Fetal capillary

Figure 16.1 Illustration of the anatomical arrangement of the syncytiotrophoblast (placental barrier) and the fetal capillaries as would appear in a cross section of a human placental villus. Reprinted from Audus [10] with permission from Elsevier B.V.

The CO diffusing capacity, DPco, of sheep was measured at various 02 tensions in a hyperbaric chamber using a method similar to that outlined above (12). DPco varied as a function of the oxygen tension. In Figure 2 the reciprocal of DPco is plotted as a function of the reciprocal of the diffusing capacity of the maternal and fetal red blood cells. From the plot the slope is the reciprocal of the value of V, the maternal and fetal capillary blood volume while the intercept is the reciprocal of Dmco- From these studies we calculated that the resistance of maternal and fetal red blood cells was approximately one-third of the total resistance while the resistance of the placental membrane per se was about two-thirds of the total resistance to 02 diffusion (12). This is in contrast to previous studies which assumed that the placental membrane per se constituted the total resistance to diffusion. 

Hg) at time t on the maternal and fetal sides, Vm and Vf are the maternal and fetal capillary blood volumes (ml) and Dp is the placental diffusing capacity for 02 [ml/(min X mm Hg)]. While these equations ignore placental tissue oxygen consumption, this will be considered later. 

Discussion of Assumptions of the Model. The pattern of maternal to fetal placental flow affects the amount of 02 transferred. It seems unlikely that the simple concurrent system shown in Figure 3 accurately represents the placental capillaries in sheep, a species in which the exchange vessels interdigitate in a nonuniform and complex manner (30, 31). The flow patterns are also complicated in humans where maternal blood enters the intervillous spaces from the base and flows upward and outward past fetal capillary loops in placental villi. Physiological studies also fail to reveal a simple geometric flow pattern. For... 

Uneven Maternal and Fetal Capillary Transit Times. The standard values chosen for maternal and fetal blood flow rates are equal. In studying effects of variations of one of the flow rates (15), the maternal and fetal capillary transit times become unequal, and the time steps of the integration, At, do not correspond to the same distance along the capillary on each side. To prevent the integration from getting out of step (diffusion not occurring perpendicular to the membrane), Equation 5 must be modified (14) to ... 

Guilbeau et al. (34) predicted a similar pattern resulting from a reduced fetal flow rate in their model but obtained lower absolute values of po2- They also pointed out the rise in fetal po2 at slow flow rates could be attributed to less hemoglobin within the fetal capillaries per unit of time. 

Figure 3. Fetal capillary-tissue-maternal bloody cylindrical arrangement Mathematical Analysis...

The terminal villi are assumed to contain only one fetal capillary. Shunts or alternate paths for the passage of fetal blood through the terminal villi are neglected. 

The assumption that only one fetal capillary is contained within a terminal villus is contrary to the known anatomy of the placenta. In-flow and out-flow of fetal blood in the villus is not a matter of parallel one-way streets. Shunts and alternate paths are provided for and called into play, especially when the normal, physiological aging process causes deposition of fibrin in and around individual villi, thereby removing them from function (10, 24). The effects of this assumption are possibly minimized by the method used in obtaining the standard length of the exchange unit (19, 25). 

Divisions of Analysis. The preceding model describes conditions within a single fetal capillary surrounded by a thin tissue cylinder and supplied by a cylindrical annulus of maternal blood, as shown in Figure 3. Since the numerical techniques required for the solution of such equations were not well defined, the determination of a steady-state concurrent solution was first obtained. Based upon the results of this work, an unsteady-state concurrent solution was assumed possible and feasible. 

For the Case 3 solution which included axial dispersion but neglected tissue effects, the mathematical equations reduced to the following Fetal capillary equation ... 

Equation (11) represents steady-state conditions within the maternal intervillous channel and is a nonlinear, partial difference equation with two independent variables. Since the dP/dr = 0 when r = R2> a special equation was also required at this position. The same techniques were used as in the fetal capillary equation. 

Figure 5. Axial partial pressure profiles in the fetal capillary for various maternal to fetal volumetric flow rate ratios. Maternal volumetric flow rate...

Figure 8 shows the effects on the fetal blood axial oxygen partial pressure profile when the maternal blood flow rate is decreased. As the maternal blood flow rate decreases, the fetal profile is shifted downward, resulting in fetal blood oxygen partial pressure values in the fetal capillary that are lower than normal. 

However, since the total quantity (not percent) transferred to fetal blood is less, the oxygen partial pressure within the fetal capillary decreases as shown in Figure 8. This analysis was confirmed by additional calculations which determined the total quantity of oxygen transported. 

The fetal blood oxygen partial pressure values in the first half of the fetal capillary increase more rapidly than those in the second half. This results from the large pressure gradient initially present between maternal and fetal streams rather than the slope of the dissociation curve. As the last half of the exchange system is reached, maternal and fetal values approach each other, the gradient is decreased, and the rate of oxygen transfer decreases. 

Similarly, the fetal capillary equation may be rearranged to give,... 

In the fetal capillary it is not so easy to predict what the effects of axial dispersion will be. The direction of axial diffusion in the fetal channel is opposite to the direction of flow, namely from the exit of the channel toward the entrance. This should have the effect of reducing the oxygen concentration of fetal blood at the fetal capillary exit. Axial diffusion, if any, in the maternal channel, however, should increase the concentration of oxygen leaving the maternal channel. This would result in an increased radial oxygen concentration gradient between maternal and fetal blood at the exit of the system which would act to increase... 

Partial pressure of oxygen calculated from the space average fractional saturation of blood, torr Radius of fetal capillary, cm Radius of maternal channel, cm Radius of tissue cylinder, cm Dimensionless radial distance Variable radius, cm Time, sec... 

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