MEMORY ALGORITHMS FOR SHORT TERM ADAPTATION OF
CEREBRAL HAEMODYNAMICS
S. S. Alzaidi1, K. T. Moorhead1, T. David1, J. G. Chase1
1
Department of Mechanical Engineering, University of Canterbury, Christchurch, New Zealand.
INTRODUCTION: The cerebral mass is supplied by the Circle of Willis (COW), Figure 1 (a), [1], which
distributes incoming oxygen rich blood from the internal carotid and basilar arteries. If the COW is
incomplete, stroke-like symptoms can result if there is any shortage in blood supply. Blood flow through
the COW is determined principally by auto-regulation, a process maintaining homeostasis by altering the
peripheral resistance as to provide a constant supply of oxygenated blood irrespective of pressure
variations [2]. A model of the auto-regulation response for normal and incomplete COW is implemented.
METHODS: Efferent arteries are represented as variable resistances. The auto-regulatory response via
vascular resistance is modelled by a PI controller, (1), where Kp and Ki are the proportional and integral
gains and e is the flow rate error. The integral error, (2), is used to implement a memory algorithm for
short term adaptation to blood flow.
R (t )  ( R(t )  Rref )  u(t )
(1a)
t
u(t )  K p e  Ki  ed
(1b)
0

t
0
t
ed  ek t   ek 1  e d
(2)
0
RESULTS: Ideal auto-regulation was replicated for normal COW as represented by the black solid line in
Figure 2 (b). The dashed and dotted lines represent the blood flow in the ipsilateral and contralateral
middle cerebral artery (MCA) for an internal carotid artery (ICA) occlusion.
Anterior (Front)
Fig. 1:Diagram
of COW.
Fig. 2:MCA flow rate with ICA occlusion .
Anterior Cerebral Artery
A2 Segment
ACA –A2
CONCLUSIONS: Basic mechanisms for auto-regulation were implemented for complete and incomplete
Anterior Cerebral Artery
Segment
COW configurations. To further develop theA1model,
other means of blood flow control mechanisms will
ACA –A1
be implemented which include effect of metabolic rate and neural control.
Anterior Communicating Artery
ACoA
Middle Cerebral Artery
MCA
Internal Carotid Artery
ICA
REFERENCES:
1
A. Vander, J. Sherman, D. Luciano,
Physiology - The Mechanisms of Body Function,
Posterior(2001)
CommunicatingHuman
Artery
PCoA
McGraw Hill, Eighth Edition.
Anterior Choroidal Artery
AChA
Posterior Cerebral Artery
P12Segment
PCA – P1
Posterior Cerebral Artery
P2 segment
J. Keener, J. Sneyd, (1991) Mathematical Physiology,
Springer.
PCA – P2
Superior Cerebellar Artery
SCbA
Left Side
Posterior (Back)
Basilar Artery
BA
Right Side