Department of Applied MathematicsWestern Science


Mair Zamir
Professor Emeritus

Department of Applied Mathematics
The University of Western Ontario
Middlesex College Rm. 209
London, ON, Canada
N6A 5B7
tel: (519) 661-2111 ext. 88779
fax: (519) 661-3523


Research Interests





Recent Publications

Hemo-Dynamics. Springer, New York, 2016.

It is remarkable how readily we accept the proposition that blood is the essence of life, our life. Yet we miss the point. The essence of life is not blood, it is blood flow. When the heart stops beating, the body dies not because of lack of blood but because of lack of blood flow.

Because of the pulsatile nature of blood flow, the integrity of blood supply to any destination within the body depends not only on the integrity of the blood vessels involved but also on the state of oscillatory dynamics of the flow. A disruption in blood supply can result from a derangement in the dynamics of the flow (dynamic pathology) in the same way that it can result from an obstruction in a blood vessel (structural pathology).

Unlike structural pathologies, dynamic pathologies do not leave a “footprint” after they have been resolved or after they have incurred their damage. Following an ischemic event, for example, whether in the heart or in the brain, indeed following a failure or discrepancy in blood supply to any other organ, only structural pathologies can usually be found. Any dynamic pathologies that may have been involved are not in evidence because they are no longer at play.

The Physics of Coronary Blood Flow. Springer, New York, 2005.

While the heart, like other parts of the body, is subject to genetic disorders and infectious diseases, only a very small proportion of heart failures are caused by such conditions. In all other cases a lack of blood supply to the heart muscle, or a lack of fuel which the muscle needs for doing its pumping work, is the principal cause of heart failure.

Yet, “heart disease” is the term most widely used in association with heart failure. The term is somewhat misleading because it suggests that the failure is due to a disease of the heart itself... The situation is not unlike that of using the term “malfunction” to describe a car engine failure caused by lack of fuel.

One of the characteristic features of the coronary circulation (the vascular system responsible for providing the heart with its own blood supply) is its capacity to increase blood flow to the heart “on demand” by as much as five or six times normal flow rate, a feature generally referred to as “coronary flow reserve”. The conundrum of coronary flow reserve is that it may “mask” the gradual shortfall in coronary blood flow at the initial stages of coronary heart disease and thereby prevent the remedial mechanism of vascular restructuring from being triggered. At the latter stages of the disease the capacity of coronary flow reserve is largely depleted and the mechanism of vascular restructuring may not have the time required for its slow course of action. Physical conditioning (exercise) may forestall this course of events by deliberately and regularly triggering the mechanism of vascular restructuring while coronary flow reserve is still intact.

The Physics of Pulsatile Flow. Springer-Verlag, New York, 2005.

Flow in a tube is the most common fluid dynamic phenomenon in biology.  Its evolution as a tool in biology is so closely intertwined with the evolution of living organisms that it is difficult to view the two as separate from each other. Not even in the realm of science fiction can we imagine the evolution of a living organism of any degree of complexity without the facility of flow in tubes.

When flow is steady, the phenomenon is particularly simple because only two forces are at play: the pressure difference between the two ends of the tube, which acts as a driving force, and viscous shear between the fluid and the tube wall, which acts as a retarding force.  When flow is pulsatile, however, the pressure difference between the two ends of the tube varies periodically in time...  This introduces other forces and other variables and the phenomenon becomes considerably more complicated particularly when the tube wall is not rigid.

Because of this added complexity, in both mathematics and physics, for far too long the subject of pulsatile blood flow has been practically inaccessible to those who need it most. My deepest hope is that in this book I have made the subject somewhat more accessible, and this I owe largely to the clinical colleagues I have worked with over the years, and to the wonderful students of all stripes who have asked questions.