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Models for microvascular regulation of blood flow Timothy W. Secomb, Julia C. Arciero and Brian E. Carlson Mathematica

. Metabolic regulation of blood flow. Goodman et al., 1978. . Autoregulation of blood flow. Johnson, 1980. ActuatorsSensorsInformation transfer. Elements of a control system. . Myogenic response. Johnson, 1980. . Myogenic response. Sun et al., 1995. . Shear-dependent response. Renal artery of cat - Melkumyants et al., 1995.

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Models for microvascular regulation of blood flow Timothy W. Secomb, Julia C. Arciero and Brian E. Carlson Mathematica

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    1. Models for microvascular regulation of blood flow Timothy W. Secomb, Julia C. Arciero and Brian E. Carlson Mathematical Biosciences Institute Columbus, Ohio January 24, 2007

    2. Metabolic regulation of blood flow

    3. Autoregulation of blood flow

    4. Elements of a control system

    5. Myogenic response

    6. Myogenic response

    7. Shear-dependent response

    8. Myogenic and shear-dependent responses

    9. Total wall tension T = PD/2 = Tp(L) + A Tma(L) Model for vascular smooth muscle - I We connect these two elements in parallel and then note that the vessel is not just in the maximally activated or passive state but has a continuum of responses in between This variation in state is represented by an activation function here which is a sigmoidal function of tension and shear in the vessel wall Note that the length-tension representation of the vessel state can be converted to pressure-diameter using the appropriate relationships This model is represented by the eight parameters C1 through C8We connect these two elements in parallel and then note that the vessel is not just in the maximally activated or passive state but has a continuum of responses in between This variation in state is represented by an activation function here which is a sigmoidal function of tension and shear in the vessel wall Note that the length-tension representation of the vessel state can be converted to pressure-diameter using the appropriate relationships This model is represented by the eight parameters C1 through C8

    10. Model for vascular smooth muscle - II There are two elements which have been modeled in this representation of the arteriolar vessel wall These two elements have been quantified in several experimental studies over the past 25 years. The first element is the passive response of the vessel to tension and can be approximated by an exponential relationship The second element is the maximally activated tension generated by the vascular smooth muscle which can be determined by subtracting the total maximally active tension from the passive response and is modeled here as a gaussian functionThere are two elements which have been modeled in this representation of the arteriolar vessel wall These two elements have been quantified in several experimental studies over the past 25 years. The first element is the passive response of the vessel to tension and can be approximated by an exponential relationship The second element is the maximally activated tension generated by the vascular smooth muscle which can be determined by subtracting the total maximally active tension from the passive response and is modeled here as a gaussian function

    11. Myogenic response

    12. Myogenic and shear-dependent responses

    13. Pressure distribution in microcirculation

    14. Representative segment network model

    15. Autoregulation with myogenic response

    16. Autoregulation with myogenic and shear-dependent response

    17. Response to oxygen

    18. Role of information transfer

    19. ATP release by red blood cells

    20. Responses to intraluminal application of ATP

    21. Conducted responses

    22. Conducted responses across the capillaries

    23. Myogenic, shear-dependent and metabolic responses Model for estimation of metabolic signal M in arterioles Oxygen saturation declines as oxygen is extracted from each vessel in proportion to oxygen consumption rate ATP is released in microvessels by red blood cells, at a rate that increases with decreasing oxygen saturation A conducted response is generated in proportion to the ATP level and propagated upstream with exponential decay

    24. Autoregulation with myogenic, shear-dependent and metabolic response

    25. Arteriolar vasomotion

    26. Dynamic model

    28. Conclusions In the microcirculation, flow is modulated strongly in response to changing needs (metabolic regulation), but maintained almost constant over a wide range of blood pressure (autoregulation). The main mechanisms involved in flow regulation include myogenic, shear-dependent, conducted and metabolic responses. In combination, the myogenic and metabolic responses are able to achieve autoregulation of blood flow, despite the opposing effect of shear-dependent responses.

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