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Microcirculatory hematocrit and blood flow
J. theor. Biol. (1988) 1 3 1 , 2 2 3 - 2 2 9
Microcirculatory Hematocrit and Blood Flow JOSEPH BOYLE, I11
New Jersey Medical School, 100 Bergen Street, Newark, NJ 07103, U.S.A. (Received 3 February 1987, and in revised form 18 September 1987) Direct measurements from many laboratories indicate that the oxygen tension in skeletal muscle is significantly less than in the large veins draining these tissues. Harris (1986) has proposed that because of the parallel anatomic arrangement of large arterioles and venules in skeletal muscle, a counter-current exchange between these vessels can occur. He theorized that diffusion of 02 between arteriole and venule would lower the Po~ in the blood as it enters capillaries and result in a decreased tissue Po: and an increase in large vein Po:. Calculations (Appendix) show that the amount of 02 transferred between arteriole and venule is inadequate to account for this difference in Po: between tissue and veins due to the small surface area that is involved. It is well documented that the microcirculatory hematocrit ranges between 20 and 50% of that in the supply vessels. The reduced hematocrit lowers the oxygen content in these vessels and results in a low oxygen tension in the surrounding tissue. True arteriovenous shunts are not present in most skeletal muscles, but 15-20% of the microvessels represent thoroughfare or preferential flow channels. It is suggested that these vessels contain a greater than normal hematocrit to account for a conservation of red cell mass across the microcirculation. Furthermore, it is shown that the hematocrit in the preferential flow channels is an inverse function of the flow rate for any level of the microcirculatory hematocrit. The increased hematocrit raises the flow resistance in these vessels which reduces flow further and represents a positive feedback condition which may contribute to the intermittent and uneven flow patterns which are present within the microcirculation. The increased hematocrit in the preferential flow channels serves as a means of transferring red cells with a high 02 content between arterioles and venules which raises the venous oxygen tension above that found in the tissues. This mechanism represents a more plausible explanation for the high venous oxygen tension and the low tissue oxygen tension than the counter-current diffusion hypothesis.
Overview T h e m i c r o c i r c u l a t i o n r e p r e s e n t s a critical a r e a o f the v a s c u l a r system w h i c h is c o n c e r n e d with the e x c h a n g e o f s u b s t a n c e s b e t w e e n the vessels a n d the tissue cells. A n u n d e r s t a n d i n g o f the m e c h a n i s m s i n v o l v e d in 02 d e l i v e r y to the cells is crucial since i n a d e q u a t e 02 d e l i v e r y ( h y p o x i a ) r e p r e s e n t s a c o m m o n c a u s e o f o r g a n d y s f u n c tion u n d e r m a n y c o n d i t i o n s . R e c e n t s t u d i e s u s i n g o x y g e n m i c r o e l e c t r o d e s i n d i c a t e t h a t tissue 02 t e n s i o n ( P o , ) varies f r o m m o m e n t to m o m e n t a n d is u s u a l l y m u c h l o w e r t h a n t h e P o : o f the v e n o u s b l o o d d r a i n i n g the tissue ( S u g i m o t o et al., 1984). F l o w p a t t e r n s in the m i c r o v a s c u l a t u r e are u n e v e n with large v a r i a t i o n s in the v e l o c i t y o f flow in different vessels a n d even in the s a m e vessel from o n e s e c o n d to the next. T o f u r t h e r c o m p l i c a t e the p r o b l e m o f 02 d e l i v e r y , the h e m a t o c r i t o f the m i c r o v a s c u l a t u r e has b e e n r e p o r t e d 223 0022-5193/88/060223+07 $03.00/0
© 1988 Academic Press Limited
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to vary from less than 20% to about 50% of that in the large feeder vessels in various tissues (Sarelius & Duling, 1982). A n u m b e r of theories have been proposed to explain why the venous 02 tension is higher than that in the tissues. These theories have been based on the presence of: arteriovenous shunts; a diffusion barrier across the vascular endothelium; counter-current diffusion between arteriole and venule; and a reduced capillary hematocrit. Each of these theories will be briefly discussed as to the effect on microcirculatory flow and tissue 02 tension as it applies to skeletal muscle. ARTERIOVENOUS
SHUNTS
Passage of red blood cells from arteriole to venule through arterivenous (a-v) shunts would certainly raise venous and lower tissue Po.- It is true that a-v shunts are c o m m o n in skin, mesentery and the external ear, but they occur only rarely or not at all in skeletal muscle (Klitzman & Duling, 1979) and so cannot explain the high venous 02 in this latter tissue.
