follows the wall's shape. The corrugation-derived excited waves appear able to push an otherwise regular travelling wave solution to KS to become chaotic, whereas its dispersive properties in this limit seem insufficiently strong to regularize chaotic motions.

Acta Applicandae Mathematicae, Feb 1, 1988

A connection between evolutionary mutation-selection dynamics on sequence space and linear repres... more A connection between evolutionary mutation-selection dynamics on sequence space and linear representations of the hyper-octahedral group (interpreted as the isometry group of the space of {0, 1-sequences relative to the Hamming distance metric) and other such wreath product groups is established and studied.

Journal of Fluid Mechanics, Oct 11, 2005

1999 Bioengineering Conference, Dec 1, 1999

Both linear and weakly nonlinear stability of a core annular flow in a corrugated tube in the lim... more Both linear and weakly nonlinear stability of a core annular flow in a corrugated tube in the limit of thin film and small corrugation are examined. Asymptotic techniques are used to derive the corrugated base flow and corresponding linear and weakly nonlinear stability equations. Interesting features show that the corrugation interaction can excite linear instability, but the nonlinearity still can suppress such instability in the weakly nonlinear regime.

Siam Journal on Applied Mathematics, 2013

ABSTRACT Prerequisite to atherogenesis is low-density lipoprotein (LDL) cholesterol transport fro... more ABSTRACT Prerequisite to atherogenesis is low-density lipoprotein (LDL) cholesterol transport from the blood into the artery wall across its endothelial cell (EC) lining. Whereas most EC junctions are tight enough to preclude LDL passage, some (approx1/2000−6000)(\approx 1/2000-6000)(approx1/2000−6000) rare ECs have temporarily-widened junctions (typically approx10−5\approx 10^{-5}approx10−5 of the problem’s radial scale) that allow passage of large molecular aggregates like LDL. In a purely diffusive transport model, Laplace's equation describes the steady tracer profile throughout the two major subendothelial wall layers, connected by matching conditions. In a diffusive and transmural-pressure-driven advective transport model, Laplace’s equation describes the steady pressure distribution in the wall, whose gradient is proportional to the advecting velocity. Both problems yield the same boundary value problem that has mixed Dirichlet/ Robin boundary conditions. We construct a linear system of integral equations that approximates the series expansion coefficients of the problem solution. We prove existence/convergence of this solution using the contraction mapping theorem and its uniqueness using Miranda's theorem. The analytical construction method yields a numerical calculation algorithm. Our analysis supports a surprising result that the series solution’s convergence rate increases as the ratio (approx10−5)(\approx 10^{-5})(approx10−5) of leaky junction width to mean half-distance between neighboring leaky cells increases. Numerical results agree well with previous ad hoc numerical methods. The subendothelial intima exhibits boundary layer scale separation. Calculations show the solution spike just beneath the leak is by far the region most sensitive to calculation accuracy. Since these models posit all LDL wall entry through these widened junctions, solution accuracy is particularly critical there.

American Journal of Physiology-heart and Circulatory Physiology, Apr 15, 2012

Zeng Z, Jan KM, Rumschitzki DS. A theory for water and macromolecular transport in the pulmonary ... more Zeng Z, Jan KM, Rumschitzki DS. A theory for water and macromolecular transport in the pulmonary artery wall with a detailed comparison to the aorta.

Studies in Surface Science and Catalysis, 1997

We propose an experimental protocol that can provide a diagnostic tool for probing the state of c... more We propose an experimental protocol that can provide a diagnostic tool for probing the state of catalyst coking and its influence on product composition in an operating reactor throughout the lifetime of the catalyst. The experimental equipment includes a vibrational microbalance, a multi-outlet fixed bed reactor, and a temperature-programmed oxidation appartus. We illustrates its use by applying it to n-heptane reformings on a commercial Pt-Re/Al 2 O 3 catalyst. The results idenfity five-memberee naphthenes (C5N) as the key source of coke and provide the data needed to develop kinetic models for both reforming and coking. From the measured or predicted C5N concentration, the models correctly predict the reactor coke profile and the reforming product composition as functions of on-stream time.

