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  • 1
    ISSN: 1435-604X
    Keywords: Mathematical model ; Laser surgery ; Optical fibres ; Tumours ; Thermal diffusion ; Multiple fibres
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine , Physics , Technology
    Notes: Abstract A mathematical model is employed to discuss the region treated by local hyperthermia, when the source of heat is a laser whose energy is directed into the treatment region through four optical fibres ending at the corners of a square. If treatment is over a period that is substantially longer than the time for the temperature distribution to reach equilibrium, a steady state model using four point sources can be employed to obtain a general idea of the temperatures reached and the region treated for different power levels and sizes of square. For shorter times, and for more accurate estimation of the regions treated, numerical calculation on a computer is essential. The details of the calculation depend on individual cases, but we demonstrate here that such computations are possible, and present a series of typical results. A comparison is made with the results of a series of experiments on canine liver, showing that it is possible to obtain good qualitative and numerical agreement.
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  • 2
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    Lasers in medical science 4 (1989), S. 55-64 
    ISSN: 1435-604X
    Keywords: Laser hyperthermia ; Mathematical model ; Tumours ; Optical coefficients ; Optical fibres ; Thermal diffusion
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine , Physics , Technology
    Notes: Abstract A time dependent mathematical model of optical energy transfer and heat conduction in tissue with strong anisotropic scattering is used to analyse the results of experiments (1) in which the livers of rats were treated by local laser hyperthermia. Good qualitative agreement to the temperature distribution is possible, but satisfactory quantitative agreement is only possible if allowance is made for temperature dependence of the optical and thermal parameters. Analysis of the volume of tissue killed by the treatment shows a marked departure from the rule used in conventional hyperthermia to determine the region treated; the reason for this is not clear, but a number of possibilities are suggested.
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  • 3
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    Transport in porous media 5 (1990), S. 27-47 
    ISSN: 1573-1634
    Keywords: Mathematical model ; percolation ; Monte Carlo ; viscous fingers ; Darcy ; relative permeability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract The model described in this paper is an approach to simulating flow through porous media on a microscopic scale. It is based on a variation of diffusion limited aggregation. The model is shown to match coreflood average saturation profiles and production histories as predicted by Darcy's equations while generating saturation distributions resembling viscous fingering. The model also is shown to simulate the limiting cases of infinite mobility ratio and zero flow rates as previously modeled by diffusion limited aggregation and percolation theory. With some simplifying assumptions, differential equations very similar to Darcy's equations are derived from the microscopic interpretation of fluid behavior in porous media used in this model.
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  • 4
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    Annals of biomedical engineering 13 (1985), S. 531-550 
    ISSN: 1573-9686
    Keywords: Input impedance ; Mathematical model ; Pulmonary circulation ; Pulmonary artery ; Ventricular septal defect
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine , Technology
    Notes: Abstract A mathematical model of the infant pulmonary vascular system was developed by altering an adult model to fit the hemodynamic properties of an infant pulmonary vascular bed. The model was designed for infants between the ages of 1 and 2 years with both normal and high mean pulmonary artery pressures (PAPs). The resulting infant model was evaluated on the basis of the computed parameters of cumulative length, volume and resistance of the pulmonary vascular bed, as well as on the basis of comparisons of the model spectra with actual computed spectra for ventricular septal defect patients who were of comparable age, had comparable mean PAPs and were not diagnosed as having pulmonary vascular disease. It was observed that the first minimum and first maximum in the modulus of the input impedance spectrum of the infant model for both normal and high mean PAPs occurred at a higher frequency than in the adult model. These observations led to the conclusion that there is a natural, age-related shift in the input impedance spectrum of infants which is not necessarily indicative of pulmonary impairment.
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  • 5
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    Annals of biomedical engineering 15 (1987), S. 139-155 
    ISSN: 1573-9686
    Keywords: Lung lymph ; Capillary permeability ; Pores ; Mathematical model
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine , Technology
    Notes: Abstract Mathematical models of solute and water exchange in the lung have been helpful in understanding factors governing the volume flow rate and composition of pulmonary lymph. As experimental data and models become more encompassing, parameter identification becomes more difficult. Pore sizes in these models should approach and eventually become equivalent to actual physiological pathway sizes as more complex and accurate models are tried. However, pore sizes and numbers vary from model to model as new pathway sizes are added. This apparent inconsistency of pore sizes can be explained if it is assumed that the pulmonary blood-lymph barrier is widely heteroporous, for example, being composed of a continuous distribution of pathway sizes. The sieving characteristics of the pulmonary barrier are reporduced by a log normal distribution of pathway sizes (log mean=−0.20, log s.d.=1.05). A log normal distribution of pathways in the microvascular barrier is shown to follow from a rather general assumption about the nature of the pulmonary endothelial junction.
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  • 6
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    Annals of biomedical engineering 17 (1989), S. 377-396 
    ISSN: 1573-9686
    Keywords: Periodic breathing ; Central apnea ; Sleep ; Mathematical model ; Hyperventilation ; Metabolic rate ; Asphyxia
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine , Technology
    Notes: Abstract Periodic breathing (recurrent central apneas) occurs frequently during sleep. Periodic breathing can arise as a result of unstable behavior of the respiratory control system. A mathematical model of the respiratory control system was used to investigate, systematically, the effect of severity of disturbances to respiration and certain system parameters on periodic breathing occurring during sleep. The model consisted of multi-compartment representation of O2 and CO2 stores, a peripheral controller sensitive to O2 and CO2, and a central controller sensitive to CO2. The effects of hypoxia and hypercapnia on the upper airway muscles were not considered in the model. Episodes of hyperventilation or asphyxia were used to disturb the control system and explore the boundaries of stable breathing. Circulation time and metabolic rate were also varied. Simulations with the model produced the following findings: The number of central apneas associated with periodic breathing were greater as circulation time increased; controller gain increases also made the number of apneas greater, although periodic breathing occurs with lower controller gains as circulation time increases. At each level of circulation time there was a range of controller gain changes which caused little change in the number of apneas. There were more apneas with hypoxia; also the number of apneas increased with sleep-associated reductions in metabolic rate. The more rapidly resting PCO2 rose at sleep onset, the greater the likelihood of recurrent apneas. Finally, the more intense the disturbance, the more apneas there were.
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  • 7
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    Annals of biomedical engineering 18 (1990), S. 123-133 
    ISSN: 1573-9686
    Keywords: Mathematical model ; Macromolecules ; Dimension ; Sieving
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine , Technology
    Notes: Abstract The pulmonary microvasculature offers a heterogeneous barrier to the motion of large solutes as they pass between blood and lymph. While this barrier has been approximated by a few discrete pathways or by statistical ensembles of many pathways, these descriptions only partly capture the structural and functional properties of the pulmonary microcirculation. The concept that this barrier may be a fractal object is explored. Endothelial cleft geometry displays scaling in junctional path length and self-similarity in its spatial organization. It is shown that a fractal cleft produces heterogeneous spaces capable of transporting water and macromolecules. Cleft location, size, and depth are characterized, in part, by a fractal dimension of approximately 0.8. The consequences for transport through a fractal barrier are then determined. Predicted sieving of macromolecules by a fractal barrier is found to be consistent with lung microvascular transport data. Nonlinear transport phenomena are one consequence of a barrier having a fractional dimension.