DIFFUSION
BARRIER
Rose & Goresky (1985) studied 02 delivery to the canine m y o c a r d i u m by means of the multiple indicator dilution technique. Labeled red cells, 02, albumin and sodium were used to study the diffusion properties in the cardiac circulation. A high resistance to 02 diffusion was found between the red cells and the m y o c a r d i u m which may explain the low tissue Po. in this tissue. Similar studies need to be carried out on the skeletal muscle circulation before any conclusions may be drawn regarding the effect of a similar diffusion barrier in this vascular bed.
COUNTER-CURRENT
DIFFUSION
Arterioles of 60 p,m and larger and their associated venules are separated by a distance of 40-80 Ixm and have blood flow in opposite directions (counter-current). Both smaller and larger arterioles are separated by much larger distances from their associated venules which would diminish the effectiveness of diffusion. Harris (1986) has theorized that counter-current diffusion between the large arterioles and venules is the basis for a low tissue oxygen tension (15-20 mm Hg) associated with a venous Po, of about 40 mm Hg. It has been well documented that there is a longitudinal Po2 gradient along the small arteries and arterioles and the Po, in these vessels decreases to 60-80 m m Hg (Duling & Berne, 1970). Therefore, 02 does diffuse out o f the arterioles or is used to support local oxidative metabolism but this change in 02 tension only represents about a 5% change in hemoglobin saturation. The a m o u n t o f O~_ transported by counter-current diffusion was estimated by several different methods, all of which indicate that counter-current diffusion is inadequate to explain the change in oxygen tension from arteriole to vein. The method presented in the Appendix is by far the simplest and requires only estimates of arteriolar volume, diameter and diffusion
HEMATOCRIT
AND
BLOOD
FLOW
225
distance. Using this method the volume of 02 transported by counter-current diffusion is estimated to be 16 ml for the entire body. The amount of 02 which diffuses under these conditions is limited primarily by the small surface area as well as the distances which are involved. Skeletal muscle represents 40-50% of body weight, receives 30% of the cardiac output and consumes 24% of basal 02 uptake (Tenney & Lamb, 1965), thus, compared to the 02 consumed, the amount of 02 transported by counter-current diffusion is about 10%. This is an inadequate amount of 02 to raise the hemoglobin saturation from approximately 30% in the capillaries to almost 75% in the veins and obviously makes the counter-current diffusion hypothesis untenable. M ICROCI RCU LATORY H EMATOCRIT
The hematocrit of the microcirculation may reach levels of less than 20% compared to that of the supply vessels (Sarelius & Duling, 1982). Only some of the decrease in hematocrit may be apparent and this is due to a difference in velocity between red cells and plasma since the red cells move in the higher velocity axial stream of the arterioles and venules. Because of the increased axial velocity fewer red cells than expected are present in the microcirculation at any instant. This effect can only account for about 30% o f the reduction in microcirculatory hematocrit (Gaehtgens et al., 1976). One explanation for the decreased hematocrit was offered by Klitzman & Duling (1979) who calculated that a 1 txm thick layer of relatively stagnant plasma next to the endothelium could account for the total reduction in hematocrit in the microcirculation. However, it is impossible to see how this could occur in true capillaries since the red cells are slightly larger than most capillaries and completely fill the capillaries during transit. This condition, termed plug flow, would displace any stagnant plasma during passage of red cells. Thus, it seems possible that there is a real decrease in the hematocrit in most of the vessels within the microvasculature. It is obvious that if the concentration of red cells is reduced in some of the exchange vessels there will be a decreased local 02 delivery which would result in a lower tissue Po,. The apparent decrease in hematocrit due to a difference in velocity between red cells and plasma does not affect 02 delivery since the increased velocity compensates for the reduced numbers of cells that are present at any one time (Gaehtgens, 1976). However, the remaining decrease in the hematocrit needs to be considered as to its cause and effect. The reduced hematocrit is caused by plasma skimming, which results when a larger proportion of plasma enters vascular side branches due to the relatively cell-free layer present near the endothelium of the smaller arterioles. It is obvious that the red cells must go from artery to vein and the question is how do they get there if the microcirculatory hematocrit is actually reduced. Most tissues, including skeletal muscle, do not have true a-v shunts (Klitzman & Duling, 1979) but the presence o f thoroughfare or preferential flow channels (PFC) between arteriole and venule may provide the answer. Zweifach (1977) has pointed out that there are PFC through the microcirculation even in skeletal muscle since there is a much smaller a-v pressure difference between
226
J. BOYLE
a fraction of vessels (15-20%) compared to other vessels in the same vascular bed. This small pressure difference indicates low resistance and therefore high flow pathways between arteriole and vein. These PFC may change from minute to minute as vasomotion alters the resistance of the various pathways. The hematocrit in these vessels is difficult to determine because of overlapping red cells and the high velocity of flow. It appears plausible that plasma skimming lowers the hematocrit in the majority of the exchange vessels and that a greater than normal proportion of the red cells traverse the microcirculation through PFC in order to conserve red cell mass. The following analysis describes the effect of these conclusions on certain flow characteristics of the microcirculation.
