A new theoretical approach was used to study the nonlinear response of a microvascular segment subjected to a pressure step at one end. The method is suitable for both large and small deformations of the vessel wall in the case of an elastic response of the segment. It is shown that the use of this simulation permits an indirect determination of the compliance of the vessel. The procedure is applied in two cases of major interest: first the in-vivo study of the intermittent blood flow in the microcirculation, and second, the analysis of experiments using micropipettes. The resulting values of the compliance agree with other values found in the previous studies. The theoretical method is particularly adapted to nonlinear equations.

1.
Arhaliass
A.
,
Dufaux
J.
,
Guiffant
G.
, and
Durussel
J. J.
,
1989
, “
Simulation de l’e´volution du champ de pression (ou de vitesse) dans un re´seau de microvaisseaux mode´lise´s par une structure en couches
,”
I.T.B.M.
,
10
,
31
,
242
242
.
2.
Baldwin
A. L.
, and
Gore
R. W.
,
1988
, “
Simultaneous measurements of capillary distensibility and hydraulic resistance
,”
Microvasc. Res.
,
38
,
1
22
.
3.
Berthault
M. F.
,
Otmane
A.
,
Guillou
J.
,
Counord
J. L.
,
Ktorza
A.
, and
Dufaux
J.
,
1994
, “
Hemorheological abnormalities in rats with experimental mild diabetes. Improving effect of troxerutine and atocopherol
,”
Clinical hemorheology
,
14
-
1
,
83
92
.
4.
Davis
M. J.
, and
Sikes
P. J.
,
1990
, “
Myogenic responses of isolated arterioles: test for a rate-sensitive mechanism
,”
Am. J. Physiol.
,
259
,
H 1890-H 1900
H 1890-H 1900
.
5.
Davis
M. J.
,
Donovitz
J. A.
, and
Hood
J. D.
,
1992
a, “
Stretch-activated single-channel and whole cell currents in vascular smooth muscle cells
,”
Am. J. Physiol.
,
262
,
C 1083-C 1088
C 1083-C 1088
.
6.
Davis
M. J.
,
Meininger
G. A.
, and
Zawieja
D. C.
,
1992
b, “
Stretch-induced increases in intracellular calcium of isolated vascular smooth muscle cells
,”
Am. J. Physiol.
,
263
,
H 1292-H 1299
H 1292-H 1299
.
7.
Dawant
B.
,
Levin
M.
, and
Popel
A. S.
,
1986
, “
Effect of dispersion of vessel diameters and lengths in stochastic networks: I. Modelling of microcirculatory flow
,”
Microvasc. Res.
,
31
,
203
222
.
8.
Duling, B. R., Gore, R. W., Dacey, R. G., Damon, J. R., and Damon, N., 1981, “Methods of isolation, cannulation and in vitro study of single microvessels,” Am. Physiol. Soc., H108.
9.
Durussel, J. J., Berthault, M. F., Guiffant, G., and Dufaux, J., 1998, “Effects of red blood cell hyperaggregation on the rat microcirculatory blood flow,” Acta Physiol. Scand., 163, (1).
10.
Fenton
B. M.
,
Wilson
D. W.
, and
Cokelet
G. R.
,
1985
, “
Analysis of the effects of measured white blood cell entrance times on hemodynamics in a computer model of a microvascular bed
,”
Pflu¨gers Arch.
,
403
,
396
401
.
11.
Gabet, L., 1992, “Esquisse d’une the´orie de´compositionnelle et application aux e´quations aux de´rive´es partielles,” The`se de Doctorat, Ecole Centrale, Paris.
12.
Gabet
L.
,
1994
, “
The theoretical foundation of the Adomian method
,”
Computers Math. Applic.
,
27
,
12
,
41
52
.
13.
Girard
H.
,
1973
, “
Arterial pressure in the chick embryo
,”
Am. J. Physiol.
,
224
,
454
460
.
14.
Gross, J. F., 1977, “The significance of pulsatile microhemodynamics,” in: G. Kaley and B. M. Altura, eds., Microcirculation, University Park Press, Baltimore, Vol. 1, pp. 365–390.
15.
Gross
J. F.
,
Intaglieta
M.
, and
Zweifach
B.
,
1974
, “
Network model of pulsatile hemodynamics in the microcirculation of the rabbit omentum
,”
Am. J. Physiol.
,
226
,
5
5
.
16.
Guiffant
G.
,
Roche
I.
,
Durussel
J. J.
, and
Dufaux
J.
,
1993
, “
Approche expe´rimentale et the´orique de l’e´tude des e´coulements intermittents dans la microcirculation
,” Comptes rendus de la Socie´te´ Franc¸aise de Biorhe´ologie Fondamentale et Clinique, 29;
Clinical Hemorheology
,
14
,
2
,
291
291
, 1993.
17.
Hamburger
V.
,
Hamilton
H. L.
,
1951
, “
A series of normal stages in the development of the chick embryo
,”
J. of Morphology
,
88
,
49
92
.
18.
Johnson
P. C.
, and
Wayland
H.
,
1967
, “
Oscillatory flow pattern in single mesenteric capillaries
,”
Bibl. Anat.
,
9
,
164
168
.
19.
Ley
K.
,
Pries
A. R.
, and
Gaehtgens
P.
,
1986
, “
Topological structure of rat mesenteric microvessel networks
,”
Microvasc. Res.