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  • 8
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    Annals of biomedical engineering 19 (1991), S. 273-289 
    ISSN: 1573-9686
    Keywords: Vagal control ; Cardiac period ; SA node ; Mathematical model ; ACh release
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine , Technology
    Notes: Abstract In 12 dogs anesthetised with α-chloralose and urethane, and β-adrenergic blocked with propranolol, the cervical vagi were stimulated for 60 seconds with supramaximal constant current pulses at frequencies between 2.0 and 10 Hz. The time course of the recovery of the cardiac period response, after cessation of vagal stimulation, was analyzed using nonlinear curve fitting techniques. It was found that the recovery phase could be reliably fitted with a function consisting of the sum of up to three exponential terms. The first term has a moderate rate constant of 0.2260±0.0112 S−1 (SE) and is independent of vagal stimulus frequency and the preceding bradycardia. We propose that this term is associated with a recovery from the bradycardia with a rate constant indicative of the reduction of acetylchloline at the pacemaker caused by hydrolysis and washout. The second term has a small rate constant of 0.0499±0.0014 s−1 (SE) and a negative gain. This term describes the time course of the post vagal tachycardia observed at cessation of stimulation. It is also independent of stimulus frequency and the preceding bradycardia. The third term has a large and variable rate constant (range: 0.247–8.01 s−1) and becomes increasingly dominant when the preceding bradycardia is large. We propose that this third component arises from a rapid return of the pacemaker focus to the dominant location prior to vagal stimulation. The mathematical characterisation of this component is important to permit the accurate derivation of the time courses of the remaining two components. Curvilinear relationships exist between the gain parameters for each of the exponential terms and the preceding bradycardia.
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  • 9
    ISSN: 1573-9686
    Keywords: Circulation ; Modeling of circulation ; Mathematical model ; Electrical model ; Hydraulic model ; Modeling of physiological systems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine , Technology
    Notes: Abstract Development, first of analog and later of digital computers, as well as algorithms for analysis of electrical circuits, stimulated the use of electrical circuits for modeling the circulation. The networks used as building blocks for electrical models can provide accurate representation of the hydrodynamic equations relating the inflow and outflow of individual segments of the circulation. These networks, however, can contain connections in which voltages and currents have no analogues in the circulation. Problems arise because (a) electrical current must flow in closed loops, whereas no such constraints exist for hydraulic models; and (b) electrical capacitors have a number of characteristics that are not analogous to those of hydraulic compliant chambers. Disregarding these differences can lead to erroneous results and misinterpretation of phenomena. To ensure against these errors, we introduce an imaginary electrical element, thenonlinear residual-charge capacitor (NRCC), with characteristics equivalent to those of a compliant chamber. If one uses appropriate circuit connections and incorporates the residual-charge capacitor, then all voltages and currents in the model are proper analogues of pressures and flows in the circulation. It is shown that the capacitive current represents the rate of change of volume of blood inside the vessel, as well as the rate of the corresponding displacement of volume of the surrounding tissue.
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  • 10
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    Annals of biomedical engineering 20 (1992), S. 517-531 
    ISSN: 1573-9686
    Keywords: Ion channel ; Kinetics ; Nonlinear dynamics ; Chaos ; Mathematical model
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine , Technology
    Notes: Abstract Models of the gating of ion channels have usually assumed that the switching between the open and closed states is a random process without a mechanistic basis. We explored the properties of a deterministic model of channel gating based on a chaotic dynamic system. The channel is modeled as a nonlinear oscillator, that has a potential function with two minima, which correspond to the stable open and closed states, and is driven by a periodic driving force. The properties of the model are like some properties of single channel data and unlike other properties. The model is like the data in that: the current switches between two well-defined states, this switching is nonperiodic, and there are subconductance states. These subconductance states are subharmonic resonances, due to the nonlinearities in the equation of the model, rather than stable conformational states due to local minima in the potential energy. The model is not like the data in that the current fluctuates too much within in each state and there are sometimes periodic fluctuations within a state. At the present time, the selection of the most appropriate channel model (Markov, chaotic, or other) is not possible, and in addition to chaotic models, other nonlinear models may be suitable.
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  • 11
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    Annals of biomedical engineering 22 (1994), S. 184-193 
    ISSN: 1573-9686
    Keywords: Mathematical model ; Factor XII ; Kallikrein ; HMWK ; Cascade ; Mass transfer
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine , Technology
    Notes: Abstract This work analyzes, for the first time, the combined role of blood flow, protein transport and the reaction network of the contact phase up to the “common pathway” of the blood coagulation cascade. The model is comprised of a set of 20 dominant reactions with 11 components. Systems of ODEs reducible to 4 coupled equations describe rigorously the dynamic behavior, while systems of algebraic equations, reducible to a single polynomial equation, model the steady state concentrations of the coagulants. The analysis showed that there is never more than onestable steady state. This is in contrast to the analysis of common pathway that gives rise to multiple concentration states. It also revealed a general robustness of the system to changes in procoagulant concentrations, inhibition rates and most activation rate constants. The system is largely impervious to the level of activated Factor XII, given that a trace (non-zero) level is present. In contrast, the system displays a dual response to flow and surface activity: A change in either of these factors alone can promote, have no effect on, or (in the case of flow) impede the progress of coagulation, depending on the value of the other factor. Their effects must therefore be examined in unison. These results may help resolve contradictory findings attributed to one or the other factor alone.
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  • 12
    ISSN: 1573-9686
    Keywords: Bioresorbable vascular graft ; Mechanical stress ; Mathematical model
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine , Technology
    Notes: Abstract Little attention has been given to the stresses within the wall of bioresorbable vascular prostheses and how they might affect the resorption process. We modeled the graft “complex” (inner tissue capsule, residual graft, and outer tissue capsule) as a three-layered compound tube under internal pressure. Using this biomechanical model, we studied the effects of alterations in the geometry (i. e., radius and thickness) and mechanical properties of each stratum on the overall transmural stress distribution. Hypothetical simulations were performed to investigate the possible-sequence of and alterations in the radial and circumferential stresses during the resorption process. Our results suggest that early in the resorption phase, the inner tissue capsule is subjected to compressive hoop stresses and concentrated, largemagnitude compressive radial stresses. This distribution gives way to the more typical distribution for a thick-walled tube when equilibration (i.e., complete resorption) is approached. The prediction of the compressive stresses in the pseudo-intima during early resorption parallels findings of an elevated mitotic index in that region at that time. This leads to a new hypothesis, namely, that compressive stresses, both in-plane and out-of-plane with respect to the regenerated vascular cells, participate in the resorption process of bioresorbable vascular grafts by modulating elevated cellular proliferative activity and may play an important role in other aspects of vascular cell biology. Results of recent experimentation support this hypothesis.