Description
of the
Model
Let us assume: (1) that a significant fraction (X) of the red cells reach venules by way of PFC leaving the remaining red cells (1 - X ) to supply the major part of the vascular bed through non-preferential flow channels (NPFC); (2) that a fraction of the plasma (X + Y) is distributed to N P F C due to plasma skimming; (3) that the microcirculatory hematocrit ( [ 1 - X ] / [ X + Y]) is maintained at some level less than the hematocrit in the supply vessels by these two mechanisms; (4) that total flow to the tissues remains constant. Figure 1 shows the relationship between the percentage of total flow through the PFC and the required hematocrit in these vessels that provides the indicated hematocrit in the remainder of the microcirculation. The data were calculated by altering the fraction of red cells flowing through N P F C and determining the volume of plasma required to provide the necessary dilution of red cells. The remaining red cells and plasma are considered to flow through the PFC. From Figure 1, it is clear that as flow through the PFC decreases, there is marked rise in the PFC hematocrit. This situation represents a positive feedback since as flow decreases, the hematocrit and the viscosity of the blood I00
80
6O I.--¢.,)
-r
40
20
0
]
I
20
i
1
t
t
40 60 PFC flow (% total)
]
1
80
I
100
FIG. 1. The relationship between flow in preferential flow channels (PFC) and the hematocrit (HCT) in these vessels which is required to maintain the hematocrit in other vessels as indicated in the inset. Additional discussion in the text. [] MHCT 15; • MHCT 20; O MHCT 30.
HEMATOCRITAND
BLOOD
FLOW
227
raises the flow resistance in that pathway and lowers flow further. This phenomenon may be the cause of the abrupt cessation of flow that occurs in certain microvessels which previously had high flow rates. The proposed mechanism would contribute to alternating periods of high and low flow in various vessels of the microcirculation. These flow patterns could be influenced by local mechanisms that are dependent on the pH and the 02 and CO2 tensions of the surrounding tissues. An increase in flow rate through PFC is perhaps limited by vasoconstriction due to the higher local Po., which the high flow rate would produce, as well as a reduction in resistance in NPFC secondary to the resultant hypoxia in these vessels. Because of these effects, flow in PFC would probably oscillate somewhere around the 50% level of total flow. This conclusion is consistent with the findings of Renkin (1971) who found both slow and fast compartments in skeletal muscle, the fast compartment comprising about 50% of the tissue volume.
Discussion
A reduced microcirculatory hematocrit results in a proportional reduction of the 02 content in NPFC capillaries. Because of the low 02 content there would be a rapid decrease in the capillary Po: as 02 diffuses into the tissues. The result would be a low tissue P02 which would depend on the local flow rate and the microhematocrit. In tissues surrounding PFC the P02 would obviously be higher due to the increased flow rate and hematocrit. Thus, this concept is compatible with the variations in tissue P02 that have been found. The venous 02 content (CvO2) can be obtained from the Fick equation: CvO2 = C a O 2 - 100 x VO2/Q where CaO2 is arterial 02 content, VO2 is the tissue 02 consumption, Q is the blood flow, and CvO2 = 1 9 - 1 0 0 x 0 . 2 / 2 - 7 = 11.6 ml O2/100 ml blood. This is equivalent to a hemoglobin saturation of 58% or a PrO2 of 35 mm Hg on a standard hemoglobin dissociation curve (Altman & Dittmer, 1971). An increase in PCO2 due to tissue metabolism would increase the PO2 several mm Hg due to the Bohr effect and bring the venous Po2 close to 40 mm Hg. Figure 2 is a three-dimensional graph of tissue Po:, as a function of capillary length and intercapillary distance, obtained using a modified Krogh model (Boyle, 1986). The data utilized to obtain this plot are consistent with the concepts discussed. The calculated tissue Po: in this example ranged from 9 to 23 mm Hg while the venous Po, is 34 mm Hg. The presence of a reduced microcirculatory hematocrit and PFC in a tissue results in a functional a-v shunt for the red cells, causing a lower Po, in tissues surrounding NPFC while maintaining a higher venous Po2The increase in PFC hematocrit enhances intermittent flow in these vessels and contributes to variations in the tissue Po:. I believe that a reduced capillary hematocrit and the presence of PFC in skeletal muscle provides a much more plausible explanation for the low tissue Po: than does the counter-current diffusion theory.
