Flow-limited Exchange model

Rapid exchange of solutes between the vascular and the extravascular space in a whole organ.

The liver sinusoids are lined by fenestrated endothelial cells.

The fenestrae are openings in the endothelial cells with a diameter of about 100 nm, much smaller than the diameter of an erythrocyte (ca. 7 µm). Therefore, erythrocytes do not cross the endothelium, they move along the sinusoids with the velocity of blood:

Indicators such as albumin or sucrose are distributed almost instantaneously between the sinusoidal lumen and the space of Disse. Their movement through the liver sinusoids is characterized by the delayed wave principle, as depicted in the following animation:

The average velocity of these tracers along the liver sinusoids is much less than that of the bulk fluid. This leads to a separation of these tracers from albumin in a similar way as in a chromatographic column.

1. Flow is confined to the vascular compartment.
2. Diffusional equilibration in the lateral direction is rapid.
3. Diffusional transport in the longitudinal direction is negligible.

An amount of label q₀ introduced instantaneously at the origin of a sinusoid is carried along by the sinusoidal flow F_s with the velocity v_F

The outflow tracer concentration for the vascular reference, (labeled red cells) at the outflow from a sinusoid of length L, at time t, is then

where δ stands for a Dirac (impulse) function.

The red cell propagates along the length as a traveling wave and emerges at the time L/v_F.

For a diffusible substance equilibrating within its extravascular space at each point along the length, the expected outflow profile will be

where γ is the ratio of its extravascular to its vascular spaces of distribution along the sinusoid. The diffusible tracer flows along the sinusoid with the velocity v_F/(1+γ) which is slower than that of the vascular reference.

The relation between the outflow curves from the whole liver for labeled red cells and for each of the diffusible interstitial substances will depend on the relation between the transit times of the large vessels and those of the sinusoids For the liver, it is assumed as a first approximation that large vessel transit times are uniform such that the flow heterogeneity is a reflexion of the flow heterogeneity among the sinusoids.

The relation between the outflow curves for each of the diffusible substances and the vascular reference, is described by the equation,

where t₀ is the common large vessel transit time.

The following tracers were injected into the portal vein of an anesthetized dog:

• Erythrocytes (Ery) labeled with ⁵¹Cr
• Albumin (Alb) labeled with Evans blue
• Sucrose (Suc) labeled with ¹⁴C
• Sodium (²²Na)
• Water (³OH¹H)

Samples from a hepatic vein were analyzed for gamma radioactivity, and the various isotopes where distinguished by gamma spectrometry.

Download the JSim project file.

Click on the title to access the abstract or the full text.

Goresky, CA. A linear method for determining liver sinusoidal and extravascular volumes. Am J Physiol 204: 626-640, 1963.

Key Terms: indicator dilution, flow-limited exchange, liver, transport, vascular volume, organ, Disse space, sinusoid, hepatocyte

JSim Tutorial

Andreas J. Schwab andreas.schwab@mcgill.ca

Back to Introduction