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  • 13
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    Annals of biomedical engineering 27 (1999), S. 208-218 
    ISSN: 1573-9686
    Keywords: Single cell model ; Multidrug resistance ; Cancer cell ; Drug influx and efflux ; Mathematical model ; Dynamic and steady-state simulation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine , Technology
    Notes: Abstract Multidrug resistance (MDR) of some cancer cells is a major challenge for chemotherapy of systemic cancers to overcome. To experimentally uncover the cellular mechanisms leading to MDR, it is necessary to quantitatively assess both drug influx into, and efflux from, the cells exposed to drug treatment. By using a novel molecular microdelivery system to enforce continuous and adjustable drug influx into single cells by controlled diffusion through a gel plug in a micropipet tip, drug resistance studies can now be performed on the single cell level. Our dynamic model of this scheme incorporates drug delivery, diffusive mixing, and accumulation inside the cytoplasm, and efflux by both passive and active membrane transport. Model simulations using available experimental information on these processes can assist in the design of MDR related experiments on single cancer cells which are expected to lead to a quantitative evaluation of mechanisms. Simulations indicate that drug resistance of a cancer cell can be quantified better by its dynamic response than by steady-state analysis. © 1999 Biomedical Engineering Society. PAC99: 8717Aa, 8719Xx
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  • 14
    ISSN: 1573-9686
    Keywords: Thrombosis ; Mathematical model ; Thrombin ; Fluid dynamics ; Mass transport ; Platelets
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine , Technology
    Notes: Abstract To better understand the mechanisms leading to the formation and growth of mural thrombi on biomaterials, we have developed a two-dimensional computational model of platelet deposition and activation in flowing blood. The basic formulation is derived from prior work by others, with additional levels of complexity added where appropriate. It is comprised of a series of convection-diffusion-reaction equations which simulate platelet-surface and platelet-platelet adhesion, platelet activation by a weighted linear combination of agonist concentrations, agonist release and synthesis by activated platelets, platelet-phospholipid-dependent thrombin generation, and thrombin inhibition by heparin. The model requires estimation of four parameters to fit it to experimental data: shear-dependent platelet diffusivity and resting and activated platelet-surface and platelet-platelet reaction rate constants. The model is formulated to simulate a wide range of biomaterials and complex flows. In this article we present the basic model and its properties; in Part II (Sorensen et al., Ann. Biomed. Eng. 27:449–458, 1999) we apply the model to experimental results for platelet deposition onto collagen. © 1999 Biomedical Engineering Society. PAC99: 8719Uv, 8380Lz, 8717Aa, 8710+e, 8768+z
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  • 15
    ISSN: 1573-9686
    Keywords: Thrombosis ; Mathematical model ; Thrombin ; Fluid dynamics ; Mass transport ; Platelets
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine , Technology
    Notes: Abstract We have previously described the development of a two-dimensional computational model of platelet deposition onto biomaterials from flowing blood (Sorensen et al., Ann. Biomed. Eng. 27:436–448, 1999). The model requires estimation of four parameters to fit it to experimental data: shear-dependent platelet diffusivity and three platelet-deposition-related reaction rate constants. These parameters are estimated for platelet deposition onto a collagen substrate for simple parallel-plate flow of whole blood in both the presence and absence of thrombin. One set of experimental results is used as a benchmark for model-fitting purposes. The “trained” model is then validated by applying it to additional test cases from the literature for parallel-plate Poiseuille flow over collagen at both higher and lower wall shear rates, and in the presence of various anticoagulants. The predicted values agree very well with the experimental results for the training cases, and good reproduction of deposition trends and magnitudes is obtained for the heparin, but not the citrate, validation cases. The model is formulated to be easily extended to synthetic biomaterials, as well as to more complex flows. © 1999 Biomedical Engineering Society. PAC99: 8719Uv, 8710+e, 8717Aa, 8768+z, 4760+i
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  • 16
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    Annals of biomedical engineering 28 (2000), S. 14-25 
    ISSN: 1573-9686
    Keywords: Coronary anatomy ; Finite element ; Network generation ; Mathematical model
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine , Technology
    Notes: Abstract A discrete anatomically accurate finite element model of the largest six generations of the coronary arterial network is developed. Using a previously developed anatomically accurate model of ventricular geometry the boundaries of the coronary mesh are defined from measured epicardial coronaries. Network topology is then generated stochastically from published anatomical data. Spatial information is added to this topological data using an avoidance algorithm accounting for global network geometry and optimal local branch angle properties. The generated vessel lengths, radii and connectivity are consistent with the published studies and a relativity even spatial distribution of vessels within the ventricular mesh is achieved. The local finite element coordinates of the coronary nodes within the ventricular mesh are calculated such that the coronary geometry can be recalculated within a deformed ventricular mesh. © 2000 Biomedical Engineering Society. PAC00: 8710+e, 8718Bb, 0270Dh
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  • 17
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    Annals of biomedical engineering 28 (2000), S. 278-290 
    ISSN: 1573-9686
    Keywords: Dehydration ; Mathematical model ; Thermoregulation ; Cardiovascular ; Respiratory ; Body water
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine , Technology
    Notes: Abstract A model of the human body that integrates the variables involved in temperature regulation and blood gas transport within the cardiovascular and respiratory systems is presented here. It expands upon previous work to describe the competition between skin and muscles when both require increased blood flows during exercise and/or heat stress. First, a detailed study of the control relations used to predict skin blood flow was undertaken. Four other control relations employed in the model were also examined and modified as indicated by empirical results found in literature. Internal responses to exercise and/or heat stress can affect both thermoregulation and the cardiorespiratory system. Dehydration was studied in addition to complete water replacement during similar environmental and exercise situations. Control relations for skin blood flow and evaporative heat loss were modified and a water balance was added to study how the loss of water through sweat can be limiting. Runoff from sweating as a function of relative humidity was introduced along with evaporation, and these results were compared to data to validate the model. © 2000 Biomedical Engineering Society. PAC00: 8719Pp, 8719Uv, 8719Ff, 8710+e
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  • 18
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    Annals of biomedical engineering 28 (2000), S. 495-511 
    ISSN: 1573-9686
    Keywords: Heart ; Epicardial and endocardial differences ; Vascular growth model ; Mathematical model ; Computer simulation ; Constrained constructive optimization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine , Technology
    Notes: Abstract There is a marked difference in the structure of the arterial tree between epi- and endocardial layers of the human heart. To model these structural variations, we developed an extension to the computational method of constrained constructive optimization (CCO). Within the framework of CCO, a model tree is represented as a dichotomously branching network of straight cylindrical tubes, with flow conditions governed by Poiseuille's law. The tree is grown by successively adding new terminal segments from randomly selected points within the perfusion volume while optimizing the geometric location and topological site of each new connection with respect to minimum intravascular volume. The proposed method of “staged growth” guides the generation of new terminal sites by means of an additional time-dependent boundary condition, thereby inducing a sequence of domains of vascular growth within the given perfusion volume. Model trees generated in this way are very similar to reality in their visual appearance and predict diameter ratios of parent and daughter segments, the distribution of symmetry, the transmural distribution of flow, the volume of large arteries, as well as the ratio of small arterial volume in subendocardial and subepicardial layers in good agreement with experimental data. From this study we conclude that the method of CCO combined with staged growth reproduces many characteristics of the different arterial branching patterns in the subendocardium and the subepicardium, which could not be obtained by applying the principle of minimum volume alone. © 2000 Biomedical Engineering Society. PAC00: 8719Uv, 8719Hh, 4760+i
