Biomedical Engineering Reference
In-Depth Information
lymphatic system also increases. At an interstitial pressure of approximately 0 mmHg, the
rate of lymph flow increases 10 times over the normal lymphatic flow rate (recall intersti-
tial hydrostatic pressure is typically
4 mmHg). As the interstitial pressure
increases to 2 mmHg, the lymphatic flow rate approaches a maximum of approximately
20 times of the normal lymphatic flow rate. The lymph flow cannot exceed this capacity
because at higher interstitial pressures (
2
3 mmHg to
2
3 mmHg), the lymphatic vessels compress,
because they cannot withstand the pressure forces. Lymphatic vessels do not have a thick
muscular wall. The possible compression of lymph vessels effectively increases the resis-
tance to flow through the lymphatic vessels to a point that the driving force cannot over-
come. Therefore, for small deviations from the normal interstitial pressure, the rate of
lymph flow does not increase significantly. As the interstitial pressure increases signifi-
cantly above the normal interstitial hydrostatic pressure level, the rate of lymph flow
increases to remove the excess fluid within the interstitial space. The major contributors to
the interstitial hydrostatic pressure are the capillary hydrostatic pressure, the osmotic pres-
sures of the capillary and the interstitial space, as well as the endothelial cell permeability.
Small changes in any of these values can have a significant effect on the hydrostatic pres-
sure of the interstitial space and therefore a major effect on the flow rate of the lymphatic
system.
.
Example
Assume for this example that the osmotic pressure of the blood vessel, the osmotic pressure
of the interstitial space, and the hydrostatic pressure of the blood vessel remains the same. Make
an approximation of the lymph flow rate at various interstitial pressures using a first-order poly-
nomial and a second-order polynomial. Plot the changes in lymph flow rate versus pressure
under both conditions.
Solution
Using linear algebra to solve for the least squares regression line through the following data
points, we get
X 5 ½ 2
4
0
2
mmHg
;
;
Y 5 ½
1
10
20
relative flow rate
;
;
First-Order Polynomial
Second-Order Polynomial
2
4
3
5
2
4
3
5 5
2
4
3
5
a
b
5
a
b
c
3
2
2
20
31
36
96
3
2
31
36
2
2
20
56
2
2
2
2 0
20
56
272
2
4583 X 2
Y 5
3
036 X 1
12
357
Y 5
0
4
083 X 1
10
:
:
:
1
:
With a second-order polynomial, the curve goes through each of the data points and this may
be the better approximation for lymph flow rate changes ( Y -axis) with changes in interstitial
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