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  • 1
    Electronic Resource
    Electronic Resource
    Some applications of theP-V relation to the study of left ventricular performance (1989)
    Springer
    Bulletin of mathematical biology 51 (1989), S. 475-484 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract There is still controversy as to which characteristics of the pressure-volume relation should be used to define myocardial contractility. In the present study a mathematical model for the left ventricle as a two-dimensional cylinder contracting radially and symmetrically was used to establish a relation between a calculated intramyocardial pressure (Dh) and theP-V relation (PVR) at end-systole. Four new indices are introduced that allow a better assessment of change in inotropic state of the myocardium, namely the calculated intramyocardial pressure (Dh), the calculated resultant pressure across the inner surface of the myocardium (Dh-P) (P=cavity pressure), the workW t related to the pressure (Dh) and the workW d related to the pressure (Dh-P). A relation betweenW t andW d and different parts of the area under the PVR is established. Indices derived in this manner from the PVR to study changes in myocardial contractility appear to have a clear physical meaning.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460085
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  • 2
    Electronic Resource
    Electronic Resource
    Some applications of the concept of body forces for the myocardium (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 819-840 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A mathematical theory of the dynamics of the myocardium based on the concept of body forces is applied to account for two different experimental results. The first result consists of a relation between oxygen consumption and the kinetic energy of the myocardium. The second set of results provides a consistent interpretation of the relationship between different indices used to assess the ventricular performance.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02465183
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Contractile analysis and kinetic energy of the myocardium (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 447-461 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The left ventricle is represented as a cylinder contracting both radially and longitudinally. A simple method is indicated to derive an expression for the rate of change of the kinetic energy of this three-dimensional model, which quantity can be used as an index for the study of the contractile behaviour of the myocardium. An application to the study of muscle mechanics is also indicated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02459433
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Note on Kepler's problem with variable angular momentum (1995)
    Springer
    Celestial mechanics and dynamical astronomy 63 (1995), S. 199-203 
    Details
    ISSN: 1572-9478
    Keywords: Elliptical orbit ; periodic motion with drag ; non-central force field ; Kepler's laws
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Based on the equations of planar motion with drag used in point dynamics, a simple derivation is presented that shows how a constant Keplerian (elliptical) orbit can be obtained with a non-central force field and variable angular momentum.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00693414
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  • 5
    Electronic Resource
    Electronic Resource
    Elliptical orbit with non-central force field in celestial mechanics (1996)
    Springer
    Celestial mechanics and dynamical astronomy 65 (1996), S. 373-388 
    Details
    ISSN: 1572-9478
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Equations describing planar motion along a constant elliptical orbit in non-central force field are derived in a simple way and discussed. The angular moment along the elliptical orbit is not a constant of motion. The problem appears to be related to the problem of planar motion with drag force. Relations with related works are discussed. In presence of drag force, conditions for the force field to be derived from the gradient of a function are discussed, and -elation of this function with the potential function is indicated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00049501
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    Paper (German National Licenses)
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  • 6
    Electronic Resource
    Electronic Resource
    The pressure-volume relation in the left ventricle and the pump function of the heart (1991)
    Springer
    Annals of biomedical engineering 19 (1991), S. 699-721 
    Details
    ISSN: 1573-9686
    Keywords: Body force model for the force of the myocardium ; Large deformation analysis for left ventricle ; Mean pressure-mean flow in the left ventricle
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine , Technology
    Notes: Abstract The concept of body force (force per unit volume) is introduced to account for the effect of the force generated in the radial direction by the active state of the myocardium in an elastic model of the left ventricle represented as a thick-walled cylinder contracting symmetrically. Experimental evidence for the validity of the model is presented. It is shown how the radial force/unit area developed by the myocardium on its inner surface can be included in the equation of the pressure-volume relation (P-V relation) of the left ventricle according to the Suga-Sagawa model, as well as in the formalism that describes the pump function of the heart.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02368077
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  • 7
    Electronic Resource
    Electronic Resource
    The application of shape-preserving splines for the solution of differential equations (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 689-695 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper investigates the use of shape-preserving interpolants based on Bernstein polynomials for the numerical solution of differential equations. A simple and accurate algorithm is presented for the integration of the initial value ordinary differential equation, as well as for the partial differential equation of the Burger type.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620200408
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    Paper (German National Licenses)
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  • 8
    Electronic Resource
    Electronic Resource
    Clinical application of end-systolic pressure-volume relation (1994)
    Springer
    Annals of biomedical engineering 22 (1994), S. 212-217 
    Details
    ISSN: 1573-9686
    Keywords: Cardiac mechanics ; Ventricular function ; Pump function ; Mathematical modeling
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine , Technology
    Notes: Abstract On the basis of a mathematical formalism derived in previous studies, properties of the end-systolic pressure-volume (P-V) relation were analyzed to define indexes that can characterize a normal or failing left ventricle. Careful analysis of different areas under the P-V line can lead to new indexes that describe the performance of the left ventricle. The possibility to distinguish between normal, midly depressed, or severely depressed left ventricles based on P-V relation is discussed. Implementation of the results for routine clinical work is examined.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02390379
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