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  • 19
    ISSN: 1573-9686
    Keywords: Mathematical model ; Receptor ; Renin ; Kinetic analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine , Technology
    Notes: Abstract Numerous studies have demonstrated changes in receptor number, protein concentration, or mRNA levels and have proposed that these subcellular changes produce physiologic effects. To date, no adequate mathematical analysis has been available to provide a framework for interpretation of such data. In the present study we have combined measurements of angiotensin receptor protein levels with the development of a mathematical model that includes two receptors with opposing actions for a single ligand. This model was used to quantify the net, physiologic response of each receptor population to ANG II stimulation and the effect of altering the expression of receptor populations by a physiologic stimulus. Altered sodium intake was used as the physiologic stimulus and quantification of Western blot analysis and revealed that high sodium diet significantly suppressed AT1 receptor protein in the adrenal gland and aorta and augmented AT2 receptor protein in the aorta. A high sodium diet did not significantly alter AT2 receptor protein in the adrenal gland. Modeling the measured sodium-induced changes in receptor concentration demonstrated that small, subcellular changes in receptor concentration can have a large impact on the net physiologic effect. This model for dual receptor–single ligand interactions should be amenable for other systems. © 2000 Biomedical Engineering Society. PAC00: 8710+e, 8714Ee
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  • 20
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    Transport in porous media 4 (1989), S. 199-212 
    ISSN: 1573-1634
    Keywords: Mathematical model ; borehole coal mining system ; sorption phenomenon of methane in coal ; methane flow in porous coal seams
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract Safety in coal mining is greatly increased by the drainage of the methane content of coal seams through boreholes, simultaneously producing significant energy. The design of suitable drainage technology is based on the mathematical modeling of methane flow in coal seams. In the calculation of the methane pressure, the new mathematical model presented in this paper considers both the sorption phenomenon of methane depending upon the methane pressure and the fact that the variation in methane pressure can create a change in the stress condition of the rock and, as a consequence of this, a change in the permeability of the coal. The new mathematical model can be used for the numerical simulation of the flow processes in coal seams and methane drainage technology can be designed more accurately.
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  • 21
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    Annals of biomedical engineering 14 (1986), S. 383-400 
    ISSN: 1573-9686
    Keywords: Mathematical model ; Protein ; Platelets ; Embolization ; Artificial surface
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine , Technology
    Notes: Abstract A theoretical model for the deposition and detachment of protein and platelets on biomaterial surfaces is presented here. This work is an extension of themodel previously reported (12). Two mechanisms of protein and platelet removal are assumed: (1) A characteristic time elapses before adsorbed protein detaches from the surface, carrying away platelets and protein which have deposited on top of it; and (2) thrombi that attain a critical size are subject to hydrodynamic forces which embolize them from the surface. A theoretical distribution of thrombus sizes is assumed. Analysis of the effects of varying model parameters on predicted protein and platelet deposition reveals that the addition of the embolization process does not change the overall structure of the deposition profiles, but does significantly affect the finer details.
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  • 22
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    Annals of biomedical engineering 21 (1993), S. 435-458 
    ISSN: 1573-9686
    Keywords: Coronary circulation ; Mathematical model ; Coronary compression ; Ischemia ; Collaterals
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine , Technology
    Notes: Abstract The dynamics of the transmyocardial coronary flow patterns during normal and ischemic conditions are complex and relatively inaccessible to measurements. Therefore, theoretical analyses are needed to help in understanding these phenomena. The proposed model employs compartmental division to three layers, each with four vessel-size compartments which are characterized by resistance and compliance. These compartments are subjected to the extravascular compressive pressure (ECP) generated by cardiac contraction, which by modifying the transmural pressure causes changes in cross-sectional area of the vessels in each compartment continuously determining the resistance and capacitance values. Autoregulation and collaterals are also included in order to simulate the flow patterns during regional ischemia. Using these features, the model predicts the typical out of phase arterial and venous flow patterns. Systolic collapse of the large intramyocardial veins during the normal cycle, as well as systolic arteriolar collapse during ischemia are predicted. The transmural flow during ischemia is characterized by alternating flows between the layers. The ECP is considered here is two ways: (a) as a function of left ventricle (LV) pressure, decreasing linearly from endocardium to epicardium and (b) as the interstitial fluid pressure, employing a multilayer muscle-collagen model of the LV. While both of these approaches can describe the dynamics of coronary flow under normal conditions, only the second approach predicts the large compressive effects due to high ECP obtained at very low cavity pressure, resulting from significant muscle shortening and radial collagen stretch. This approach, combining a detailed description of transmural coronary circulation interacting with the contracting myocardium agrees with many observations on the dynamics of coronary flow and suggests that the type of LV mechanical model is important for that interaction.
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  • 23
    ISSN: 1573-9686
    Keywords: Invasion ; Collagen gel ; Mathematical model ; Metastasis ; Migration ; Cell tracking
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine , Technology
    Notes: Abstract Anin vitro assay proposed to systematically characterize and compare cell invasion under different conditions is the collagen gel invasion assay where cells, initially seeded onto the surface of a type I collagen gel, penetrate the surface and migrate within the gel over time. Using simplifying assumptions about cell transport across the gel surface and migration within the gel, we formulate and solve a mathematical model of this assay which predicts the resulting cell distribution based on three phenomenological parameters characterizing the ability of cells to penetrate the gel surface interface, migrate randomly within the gel, and return to the gel surface. An index of cell invasiveness is defined based on these parameters that reflects the overall ability of cells to transport across the gel surface interface, that is, invade the gel. Cell concentration profiles predicted by the model correspond well to measured profiles for murine melanoma cells invading gels supplemented with extracellular matrix proteins fibronectin and type IV collagen as well as unsupplemented gels, allowing these parameters to be estimated by a nonlinear regression fit of the model solution to the measured profiles. Our analysis suggests that type IV collagen and fibronectin primarily modulate cell transport across the gel surface interface rather than migration within the gel. Further, we validate the key model assumptions and obtain independent, direct estimates of model parameters by time-lapse video microscopy and digital image analysis of cell penetration of the gel surface and migration within the gel during the assay.