228
J. B O Y L E Cap.
73
Cap
a= 80
POz
v =
0
5I
34
0
Dislonce (~m) FIG. 2. A three dimensional graph of capillary and tissue Po, plotted as a function of distance along the capillary (Length) and the intercapillary distance (Distance). The data were calculated using a modified Krogh model (Boyle, 1986) and data consistent with a microcirculatory hematocrit of 20 and a flow rate equivalent to 50% of total normal flow through preferential flow channels. REFERENCES ALTMAN, P. L. & DITTMER, D. S. (1971). Respiration and Circulation. Bethesda: FASEB BOYLE 111, J. (1986). A microcomputer program of pulmonary and tissue gas exchange. Annals t?/" Biomedical Engineering. 14, 425-435. DULING, B. R. & BERNE, R. M. (1970). Longitudinal gradients in periarteriolar oxygen tension. Circ. Res. 27, 669-678. GAEHTGENS, P., BENNER, K. U., S(_'KI('KENDANTZ,S. & ALBRECHT, K. H. (1976). Method for simultaneous determination of red cell and plasma flow velocity in vitro and in t~ivo..tffTugers Arch. 361, 191-195. HARRIS, P. D. (1986). Movement of oxygen in skeletal muscle. NIPS. 1:147-149. KLITZMAN, B. & DULING, B. R. (1979). Microvascular hematocrit and red cell flow in resting and contracting striated muscle. Am. J. Physiol. 234 (Heart Circ. Physiol. 6), H481-H490. RENKIN, E. M. (1971). Nutritional-shunt flow hypothesis in skeletal muscle circulation. Circ. Res. 28 (Suppl. 1), 21-25. RosE, C. P. & GORESKY, C. A. (1985). Limitations of tracer oxygen uptake in the canine coronary circulation. Circ'. Res. 56, 57-71. SARELIUS, I. H. & DULING, B. R. (1982). Direct measurement of microvessel hematocrit, red cell flux, velocity, and transit time. Am. J. Physiol. 243 (Heart Circ. Physiol. 12), H I018-H 1026. SUGIMOTO, H., OHASHI, N., SAWADA, Y. YOSHIKA, T. & SUGIMOTO, T. (1984). Effects of positive end-expiratory pressure on tissue gas tensions and oxygen transport. Critical Care Med. 12, 661-663. TENNEY, S. M. & LAMB, T. W. (1965). Physiological consequences of Hyperventilation and Hypoventilation. In: Handbook of Physiology. Section 3. Respiration Physiology, Vol. 2, (Fenn, W. O. & Rahn, H. eds). Washington, DC: American Physiological Society. ZWEIFA('H, B. W. (1977). Perspectives in Microcirculation in Microcirculation, vol. 1. ( Kaley, G. & Altura, B. M. eds) Baltimore: University Park Press. APPENDIX
Calculation of Counter-current 02 Diffusion U t i l i z i n g t h e F i c k d i f f u s i o n e q u a t i o n a n d c a l c u l a t i n g t h e v o l u m e o f O~ t r a n s p o r t e d b y c o u n t e r - c u r r e n t d i f f u s i o n ( 3 0 : ) in t h e b o d y :
Jo,=
K dPA/d
HEMATOCRIT
AND
BLOOD
FLOW
229
where: K = K r o g h diffusion constant = 2.1 x 10 -s d P = difference in O2 tension between arteriole and venule (atrn) = 5.3 x 10 -2 d = distance between arteriole and venule A = surface area. Considering the arterioles to be cylindrical, A = "rrDLN D = arteriolar diameter L = arteriolar length N = n u m b e r o f arterioles L can be defined in terms o f the arteriolar v o l u m e ( V):
L = V/(Tr(D/2)ZN) Substituting for L gives: A = ~4DVN/(TrD2N) =4V/D,
Jo, = K dP 4V/(dD).
The average "large arteriole" is taken to have a diameter of 100 l~m with a separation between arteriole and venule of 40-80 p,m (Harris, 1986). The volume of blood in arterioles of this size is estimated to be 3 - 4 % of total blood volume or 220 ml in a normal human. Thus, Jo~ =
2.1x 10-5x5.3 x 1 0 - 2 x 4 x 2 2 0 0.006 x 0.01 -
16 ml O2/min for the entire body. The estimated amount of 02 transferred by counter-current diffusion represents only 6% of 02 consumption and less than 3% o f the 02 delivered to the b o d y tissues per minute. This amount ofO2 is much less than that required to raise the hemoglobin saturation from 30% (equivalent to a Po, of 20 m m Hg) in the capillaries to 75% (equivalent to a Po: of 40 m m Hg) in the veins as proposed by Harris (1986). The conclusion is that some mechanism other than counter-current diffusion must be involved in raising the venous Po, from the value found in most tissue capillaries.
