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

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

1 D and 3 D Geometry 1 D Model3 D Model CAD reconstruction of MRA scan Porous block represents capillary bed effects Efferent arteries resistances time-variable Circulus and afferent artery resistances constant

Dynamic Auto-Regulation Resistance dynamics of contraction/dilation Standard PI feedback control law Amount of change is limited 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 Resistance limits Deadband Memory Peripheral resistance ratio based on Hillen (1986) 6:3:4:75:75 Total influx = 12.5 cm 3 s -1

1 D Fluid Model R P1P1 P2P2 q Constant resistance between nodes captured by simple circuit analogy: Poiseuille Flow System is highly nonlinear: A(x(t))*x(t) = b(t) Solve system iteratively between resistance and flow rates Error in flowrate Change in control input Change in resistance Calculate new flowrate q = qref? NO YES

3 D Model Geometry

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

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

Results – Absent Ipsilateral ACA 1 1 D model has the ACoA resistance increased 9-fold as previously Ipsilateral ACA 2 can not reach its reference flowrate even before a pressure drop is imposed Good agreement between models – models get same “wrong” answer Ipsilateral Efferent flowrates ACA 2

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

Punishment of the Innocent Questions ???