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  • 24
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    Annals of biomedical engineering 23 (1995), S. 48-60 
    ISSN: 1573-9686
    Keywords: Mathematical model ; Soluble gas exchange ; Alcohol breath test
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine , Technology
    Notes: Abstract A previously developed mathematical model that describes the relationship between blood alcohol (ethanol) concentration and the concentration of alcohol in the exhaled breath at end-exhalation (BrAC) has been used to quantitate the effect of pretest breathing conditios on BrAC. The model was first used to “condition” the airways with different breathing maneuvers prior to simulating a single exhalation maneuver, the maneuver used in standard breath alcohol testing. On inspiration, the alcohol in the air reaches local equilibrium with the alcohol in the bronchial capillary bed prior to entering the alveolar region. On expiration, approximately 50% of the alcohol absorbed on inspiration is desorbed back to the airways. BrAC correlates with the amount of alcohol that is desorbed to the airways. The six pretest breathing conditions and the percent change in BrAC relative to the control maneuver were: hyperventilation (−4.4%), hypoventilation (3.7%), hot-humid air (−2.9%), hot-dry air (0.66%), cold-humid air (0.13%), and cold-dry air (0.53%). The mechanism underlying these responses is not due to changes in breath temperature, but, rather to changes in the axial profile of alcohol content in the mucous lining of the airways.
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  • 25
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    Annals of biomedical engineering 23 (1995), S. 164-177 
    ISSN: 1573-9686
    Keywords: Arterial system ; Mathematical model ; Total arterial compliance ; Aortic characteristic impedance ; Nonlinear pressure-volume relationship ; Parameter estimation ; Energy balance
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    Notes: Abstract A new one-step computational procedure is presented for estimating the parameters of the nonlinear three-element windkessel model of the arterial system incorporating a pressure-dependent compliance. The data required are pulsatile aortic pressure and flow. The basic assumptions are a steadystate periodic regime and a purely elastic compliant element. By stating two conditions, zero mean flow and zero mean power in the compliant element, peripheral and characteristic resistances are determined through simple closed form formulas as functions of mean values of the square of aortic pressure, the square of aortic flow, and the product of aortic pressure with aortic flow. The pressure across as well as the flow through the compliant element can be then obtained so allowing the calculation of volume variation and compliance as functions of pressure. The feasibility of this method is studied by applying it to both simulated and experimental data relative to different circulatory conditions and comparing the results with those obtained by an iterative parameter optimization algorithm and with the actual values when available. The conclusion is that the proposed method appears to be effective in identifying the three-element windkessel even in the case of nonlinear compliance.
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    Annals of biomedical engineering 23 (1995), S. 299-307 
    ISSN: 1573-9686
    Keywords: Signal transduction ; Antagonist ; Mathematical model ; Diffusion ; Computer simulation ; Smooth muscle cells ; Phenylephrine ; Prazosin
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    Notes: Abstract Cells have evolved elaborate strategies for sensing, responding to, and interacting with their environment. In many systems, interaction of cell surface receptors with extracellular ligand can activate cellular signal transduction pathways leading to G-protein activation and calcium mobilization. In BC3H1 smooth muscle-like cells, we find that the speed of calcium mobilization as well as the fraction of cells which mobilize calcium following phenylephrine stimulation is dependent upon receptor occupation. To determine whether receptor inactivation affects calcium mobilization, we use the receptor antagonist prazosin to block a fraction of cell surface receptors prior to phenylephrine stimulation. For cases of equal receptor occupation by agonist, cells with inactivated or blocked receptors show diminished calcium mobilization following phenylephrine stimulation as compared to cells without inactivated receptors. Ligand/receptor binding and two-dimensional diffusion of receptors and G-proteins in the cell membrane are studied using a Monte Carlo model. The model is used to determine if receptor inactivation affects G-protein activation and thus the following signaling events for cases of equal equilibrium receptor occupation by agonist. The model predicts that receptor inactivation by antagonist binding results in lower G-protein activation not only by reducing the number of receptors able to bind agonist but also by restricting the movement of agonist among free receptors. The latter process is important to increasing the access of bound receptors to G-proteins.
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  • 27
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    Annals of biomedical engineering 26 (1998), S. 166-178 
    ISSN: 1573-9686
    Keywords: ARDS ; Intravenous oxygenation ; Artificial lung ; Mathematical model ; Model ; Gas exchange ; Oxygenator
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    Notes: Abstract Acute respiratory distress syndrome (ARDS) is a pulmonary edemic condition which reduces respiratory exchange in 150,000 people per year in the United States. The currently available therapies of mechanical ventilation and extracorporeal membrane oxygenation are associated with high mortality rates, so intravenous oxygenation represents an attractive, alternative support modality. We are developing an intravenous membrane oxygenator (IMO) device intended to provide 50% of basal oxygen and carbon dioxide exchange requirements for ARDS patients. A unique aspect of the IMO is its use of an integral balloon to provide active mixing. This paper describes a mathematical model which was developed to quantify and optimize the gas exchange performance of the IMO. The model focuses on balloon activated mixing, uses a lumped compartment approach, and approximates the blood-side mass transfer coefficients with cross-flow correlations. IMO gas exchange was simulated in water and blood, for a variety of device geometries and balloon pulsation rates. The modeling predicts the following: (1) gas exchange efficiency is reduced by a buildup of oxygen in the fluid near the fibers; (2) the IMO gas exchange rate in blood is normally about twice that in water under comparable conditions; (3) a balloon diameter of about 1.5 cm leads to optimal gas exchange performance; and (4) in vivo positioning can affect gas exchange rates. The numerically predicted gas transfer rates correlate closely with those experimentally measured in vitro for current IMO prototypes. © 1998 Biomedical Engineering Society. PAC98: 8710+e, 8790+y, 8265Fr
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  • 28
    ISSN: 1573-9686
    Keywords: Oxygen transport ; Microcirculation ; Cerebral circulation ; Hypoxia ; Carbon monoxide ; Mathematical model ; Computer simulation ; Anemia ; Hematocrit ; Brain
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    Notes: Abstract Cerebral blood flow (CBF) increases as arterial oxygen content falls with hypoxic (low PO2), anemic (low hemoglobin) and carbon monoxide (CO) (high carboxyhemoglobin) hypoxia. Despite a higher arterial PO2, CO hypoxia provokes a greater increase in CBF than hypoxic hypoxia. We analyzed published data using a compartmental mathematical model to test the hypothesis that differences in PO2 in tissue, or a closely related vascular compartment, account for the greater response to CO hypoxia. Calculations showed that tissue, but not arteriolar, PO2 was lower in CO hypoxia because of the increased oxyhemoglobin affinity with CO hypoxia. Analysis of studies in which oxyhemoglobin affinity was changed independently of CO supports the conclusion that changes in tissue PO2 (or closely related capillary or venular PO2) are predictive of alterations in CBF. We then sought to determine the role of tissue PO2 in anemic hypoxia, with no change in arterial and little, if any, change in venous PO2. Calculations predict a small fall in tissue PO2 as hematocrit decreases from 55% to 20%. However, calculations show that changes in blood viscosity can account for the increase in CBF in anemic hypoxia over this range of hematocrits. © 1998 Biomedical Engineering Society. PAC98: 8710+e, 8722-q, 8745Ft