Microcirculatory Hematocrit and Blood Flow JOSEPH BOYLE, I11
New Jersey Medical School, 100 Bergen Street, Newark, NJ 07103, U.S.A. (Received 3 February 1987, and in revised form 18 September 1987) Direct measurements from many laboratories indicate that the oxygen tension in skeletal muscle is significantly less than in the large veins draining these tissues. Harris (1986) has proposed that because of the parallel anatomic arrangement of large arterioles and venules in skeletal muscle, a counter-current exchange between these vessels can occur. He theorized that diffusion of 02 between arteriole and venule would lower the Po~ in the blood as it enters capillaries and result in a decreased tissue Po: and an increase in large vein Po:. Calculations (Appendix) show that the amount of 02 transferred between arteriole and venule is inadequate to account for this difference in Po: between tissue and veins due to the small surface area that is involved. It is well documented that the microcirculatory hematocrit ranges between 20 and 50% of that in the supply vessels. The reduced hematocrit lowers the oxygen content in these vessels and results in a low oxygen tension in the surrounding tissue. True arteriovenous shunts are not present in most skeletal muscles, but 15-20% of the microvessels represent thoroughfare or preferential flow channels. It is suggested that these vessels contain a greater than normal hematocrit to account for a conservation of red cell mass across the microcirculation. Furthermore, it is shown that the hematocrit in the preferential flow channels is an inverse function of the flow rate for any level of the microcirculatory hematocrit. The increased hematocrit raises the flow resistance in these vessels which reduces flow further and represents a positive feedback condition which may contribute to the intermittent and uneven flow patterns which are present within the microcirculation. The increased hematocrit in the preferential flow channels serves as a means of transferring red cells with a high 02 content between arterioles and venules which raises the venous oxygen tension above that found in the tissues. This mechanism represents a more plausible explanation for the high venous oxygen tension and the low tissue oxygen tension than the counter-current diffusion hypothesis.
Overview T h e m i c r o c i r c u l a t i o n r e p r e s e n t s a critical a r e a o f the v a s c u l a r system w h i c h is c o n c e r n e d with the e x c h a n g e o f s u b s t a n c e s b e t w e e n the vessels a n d the tissue cells. A n u n d e r s t a n d i n g o f the m e c h a n i s m s i n v o l v e d in 02 d e l i v e r y to the cells is crucial since i n a d e q u a t e 02 d e l i v e r y ( h y p o x i a ) r e p r e s e n t s a c o m m o n c a u s e o f o r g a n d y s f u n c tion u n d e r m a n y c o n d i t i o n s . R e c e n t s t u d i e s u s i n g o x y g e n m i c r o e l e c t r o d e s i n d i c a t e t h a t tissue 02 t e n s i o n ( P o , ) varies f r o m m o m e n t to m o m e n t a n d is u s u a l l y m u c h l o w e r t h a n t h e P o : o f the v e n o u s b l o o d d r a i n i n g the tissue ( S u g i m o t o et al., 1984). F l o w p a t t e r n s in the m i c r o v a s c u l a t u r e are u n e v e n with large v a r i a t i o n s in the v e l o c i t y o f flow in different vessels a n d even in the s a m e vessel from o n e s e c o n d to the next. T o f u r t h e r c o m p l i c a t e the p r o b l e m o f 02 d e l i v e r y , the h e m a t o c r i t o f the m i c r o v a s c u l a t u r e has b e e n r e p o r t e d 223 0022-5193/88/060223+07 $03.00/0
© 1988 Academic Press Limited
224
J. BOYLE
to vary from less than 20% to about 50% of that in the large feeder vessels in various tissues (Sarelius & Duling, 1982). A n u m b e r of theories have been proposed to explain why the venous 02 tension is higher than that in the tissues. These theories have been based on the presence of: arteriovenous shunts; a diffusion barrier across the vascular endothelium; counter-current diffusion between arteriole and venule; and a reduced capillary hematocrit. Each of these theories will be briefly discussed as to the effect on microcirculatory flow and tissue 02 tension as it applies to skeletal muscle. ARTERIOVENOUS
SHUNTS
Passage of red blood cells from arteriole to venule through arterivenous (a-v) shunts would certainly raise venous and lower tissue Po.- It is true that a-v shunts are c o m m o n in skin, mesentery and the external ear, but they occur only rarely or not at all in skeletal muscle (Klitzman & Duling, 1979) and so cannot explain the high venous 02 in this latter tissue.
