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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.