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  • 29
    ISSN: 1573-9686
    Keywords: Mathematical model ; Parameter estimation ; Flow heterogeneity ; Skeletal muscle ; Glucose ; Blood flow heterogeneity ; Modeling transcapillary exchange
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    Notes: Abstract Distributed models of blood-tissue exchange are widely used to measure kinetic events of various solutes from multiple tracer dilution experiments. Their use requires, however, a careful description of blood flow heterogeneity along the capillary bed. Since they have mostly been applied in animal studies, direct measurement of the heterogeneity distribution was possible, e.g., with the invasive microsphere method. Here we apply distributed modeling to a dual tracer experiment in humans, performed using an intravascular (indocyanine green dye, subject to distribution along the vascular tree and confined to the capillary bed) and an extracellular ([3H]-D-mannitol, tracing passive transcapillary transfer across the capillary membrane in the interstitial fluid) tracer. The goal is to measure relevant parameters of transcapillary exchange in human skeletal muscle. We show that assuming an accurate description of blood flow heterogeneity is crucial for modeling, and in particular that assuming for skeletal muscle the well-studied cardiac muscle blood flow heterogeneity is inappropriate. The same reason prevents the use of the common method of estimating the input function of the distributed model via deconvolution, which assumes a known blood flow heterogeneity, either defined from literature or measured, when possible. We present a novel approach for the estimation of blood flow heterogeneity in each individual from the intravascular tracer data. When this newly estimated blood flow heterogeneity is used, a more satisfactory model fit is obtained and it is possible to reliably measure parameters of capillary membrane permeability-surface product and interstitial fluid volume describing transcapillary transfer in vivo. © 1998 Biomedical Engineering Society. PAC98: 8745Ft, 8710+e, 8722Fy
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  • 30
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    Annals of biomedical engineering 26 (1998), S. 1036-1043 
    ISSN: 1573-9686
    Keywords: Mathematical model ; Perfusion ; Diffusion ; Collagen ; Nitric oxide (NO) inhibition ; Platelet adhesion
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    Topics: Medicine , Technology
    Notes: Abstract Nitric oxide (NO) is a simple biological molecule which inhibits adhesion and aggregation of platelets. A novel NO delivery device has been developed to quantitatively study the effects of NO concentration and flux on the adhesion of platelets to a surface. The slit-flow device is lined with a protein-coated membrane through which NO gas permeates into a perfusing platelet suspension. A model predicting spatial NO concentrations and fluxes within the flow slit was validated. At a wall shear rate of 250s-1, platelet adhesion was inhibited 87% relative to controls for exposures as low as 0.1 ppm NO. Corresponding model predictions of the aqueous NO concentration and fluxes at the surface were 0.15 nM, and between 0.5 and 1.1 nanomoles cm-2 s-1, respectively. Endo-thelial cells, which release NO to inhibit platelet adhesion in vivo, generate NO at an estimated flux similar to the above values. At a NO exposure of 0.02 ppm, platelet inhibition was only 10%. The delivery device is useful for other studies in which a knowledge of the spatial NO fluxes or concentrations is desired. Knowledge of these fluxes or concentrations is beneficial towards the design of biomaterials incorporating NO to inhibit platelet adhesion. © 1998 Biomedical Engineering Society. PAC98: 8745Hw, 8722Fy, 8780+s, 8710+e, 8380Lz
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    Annals of biomedical engineering 26 (1998), S. 1044-1054 
    ISSN: 1573-9686
    Keywords: Lung ; Gas exchange ; Mathematical model ; O2 and CO2 transfer ; Microporous hollow fibers
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    Notes: Abstract An intravascular gas exchange device for the treatment of respiratory failure consisted of a multitude of blind-ended hollow fibers glued in a pine-needle arrangement to a central gas supply catheter. It has previously been shown that gas desorption rates can be significantly enhanced by cycling gas pressure between a hypobaric level of 130 and an ambient level of 775 Torr. In this study, influences of the cycling frequency (f) and the cycle fraction during which hypobaric pressure is applied (Θ) were investigated. Rates of O2 desorption from O2-saturated water and CO2 desorption from CO2-saturated water into a manifold containing 198 fibers, 380 μm in diameter, were measured over a range of f from 0.2 to 1.0 Hz, Θ from 0.1 to 0.8, and fiber lengths from 4 to 16 cm. Relative to operation at ambient pressure, pressure cycling increased O2 transfer 3–4 times and CO2 transfer 4–6 times when the water flowed over the fiber manifold at 2.3 l/min. Transfer rates were relatively insensitive to f and Θ with 80–90% of maximum enhancement obtained when Θ was as low as 0.2. Transfer rates increased continuously with fiber length, implying that pressure cycling reduced the intra-fiber resistance to gas diffusion. A mathematical diffusion model which utilized only two adjustable parameters, a mass transfer coefficient for O2 and for CO2, simulated the trends exhibited by desorption data. © 1998 Biomedical Engineering Society. PAC98: 8745Hw, 8790+y
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  • 32
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    Annals of biomedical engineering 26 (1998), S. 911-913 
    ISSN: 1573-9686
    Keywords: Physiological database ; Mathematical model ; Physiome: microcirculation
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    Topics: Medicine , Technology
    Notes: Abstract Presented is a discussion of steps towards the creation of a database of the microcirculation encompassing anatomical and functional experimental data, and conceptual and computational models. The discussion includes issues of database utility, organization, data deposition, and linkage to other databases. The database will span levels from gene to tissue and will serve both research and educational purposes. © 1998 Biomedical Engineering Society. PAC98: 8745Ft, 8710+e, 0130Cc
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  • 33
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    Annals of biomedical engineering 26 (1998), S. 914-930 
    ISSN: 1573-9686
    Keywords: Flow distribution ; Axial diffusion ; Mathematical model ; Perfusion heterogeneity ; Relative dispersion ; Heterogeneity ; Capillary transit times ; Indicator dilution
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    Notes: Abstract To mathematically model multiple indicator dilution (MID) data for the purpose of estimating parameters descriptive of indicator-tissue interactions, it is necessary to account for the effects of the distribution of capillary transit times, hc(t) In this paper, we present an efficient approach for incorporating hc(t) in the mathematical modeling of MID data. In this method, the solution of the model partial differential equations obtained at different locations along the model capillary having the longest transit time provides the outflow concentrations for all capillaries. When weighted by hc(t) these capillary outflow concentrations provide the outflow concentration versus time curve for the capillary bed. The method is appropriate whether the available data on capillary dispersion are in terms of capillary transit time or relative flow distributions, and whether the dispersion results from convection time differences among heterogeneous parallel pathways or axial diffusion along individual pathways. Finally, we show that the knowledge of a relationship among the moments of hc(t) rather than hc(t) per se, is sufficient information to account for the effect of hc(t) in the mathematical modeling interpretation of MID data. This relationship can be determined by including a flow-limited indicator in the injected bolus, thus providing an efficient means for obtaining the experimental data sufficient to account for capillary flow and transit time heterogeneity in MID modeling. © 1998 Biomedical Engineering Society. PAC98: 8745Ft, 8710+e, 0230Jr
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  • 34
    ISSN: 1573-9686
    Keywords: Cardiopulmonary resuscitation ; Mathematical model ; Intrathoracic pressure