Industrial & Engineering Chemistry Research, Nov 27, 2002

ABSTRACT We reported previously that coke can indiscriminately deposit on the metal, acid, and al... more ABSTRACT We reported previously that coke can indiscriminately deposit on the metal, acid, and already-coked sites on a Pt−Re/Al2O3 reforming catalyst. Here we show that the thus-deposited coke, when still in a freshly formed state, can be indiscriminately gasified by hydrogen at temperatures as low as 477 °C. Once the freshly formed coke transforms into a more refractory form, it cannot be gasified by hydrogen. The kinetics of coke hydrogasification is first order with respect to both the concentration of the freshly formed coke and hydrogen partial pressure, with an apparent activation energy of 9.2 kcal/mol. A random coke deposition model offers a theoretical basis for correlating the decoking data.

American Journal of Physiology-heart and Circulatory Physiology, Jun 1, 2007

The heart valve leaflets of 29-day cholesterol-fed rabbits were examined by ultrarapid freezing w... more The heart valve leaflets of 29-day cholesterol-fed rabbits were examined by ultrarapid freezing without conventional chemical fixation/processing, followed by rotary shadow freeze-etching. This procedure images the leaflets' subendothelial extracellular matrix in extraordinary detail, and extracellular lipid liposomes, from 23 to 220 nm in diameter, clearly appear there. These liposomes are linked to matrix filaments and appear in clusters. Their size distribution shows 60.7% with diameters 23-69 nm, 31.7% between 70 and 119 nm, 7.3% between 120 and 169 nm, and 0.3% between 170 and 220 nm (superlarge) and suggests that smaller liposomes can fuse into larger ones. We couple our model from Part II of this series (Zeng Z, Yin Y, Jan KM, Rumschitzki DS.

American Journal of Physiology-heart and Circulatory Physiology, Jun 1, 2007

This paper proposes a new, two-dimensional convection-diffusion model for macromolecular transpor... more This paper proposes a new, two-dimensional convection-diffusion model for macromolecular transport in heart valves based on horseradish peroxidase (HRP) experiments on rats presented in the first of the papers in this series (

Chemical Engineering Science, 1988

In two recent articles, connections were drawn between reaction network structure and the possibi... more In two recent articles, connections were drawn between reaction network structure and the possibility of multiple steady states in complex isothermal reactors. The particular applicability of these results to continuous flow stirred tank reactors is studied. It is shown that CFSTRs involving heterogeneous catalysis will often be good candidates for application of existing theory. On the other hand, it is also shown that homogeneous CFSTRs will generally require different ideas. This last observation provides motivation for a companion paper. f. INTRODUCTION In two recent articles (Feinberg, 1987, 1988) connections were drawn between the behavior of complex isothermal reactors and the structure of the underlying reaction network. Special emphasis was placed on the relationship between reaction network structure and the possibility of multiple steady states. The results permit one to determine for each reaction network within a certain large class whether multiple steady states can be admitted by the corresponding differential equations. Although continuous flow stirred tank reactors (CFSTRs) were considered in some examples, the theory was intended to be sufficiently general as to be applicable to wide varieties of reactors and to CFSTRs only incidentally. This is the first in a series of articles dedicated speczficaily to questions about steady state multiplicity in isothermal CFSTRs. Here we will show that for CFSTRs involving heterogeneous catalysis the theory given by Feinberg (1988) can often provide the basis for an incisive analysis of multiplicity questions. On the other hand, we will also show why the situation is not nearly as satisfactory for homogeneous CFSTRs. This last observation will provide motivation for a companion article that contains theory constructed especially for homogeneous CFSTRs. Readers of this article should already have some understanding of how CFSTRs are described in terms 'The research described here was done while D. Rumschitzki was a visitor from the University of California, Berkeley, where he was a Ph.D. candidate.

Aiche Journal, Oct 1, 1989

This paper focuses on the problem of scale-up of two-phase (e.g., solid-fluid) reactors. It outli... more This paper focuses on the problem of scale-up of two-phase (e.g., solid-fluid) reactors. It outlines a class of such reactors which, for firstorder reactions, scale in the familiar single-phase manner via an analog of the usual residence time distribution formula. The differences lie in the fact that the appropriate tracer experiment entering the formalism for this reactor class refers to a nonadsorbing tracer, and the analog of the plug flow solution is the solution for a fixed bed with fluid-phase plug flow. Surprisingly, unlike single-phase systems, there exist two-phase reactors, outside of the class defined, that do not scale in this manner, even when, say, the true catalyst surface chemistry is purely first-order. The paper discusses a few examples and implications for the design of two-phase reactors, including fluidized beds.

American Journal of Physiology-heart and Circulatory Physiology, Apr 1, 1997