42
Dynamics
of
the Vascular System
form
a
dimensional matrix, a priori knowledge of pertinent physical
parameters
is
necessary.
For instance,
if
8
physical quantities are
important for the description of blood flow in arteries, and there are
3
basic units
(My
L,
T)
to
represent them, then we are be able to obtain
8-3
=
5
dimensionless Pi--numbers. In general, the number
of
dimensionless
Pi-numbers are determined by the number of physical quantities minus
the rank of the dimensional matrix.
To use the
MLT
system, one needs to first express explicitly any
variable in its physical units, either using the
CGS
(cm,g,s) or the
MKS
(m,Kg,s) system or
SI
units
of
representation.
For instance, blood
pressure
is
commonly measured in mmHg and must be converted to
g/cm
s2.
Thus, pressure (p) is given
as
force per unit area,
p
=
F
=
[MIL]-'
A
(3.1.1)
where
A
has the dimension of cm2, or
[LI2,
and force is mass times
acceleration,
F
=
m
*
a
=
[MIL]/[T]-2
(3.1.2)
where a is the acceleration in cm/s/s
=
cm/s2
The left ventricular volume
V,
has the unit of ml
or
cm3, and a dimension
of
v
=
[LI3
(3.1.3)
The aortic flow
Q,
as a rate
of
change of ventricular volume, has the unit
of ml/s, or
dV
dt
Q
=
-
=
[L]3
/[TI
(3.1.4)
Linear flow velocity has the dimension of