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    Notes: Abstract Whether blood flow during cardiopulmonary resuscitation (CPR) results from intrathoracic pressure fluctuations or direct cardiac compression remains controversial. We developed a mathematical model that predicts that blood flow due to intrathoracic pressure fluctuations should be insensitive to compression rate over a wide range but dependent on the applied force and compression duration. If direct compression of the heart plays a major role, however, the model predicts that flow should be dependent on compression rate and force, but above a threshold, insensitive to compression duration. These differences in hemodynamics produced by changes in rate and duration form a basis for determining whether blood flow during CPR results from intrathoracic pressure fluctuations or from direct cardiac compression. The model was validated for direct cardiac compression by studying the hemodynamics of cyclic cardiac deformation following thoracotomy in four anesthetized, 21–32-kg dogs. As predicted by the model, there was no change in myocardial or cerebral perfusion pressures when the duration of compression was increased from 15% to 45% of the cycle at a constant rate of 60/min. There was, however, a significant increase in perfusion pressures when rate was increased from 60 to 150/min at a constant duration of 45%. The model was validated for intrathoracic pressure changes by studying the hemodynamics produced by a thoracic vest (vest CPR) in eight dogs. The vest contained a bladder that was inflated and deflated. Vest CPR changed intrathoracic pressure without direct cardiac compression, since sternal displacement was 〈0.8 cm. As predicted by the model and opposite to direct cardiac compression, there was no change in perfusion pressures when the rate was increased from 60 to 150/min at a constant duration of 45% of the cycle. Manual CPR was then studied in eight dogs. There was no surgical manipulation of the chest. Myocardial and cerebral blood flows were determined with radioactive microspheres and behaved as predicted from the model of intrathoracic pressure, not direct cardiac compression. At nearly constant peak sternal force (378–426 N), flow was significantly increased when the duration of compression was increased from short (13%–19% of the cycle) to long (40%–47%), at a rate of 60/min. Flow was unchanged, however, for an increase in rate from 60 to 150/min at constant compression duration. In addition, myocardial and cerebral flow correlated with their respective perfusion pressures. Thus vital organ perfusion pressures and flow for manual external chest compression are dependent on the duration of compression, but not on rates of compression of 60 and 150/min. These data are of course similar to those produced by vest CPR, where intrathoracic pressure is manipulated without sternal displacement, and to those predicted for movement of blood by intrathoracic pressure changes. These data are, however, opposite to those produced by cardiac deformation and to those predicted for movement blood by direct cardiac compression. We conclude that intrathoracic pressure fluctuations generate blood flow during manual CPR.
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  • 35
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    Annals of biomedical engineering 17 (1989), S. 13-38 
    ISSN: 1573-9686
    Keywords: Oxygen transport ; Microcirculation ; Cerebral circulation ; Carbon monoxide ; Mathematical model ; Computer simulation
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    Notes: Abstract A compartmental model is formulated for oxygen transport in the cerebrovascular bed of the brain. The model considers the arteriolar, capillary and venular vessels. The vascular bed is represented as a series of compartments on the basis of blood vessel diameter. The formulation takes into account such parameters as hematocrit, vascular diameter, blood viscosity, blood flow, metabolic rate, the nonlinear oxygen dissociation curve, arterial PO2, P50 (oxygen tension at 50% hemoglobin saturation with O2) and carbon monoxide concentration. The countercurrent diffusional exchange between paired arterioles and venules is incorporated into the model. The model predicts significant longitudinal PO2 gradients in the precapillary vessels. However, gradients of hemoglobin saturation with oxygen remain fairly small. The longitudinal PO2 gradients in the postcapillary vessels are found to be very small. The effect of the following variables on tissue PO2 is studied: blood flow, PO2 in the arterial blood, hematocrit, P50, concentration of carbon monoxide, metabolic rate, arterial diameter, and the number of perfused capillaries. The qualitative features of PO2 distrbution in the vascular network are not altered with moderate variation of these parameters. Finally, the various types of hypoxia, namely hypoxic, anemic and carbon monoxide hypoxia, are discussed in light of the above sensitivity analysis.
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    Annals of biomedical engineering 16 (1988), S. 445-461 
    ISSN: 1573-9686
    Keywords: Periodic breathing ; Respiratory control ; Mathematical model ; CO2 mass transport ; Stability
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    Notes: Abstract A stability analysis of respiratory chemical control is developed using a mathematical model of CO2 mass transport dynamics. Starting with a 3-compartment model of CO2 stores that distinguishes alveolar, muscle, and other tissue, model reduction techniques are applied to obtain a first-order representation of the respiratory plant. This model contains an effective tissue volume for CO2, whose derived value is much smaller than previously predicted. To investigate oscillatory instabilities, a controller which incorporates only peripheral chemoreceptor responses was added to the first-order plant model. An explicit stability index (SI) is obtained analytically from a linearized version of this model. SI varies directly with the controller gain and circulation delay time and inversely with the effective tissue volume and inspired CO2 concentration. Numerical simulations using the first-order nonlinear model show that SI is a good predictor of system stability. According to the linearized model, the system is stable for SI〈1; from the nonlinear model, the system is stable for SI〈1.1. For typical normal adults, the SI value is well within the stable region.
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  • 37
    ISSN: 1573-9686
    Keywords: SA node ; Mathematical model ; Vagal control ; ACh
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    Notes: Abstract We present a new mathematical model for vagal control of rabbit sinoatrial (SA) node electrical activity based on the DiFrancesco-Noble equations. The original equations were found to be unstable, resulting in progressive cycle by cycle depletion or accumulation of ions in intra- and extracellular compartments. This problem was overcome by modifying the maximum Na−K pump current and the time constant for uptake of intracellular calcium. We also included a formulation for the acetylcholine (ACh)-activated potassium current which was consistent with experimental data. This formulation was based on kinetics first proposed by Osterrieder and later modified by Yanagihara. The resulting model exhibits cycle-cycle ionic stability, and includes an ACh-activated potassium current which accurately reproduces experimentally observed effects of vagal stimulation on both the membrane potential and its timederivative. Simulations were performed for both brief-burst and prolonged vagal stimulation using simplified square wave profiles for the concentration of ACh in the synaptic cleft space. This protocol permits the isolation of cardiac period dynamics caused by changes in membrane potential and intra- and extracellular ionic concentrations from those caused by other mechanisms including the dynamics of ACh release, diffusion, hydrolysis and washout. Simulation results for the effects of brief-burst single cycle stimulation on the cardiac period agree closely with experimental data reported in the literature, accurately reproducing changes in membrane potential and the phasic dependency of the response to the position of vagal stimulus bursts within the cycle. Simulation of the effects of prolonged vagal stimulation accurately reproduced the steady-state characteristics of heart period response, but did not yield the complex multimodal dynamics of the recovery phase, or the pronounced post vagal tachycardia observed experimentally at the termination of the stimulus. Our results show that the major chronotropic effects of vagal stimulation on the SA cell membrane can be explained in terms of the ACh-activated potassium current. The effects of this membrane current however are generally fast acting and cannot contribute to any long lasting dynamics of the cardiac period response. The modified DiFrancesco-Noble model presented in this article provides a valuable theoretical tool for further analysis of the dynamics of vagal control of the cardiac pacemaker.