,
33
,
315
332
.
20.
Levasseur
J. E.
,
Funk
F. C.
, and
Patterson
J. L.
,
1969
, “
Physiological pressure transducer for microhemocirculatory studies
,”
J. Appl. Physiol.
,
27
,
422
425
.
21.
Mayhan
W. G.
,
1989
, “
Impairment of endothelium dependent dilatation of cerebral arterioles during diabetes mellitus
,”
Am. J. Physiol.
,
256
,
621
25
.
22.
Mayrovitz, H. N., Wiedeman, M. P., and Noordergraaf, A., 1978, “Interaction in the microcirculation,” in: J. Baan, A. Noordergraff, and J. Raines, eds., Cardiovascular System Dynamics, MIT Press, Cambridge, MA, pp. 194–204.
23.
Miller
V.
, and
Burnett
J. E.
,
1992
, “
Modulation of NO and endothelin by chronic increases in blood flow in canine femoral arteries
,”
Am. J. Physiol.
,
263
,
103
105
.
24.
Papenfuss
H. D.
, and
Gross
J. F.
,
1981
, “
Microhemodynamics of capillary networks
,”
Biorheology
,
18
,
673
692
.
25.
Papenfuss, H. D., and Gross, J. F., 1986, “Mathematical simulation of blood flow in microcirculatory networks,” A. S. Popel and P. C. Johnson, eds., Microvascular Networks: Experimental and Theoretical Studies, Karger, Basel, pp. 168–181.
26.
Pries
A. R.
,
Secomb
T. W.
, and
Gaehtgens
P.
,
1996
, “
Relationship between structural and hemodynamic heterogeneity in microvascular networks
,”
Am. J. Physiol.
,
270
,
H545–H553
H545–H553
.
27.
Roche, I., Guiffant, G., Durussel, J. J., and Dufaux, J., 1994, “Linear description of blood flow in microvascular networks,” Application to the study of intermittent flows. SEB Symposium “Biological fluid dynamics,” Leeds, June 4–9.
28.
Seki, J., 1994, “Flow pulsation and network structure in mesenteric microvasculature of rats,” American Physiological Society, H811.
29.
Schmid-Scho¨nbein
G. W.
,
Skalak
R.
,
Usami
S.
, and
Chien
S.
,
1980
, “
Cell distribution in capillary networks
,”
Microvasc. Res.
,
19
,
18
44
.
30.
Schmid-Scho¨nbein
G. W.
,
Usami
S.
,
Skalak
R.
, and
Chien
S.
,
1980
, “
Cell distribution in capillary networks
,”
Microvasc. Res.
,
19
,
18
44
.
31.
Schmid-Scho¨nbein
G. W.
,
Lee
S. Y.
, and
Sutton
D.
,
1989
, “
Dynamic viscous flow in distensible vessels of skeletal muscle microcirculation: application to pressure and flow transient
,”
Biorheology
,
26
,
215
227
.
32.
Shumko
J. Z.
,
Defouw
D. O.
, and
Feinberg
R. N.
,
1988
, “
Vascular histodifferentiation in the chick chorioallantoic membrane; a morphometric study
,”
The Anat. Rec.
,
220
,
179
189
.
33.
Skalak
T. C.
, and
Schmid-Scho¨nbein
G. W.
,
1986
, “
Viscoelastic properties of microvessels in rat spinotrapezius muscle
,”
ASME JOURNAL OF BIOMECHANICAL ENGINEERING
,
108
,
193
193
.
34.
Smaje
L. H.
, and
Swayne
G. T. G.
,
1984
, “
The effects of compliance on measurement of hydraulic conductivity in microvessels
,”
Biorheology
,
21
,
171
179
.
35.
Swayne
G. T. G.
, and
Smaje
L. H.
,
1984
, “
The distensibility of microvessels of the frog and rat mesentery
,”
Int. J. Microcirc. Clin. Exp.
,
3
,
355
355
.
36.
Swayne
G. T. G.
, and
Smaje
L. H.
,
1989
, “
Dynamic compliance of single perfused mesenteric capillaries and rat venules: a filtration coefficient correction
,”
Int. J. Microcirc. Clin. Exp.
,
8
,
43
52
.
37.
Warnke
K. C.
, and
Skalak
T. C.
,
1990
, “
The effects of leukocytes on blood flow in a model skeletal muscle capillary network
,”
Microvascular Research
,
40
,
118
136
.
38.
Wiegman
D. L.
,
Harris
P. D.
,
Longnecker
D. E.
, and
Miller
F. N.
,
1975
, “
Microvascular response to hypoxia, hyperoxia, hypercarbia and localised acidosis
,”
Bibl. Anat.
,
13
,
159
160
.
39.
Wieringa
P. A.
,
Spaan
J. A.
,
Stassen
H. Q.
, and
Laird
J. D.
,
1982
, “
Heterogeneous flow distribution in a three dimensional network simulation of the myocardial microcirculation. A hypothesis
,”
Microcirculation
,
2
,
195
216
.
40.
Zweifach, B. W., and Lipowski, H. H., 1984, “Pressure-flow relations in blood and lymph microcirculation,” Handbook of Physiology, Vol. 4, E. Renkin and C. C. Michel, eds., American Physiological Society, Bethesda, MD, 251–305.
This content is only available via PDF.
You do not currently have access to this content.