DIFFUSION
BARRIER
Rose & Goresky (1985) studied 02 delivery to the canine m y o c a r d i u m by means of the multiple indicator dilution technique. Labeled red cells, 02, albumin and sodium were used to study the diffusion properties in the cardiac circulation. A high resistance to 02 diffusion was found between the red cells and the m y o c a r d i u m which may explain the low tissue Po. in this tissue. Similar studies need to be carried out on the skeletal muscle circulation before any conclusions may be drawn regarding the effect of a similar diffusion barrier in this vascular bed.
COUNTER-CURRENT
DIFFUSION
Arterioles of 60 p,m and larger and their associated venules are separated by a distance of 40-80 Ixm and have blood flow in opposite directions (counter-current). Both smaller and larger arterioles are separated by much larger distances from their associated venules which would diminish the effectiveness of diffusion. Harris (1986) has theorized that counter-current diffusion between the large arterioles and venules is the basis for a low tissue oxygen tension (15-20 mm Hg) associated with a venous Po, of about 40 mm Hg. It has been well documented that there is a longitudinal Po2 gradient along the small arteries and arterioles and the Po, in these vessels decreases to 60-80 m m Hg (Duling & Berne, 1970). Therefore, 02 does diffuse out o f the arterioles or is used to support local oxidative metabolism but this change in 02 tension only represents about a 5% change in hemoglobin saturation. The a m o u n t o f O~_ transported by counter-current diffusion was estimated by several different methods, all of which indicate that counter-current diffusion is inadequate to explain the change in oxygen tension from arteriole to vein. The method presented in the Appendix is by far the simplest and requires only estimates of arteriolar volume, diameter and diffusion
HEMATOCRIT
AND
BLOOD
FLOW
225
distance. Using this method the volume of 02 transported by counter-current diffusion is estimated to be 16 ml for the entire body. The amount of 02 which diffuses under these conditions is limited primarily by the small surface area as well as the distances which are involved. Skeletal muscle represents 40-50% of body weight, receives 30% of the cardiac output and consumes 24% of basal 02 uptake (Tenney & Lamb, 1965), thus, compared to the 02 consumed, the amount of 02 transported by counter-current diffusion is about 10%. This is an inadequate amount of 02 to raise the hemoglobin saturation from approximately 30% in the capillaries to almost 75% in the veins and obviously makes the counter-current diffusion hypothesis untenable. M ICROCI RCU LATORY H EMATOCRIT
The hematocrit of the microcirculation may reach levels of less than 20% compared to that of the supply vessels (Sarelius & Duling, 1982). Only some of the decrease in hematocrit may be apparent and this is due to a difference in velocity between red cells and plasma since the red cells move in the higher velocity axial stream of the arterioles and venules. Because of the increased axial velocity fewer red cells than expected are present in the microcirculation at any instant. This effect can only account for about 30% o f the reduction in microcirculatory hematocrit (Gaehtgens et al., 1976). One explanation for the decreased hematocrit was offered by Klitzman & Duling (1979) who calculated that a 1 txm thick layer of relatively stagnant plasma next to the endothelium could account for the total reduction in hematocrit in the microcirculation. However, it is impossible to see how this could occur in true capillaries since the red cells are slightly larger than most capillaries and completely fill the capillaries during transit. This condition, termed plug flow, would displace any stagnant plasma during passage of red cells. Thus, it seems possible that there is a real decrease in the hematocrit in most of the vessels within the microvasculature. It is obvious that if the concentration of red cells is reduced in some of the exchange vessels there will be a decreased local 02 delivery which would result in a lower tissue Po,. The apparent decrease in hematocrit due to a difference in velocity between red cells and plasma does not affect 02 delivery since the increased velocity compensates for the reduced numbers of cells that are present at any one time (Gaehtgens, 1976). However, the remaining decrease in the hematocrit needs to be considered as to its cause and effect. The reduced hematocrit is caused by plasma skimming, which results when a larger proportion of plasma enters vascular side branches due to the relatively cell-free layer present near the endothelium of the smaller arterioles. It is obvious that the red cells must go from artery to vein and the question is how do they get there if the microcirculatory hematocrit is actually reduced. Most tissues, including skeletal muscle, do not have true a-v shunts (Klitzman & Duling, 1979) but the presence o f thoroughfare or preferential flow channels (PFC) between arteriole and venule may provide the answer. Zweifach (1977) has pointed out that there are PFC through the microcirculation even in skeletal muscle since there is a much smaller a-v pressure difference between
226
J. BOYLE
a fraction of vessels (15-20%) compared to other vessels in the same vascular bed. This small pressure difference indicates low resistance and therefore high flow pathways between arteriole and vein. These PFC may change from minute to minute as vasomotion alters the resistance of the various pathways. The hematocrit in these vessels is difficult to determine because of overlapping red cells and the high velocity of flow. It appears plausible that plasma skimming lowers the hematocrit in the majority of the exchange vessels and that a greater than normal proportion of the red cells traverse the microcirculation through PFC in order to conserve red cell mass. The following analysis describes the effect of these conclusions on certain flow characteristics of the microcirculation.
