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  • Articles  (10)
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  • Articles  (10)
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  • Articles: DFG German National Licenses  (10)
  • Latest Papers from Table of Contents or Articles in Press
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  • Springer  (10)
  • American Chemical Society (ACS)
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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
    Electronic Resource
    Electronic Resource
    Springer
    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
    Electronic Resource
    Electronic Resource
    Springer
    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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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    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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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    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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  • 6
    Electronic Resource
    Electronic Resource
    Springer
    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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  • 7
    Electronic Resource
    Electronic Resource
    Springer
    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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  • 8
    ISSN: 1573-9686
    Keywords: Cardiopulmonary resuscitation ; Mathematical model ; Intrathoracic pressure
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine , Technology
    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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  • 9
    Electronic Resource
    Electronic Resource
    Springer
    Annals of biomedical engineering 17 (1989), S. 13-38 
    ISSN: 1573-9686
    Keywords: Oxygen transport ; Microcirculation ; Cerebral circulation ; Carbon monoxide ; Mathematical model ; Computer simulation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine , Technology
    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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  • 10
    Electronic Resource
    Electronic Resource
    Springer
    Annals of biomedical engineering 16 (1988), S. 445-461 
    ISSN: 1573-9686
    Keywords: Periodic breathing ; Respiratory control ; Mathematical model ; CO2 mass transport ; Stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine , Technology
    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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