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1D and 3D Models of Auto-Regulated Cerebrovascular Flow

1D and 3D Models of Auto-Regulated Cerebrovascular Flow

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1D and 3D Models of Auto-Regulated Cerebrovascular Flow

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  1. 1D and 3D Models of Auto-Regulated Cerebrovascular Flow THE 26th ANNUAL INTERNATIONAL CONFERENCE OF THE IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY K T Moorhead, S M Moore, J G Chase, T David, J Fink Department of Mechanical Engineering University of Canterbury Christchurch, New Zealand

  2. Structure of the CoW • Responsible for distributing blood to the major regions of the brain • Blood can be re-routed through the circle to maintain homeostasis • Previous Models • No auto-regulation • No transient dynamics

  3. 1 D and 3 D Geometry 1 D Model 3 D Model Efferent arteries resistances time-variable Circulus and afferent artery resistances constant CAD reconstruction of MRA scan Porous block represents capillary bed effects

  4. Standard PI feedback control law Resistance dynamics of contraction/dilation Amount of change is limited Dynamic Auto-Regulation • Resistance limits • Deadband • Memory • Peripheral resistance ratio based on Hillen (1986) 6:3:4:75:75 • Total influx = 12.5 cm3s-1 Control gains match the time dependent velocity profile of the MCA from thigh cuff experiments of Newell et al. (1994) - 20 sec response time for a 20% pressure drop

  5. Error in flowrate NO YES q = qref? Change in control input Calculate new flowrate Change in resistance R P2 P1 q 1 D Fluid Model Poiseuille Flow Constant resistance between nodes captured by simple circuit analogy: System is highly nonlinear: A(x(t))*x(t) = b(t) Solve system iteratively between resistance and flow rates

  6. 3 D Model Geometry

  7. Results – Ideal Configuration Ipsilateral Efferent flowrates • All circulus vessels present • 20 mmHg pressure drop in the RICA • Very good agreement in efferent flux profiles between models

  8. Results – Ideal Configuration Circulus Flowrates • 1 D model ACoA experiences greater pressure losses because this artery is least well approximated by Poiseuille Flow • Increase resistance of the ACoA 9-fold in the 1 D model to produce same effective resistance as 3 D model Significant improvement

  9. Results – Absent Ipsilateral ACA1 ACA2 Ipsilateral Efferent flowrates • 1 D model has the ACoA resistance increased 9-fold as previously • Ipsilateral ACA2 can not reach its reference flowrate even before a pressure drop is imposed • Good agreement between models – models get same “wrong” answer

  10. Conclusions • 1 D and 3 D CoW models created • Models include non-linear dynamics of auto-regulation using PI controller • Model verified against limited clinical data and prior research • Excellent agreement between models for efferent flux profiles • 1 D ACoA not well approximated by Poiseuille flow increase ACoA resistance 9-fold to obtain good agreement in circulus flowrates between models Future work includes more physiologically accurate auto-regulation and geometry modelling, more clinical verification using existing data, and modelling of greater variety of potential structures and pathological conditions

  11. Punishment of the Innocent Questions ???