Description
of the
Model
Let us assume: (1) that a significant fraction (X) of the red cells reach venules by way of PFC leaving the remaining red cells (1 - X ) to supply the major part of the vascular bed through non-preferential flow channels (NPFC); (2) that a fraction of the plasma (X + Y) is distributed to N P F C due to plasma skimming; (3) that the microcirculatory hematocrit ( [ 1 - X ] / [ X + Y]) is maintained at some level less than the hematocrit in the supply vessels by these two mechanisms; (4) that total flow to the tissues remains constant. Figure 1 shows the relationship between the percentage of total flow through the PFC and the required hematocrit in these vessels that provides the indicated hematocrit in the remainder of the microcirculation. The data were calculated by altering the fraction of red cells flowing through N P F C and determining the volume of plasma required to provide the necessary dilution of red cells. The remaining red cells and plasma are considered to flow through the PFC. From Figure 1, it is clear that as flow through the PFC decreases, there is marked rise in the PFC hematocrit. This situation represents a positive feedback since as flow decreases, the hematocrit and the viscosity of the blood I00
80
6O I.--¢.,)
-r
40
20
0
]
I
20
i
1
t
t
40 60 PFC flow (% total)
]
1
80
I
100
FIG. 1. The relationship between flow in preferential flow channels (PFC) and the hematocrit (HCT) in these vessels which is required to maintain the hematocrit in other vessels as indicated in the inset. Additional discussion in the text. [] MHCT 15; • MHCT 20; O MHCT 30.
HEMATOCRITAND
BLOOD
FLOW
227
raises the flow resistance in that pathway and lowers flow further. This phenomenon may be the cause of the abrupt cessation of flow that occurs in certain microvessels which previously had high flow rates. The proposed mechanism would contribute to alternating periods of high and low flow in various vessels of the microcirculation. These flow patterns could be influenced by local mechanisms that are dependent on the pH and the 02 and CO2 tensions of the surrounding tissues. An increase in flow rate through PFC is perhaps limited by vasoconstriction due to the higher local Po., which the high flow rate would produce, as well as a reduction in resistance in NPFC secondary to the resultant hypoxia in these vessels. Because of these effects, flow in PFC would probably oscillate somewhere around the 50% level of total flow. This conclusion is consistent with the findings of Renkin (1971) who found both slow and fast compartments in skeletal muscle, the fast compartment comprising about 50% of the tissue volume.
Discussion
A reduced microcirculatory hematocrit results in a proportional reduction of the 02 content in NPFC capillaries. Because of the low 02 content there would be a rapid decrease in the capillary Po: as 02 diffuses into the tissues. The result would be a low tissue P02 which would depend on the local flow rate and the microhematocrit. In tissues surrounding PFC the P02 would obviously be higher due to the increased flow rate and hematocrit. Thus, this concept is compatible with the variations in tissue P02 that have been found. The venous 02 content (CvO2) can be obtained from the Fick equation: CvO2 = C a O 2 - 100 x VO2/Q where CaO2 is arterial 02 content, VO2 is the tissue 02 consumption, Q is the blood flow, and CvO2 = 1 9 - 1 0 0 x 0 . 2 / 2 - 7 = 11.6 ml O2/100 ml blood. This is equivalent to a hemoglobin saturation of 58% or a PrO2 of 35 mm Hg on a standard hemoglobin dissociation curve (Altman & Dittmer, 1971). An increase in PCO2 due to tissue metabolism would increase the PO2 several mm Hg due to the Bohr effect and bring the venous Po2 close to 40 mm Hg. Figure 2 is a three-dimensional graph of tissue Po:, as a function of capillary length and intercapillary distance, obtained using a modified Krogh model (Boyle, 1986). The data utilized to obtain this plot are consistent with the concepts discussed. The calculated tissue Po: in this example ranged from 9 to 23 mm Hg while the venous Po, is 34 mm Hg. The presence of a reduced microcirculatory hematocrit and PFC in a tissue results in a functional a-v shunt for the red cells, causing a lower Po, in tissues surrounding NPFC while maintaining a higher venous Po2The increase in PFC hematocrit enhances intermittent flow in these vessels and contributes to variations in the tissue Po:. I believe that a reduced capillary hematocrit and the presence of PFC in skeletal muscle provides a much more plausible explanation for the low tissue Po: than does the counter-current diffusion theory.