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  • 38
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    Annals of biomedical engineering 26 (1998), S. 28-36 
    ISSN: 1573-9686
    Keywords: Mathematical model ; Tissue factor ; Wall shear rate ; FXa generation ; TF:FVIIa ; Rat ; Vascular ; Smooth muscle ; Factor X ; Coagulation ; Clot
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine , Technology
    Notes: Abstract A computational model was developed to investigate the contribution of classical mass transport and flow parameters to factor X (FX) activation by the tissue factor–factor VIIa complex (TF:VIIa) on one wall of a parallel-plate flow chamber. The computational results were compared to previously obtained experimental data for the generation of factor Xa (FXa) by TF:VIIa on the surface of cultured rat vascular smooth muscle cells. In this study, the complete steady-state convection–diffusion equation was solved using the commercial software package, FLUENT (Fluent Inc., Lebanon, New Hampshire). A user-defined subroutine interfaced with FLUENT implemented the surface reaction which was modeled using classical Michaelis–Menten reaction kinetics. The numerical solutions were obtained for 12 cases which used combinations of three wall shear rates and four reaction rates. The numerically obtained fluxes for a given reaction rate displayed a wall shear rate dependence which ranged from classical kinetic reaction control (no dependence) to pure diffusional control (maximum dependence). The experimental data, however, were not represented by numerical data generated using a single reaction rate. The three numerically obtained fluxes which corresponded most closely to the experimental fluxes were determined using three different V max values. This finding supports the hypothesis that there may be a direct effect of flow on the TF:VIIa complex or the cell membrane. © 1998 Biomedical Engineering Society. PAC98: 8722-q, 8710+e
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  • 39
    ISSN: 1573-9686
    Keywords: Mannitol ; Deconvolution ; Mathematical model ; Transport function ; Recirculation ; Indicator dilution
    Source: Springer Online Journal Archives 1860-2000
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    Notes: Abstract The transport function of an indicator through an organ allows the calculation of important physiological parameters, but its estimation, especially in the presence of recirculation, can be difficult. In this paper, we estimate the transport function of 3H-mannitol (an extracellular tracer of glucose) in the human leg skeletal muscle. To do so, an indicator bolus is administered into the femoral artery and its recirculating dilution curves are nonuniformly sampled in both the femoral artery and the femoral vein. A new deconvolution-based method is used to simultaneously estimate the indicator transport function and the organ plasma flow. Subsequently, the indicator mean transit time and distribution volume are calculated. The reliability of the method is assessed by Monte Carlo simulation. The ability to estimate parameters, like mean transit time and extracellular distribution volume, is critical to the study of pathophysiologic states such as diabetes, insulin resistance, and hypertension. © 1998 Biomedical Engineering Society. PAC98: 8710+e, 0270Lq, 8745Hw
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  • 40
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    Annals of biomedical engineering 26 (1998), S. 417-430 
    ISSN: 1573-9686
    Keywords: Capillary permeability ; Acute respiratory distress syndrome ; Mathematical model ; Alloxan lung injury ; Pulmonary edema ; Lung fluid balance ; Indicator dilution: optical ; Indicator dilution: radioisotope
    Source: Springer Online Journal Archives 1860-2000
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    Notes: Abstract The objective of this study was a validation of an optical multiple indicator dilution technique for measuring microvascular exchange parameters in edematous lungs by comparison to conventional radioisotope multiple indicator dilution methods. Six anesthetized dogs were studied at baseline and after alloxan infusion to increase capillary permeability. In addition, 11 isolated, perfused dog lungs were studied at baseline and after edema was created by increasing venous pressure or by infusing alloxan to increase vascular permeability. Increased capillary permeability from alloxan infusion led to increases in most but not all capillary exchange parameters as analyzed by mathematical models and measured by both optical and radioisotope methods. Increased vascular pressure led to increased edema but no significant increases in capillary exchange parameters. Two-way analysis of variance (ANOVA; variations in baseline versus pressure or alloxan and variation in optical versus radioisotope for each transport parameter derived from the mathematical models) indicated few significant differences in capillary exchange parameters between optical and radioisotope measures. Newman–Keuls multiple comparison tests did uncover some variations between a few of the group-mean values derived from optical and radioisotope methods. However, optical and radioisotope parameter measurements were highly correlated for all studies regardless of the mathematical model used for analysis.
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  • 41
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    Annals of biomedical engineering 27 (1999), S. 525-537 
    ISSN: 1573-9686
    Keywords: Biosensors ; Mathematical model ; Algorithms ; Inverse problems ; Input estimation ; Regularization
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    Notes: Abstract An approach for inference of blood glucose concentrations in real time is considered. First, a model that predicts the subcutaneous glucose concentration from the blood glucose concentration is presented. The model includes diffusive transport from the blood to the subcutaneous tissue and reactive-like cellular uptake of glucose. Next, the Phillips-Tikhonov regularization method is considered to solve the real-time input estimation problem that determines the blood glucose concentration given the subcutaneous glucose concentration. The inverse problem is regularized by imposing a smoothing condition to obtain a stable solution. Three different penalization functionals were considered in evaluating the regularization method using a synthetic function that approximates the subcutaneous glucose response to an oral glucose tolerance test in a human subject. Various levels of either white noise or time-correlated noise were superimposed onto the synthetic response to evaluate the sensitivity of the inverse to measurement error. For inversion assuming only diffusive transport, the optimal time interval of integration of previous subcutaneous measurements was found to be about 1.5/ $$\hat \alpha $$ , where $$\hat \alpha $$ -1 is the dominant time constant for the exchange of glucose between the blood and subcutaneous tissue. The optimal sampling rate was found to be 54 $$\hat \alpha $$ . Linear regularizations based on minimization of first or second derivatives of the blood glucose concentration were found to be satisfactory, each yielding a minimum error that was about 50% greater than the measurement error. Including nonlinear, reactive-like uptake of glucose was found to decrease the error magnification factor slightly. Both the model and the inverse method relating blood and subcutaneous glucose concentrations are successfully applied to experimental measurements using glucose biosensors reported by Schmidtke et al. (Proc. Natl. Acad. Sci. USA 95:294–299, 1998). © 1999 Biomedical Engineering Society. PAC99: 8780-y, 8717Aa
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