228
J. B O Y L E Cap.
73
Cap
a= 80
POz
v =
0
5I
34
0
Dislonce (~m) FIG. 2. A three dimensional graph of capillary and tissue Po, plotted as a function of distance along the capillary (Length) and the intercapillary distance (Distance). The data were calculated using a modified Krogh model (Boyle, 1986) and data consistent with a microcirculatory hematocrit of 20 and a flow rate equivalent to 50% of total normal flow through preferential flow channels. REFERENCES ALTMAN, P. L. & DITTMER, D. S. (1971). Respiration and Circulation. Bethesda: FASEB BOYLE 111, J. (1986). A microcomputer program of pulmonary and tissue gas exchange. Annals t?/" Biomedical Engineering. 14, 425-435. DULING, B. R. & BERNE, R. M. (1970). Longitudinal gradients in periarteriolar oxygen tension. Circ. Res. 27, 669-678. GAEHTGENS, P., BENNER, K. U., S(_'KI('KENDANTZ,S. & ALBRECHT, K. H. (1976). Method for simultaneous determination of red cell and plasma flow velocity in vitro and in t~ivo..tffTugers Arch. 361, 191-195. HARRIS, P. D. (1986). Movement of oxygen in skeletal muscle. NIPS. 1:147-149. KLITZMAN, B. & DULING, B. R. (1979). Microvascular hematocrit and red cell flow in resting and contracting striated muscle. Am. J. Physiol. 234 (Heart Circ. Physiol. 6), H481-H490. RENKIN, E. M. (1971). Nutritional-shunt flow hypothesis in skeletal muscle circulation. Circ. Res. 28 (Suppl. 1), 21-25. RosE, C. P. & GORESKY, C. A. (1985). Limitations of tracer oxygen uptake in the canine coronary circulation. Circ'. Res. 56, 57-71. SARELIUS, I. H. & DULING, B. R. (1982). Direct measurement of microvessel hematocrit, red cell flux, velocity, and transit time. Am. J. Physiol. 243 (Heart Circ. Physiol. 12), H I018-H 1026. SUGIMOTO, H., OHASHI, N., SAWADA, Y. YOSHIKA, T. & SUGIMOTO, T. (1984). Effects of positive end-expiratory pressure on tissue gas tensions and oxygen transport. Critical Care Med. 12, 661-663. TENNEY, S. M. & LAMB, T. W. (1965). Physiological consequences of Hyperventilation and Hypoventilation. In: Handbook of Physiology. Section 3. Respiration Physiology, Vol. 2, (Fenn, W. O. & Rahn, H. eds). Washington, DC: American Physiological Society. ZWEIFA('H, B. W. (1977). Perspectives in Microcirculation in Microcirculation, vol. 1. ( Kaley, G. & Altura, B. M. eds) Baltimore: University Park Press. APPENDIX
Calculation of Counter-current 02 Diffusion U t i l i z i n g t h e F i c k d i f f u s i o n e q u a t i o n a n d c a l c u l a t i n g t h e v o l u m e o f O~ t r a n s p o r t e d b y c o u n t e r - c u r r e n t d i f f u s i o n ( 3 0 : ) in t h e b o d y :
Jo,=
K dPA/d
HEMATOCRIT
AND
BLOOD
FLOW
229
where: K = K r o g h diffusion constant = 2.1 x 10 -s d P = difference in O2 tension between arteriole and venule (atrn) = 5.3 x 10 -2 d = distance between arteriole and venule A = surface area. Considering the arterioles to be cylindrical, A = "rrDLN D = arteriolar diameter L = arteriolar length N = n u m b e r o f arterioles L can be defined in terms o f the arteriolar v o l u m e ( V):
L = V/(Tr(D/2)ZN) Substituting for L gives: A = ~4DVN/(TrD2N) =4V/D,
Jo, = K dP 4V/(dD).
The average "large arteriole" is taken to have a diameter of 100 l~m with a separation between arteriole and venule of 40-80 p,m (Harris, 1986). The volume of blood in arterioles of this size is estimated to be 3 - 4 % of total blood volume or 220 ml in a normal human. Thus, Jo~ =
2.1x 10-5x5.3 x 1 0 - 2 x 4 x 2 2 0 0.006 x 0.01 -
16 ml O2/min for the entire body. The estimated amount of 02 transferred by counter-current diffusion represents only 6% of 02 consumption and less than 3% o f the 02 delivered to the b o d y tissues per minute. This amount ofO2 is much less than that required to raise the hemoglobin saturation from 30% (equivalent to a Po, of 20 m m Hg) in the capillaries to 75% (equivalent to a Po: of 40 m m Hg) in the veins as proposed by Harris (1986). The conclusion is that some mechanism other than counter-current diffusion must be involved in raising the venous Po, from the value found in most tissue capillaries.