Mechanisms underlying the volume regulation of interstitial fluid by capillaries: a simulation study

Abstract

Background: Control of the extracellular fluid volume is one of the most indispensable issues for homeostasis of the internal milieu. However, complex interdependence of the pressures involved in determination of fluid exchange makes it difficult to predict a steady-state tissue volume under various physiological conditions without mathematical approaches.

Methods: Here, we developed a capillary model based on the Starling's principle, which allowed us to clarify the mechanisms of the interstitial-fluid volume regulation. Three well known safety factors against edema: (1) low tissue compliance in negative pressure ranges; (2) lymphatic flow driven by the tissue pressure; and (3) protein washout by the lymph, were incorporated into the model in sequence.

Results: An increase in blood pressure at the venous end of the capillary induced an interstitial-fluid volume increase, which, in turn, reduced negative tissue pressure to prevent edema. The lymphatic flow alleviated the edema by both carrying fluid away from the tissue and decreasing the colloidal osmotic pressure. From the model incorporating all three factors, we found that the interstitial-fluid volume changed quickly after the blood pressure change, and that the protein movement towards a certain equilibrium point followed the volume change.

Conclusion: Mathematical analyses revealed that the system of the capillary is stable near the equilibrium point at steady state and normal physiological capillary pressure. The time course of the tissue-volume change was determined by two kinetic mechanisms: rapid fluid exchange and slow protein fluxes.

Keywords: capillary; fluid exchange; interstitial fluid; volume regulation.

Fig. 1

Schematic representation of a single capillary. (A) Effective filtration pressure along the capillary. (B, C) Compartmentalization of a single capillary model and interstitial fluid facing to the capillary. Lymph drains from the interstitial space.

Fig. 2

Nonlinear relationship used in models. (A) Relationship between V_isf and P_isf introduced in Models 2–4. (B) Relationship between P_isf and relative lymph flow introduced in Models 3 and 4.

Fig. 3

Implementation of protein dynamics into Model 4. (A) Cross-section of capillary membrane showing transmembrane protein transport. (B) Relationship between protein concentration and colloidal osmotic pressure. An equation (pink) was fitted to a curve from a textbook (blue).

Fig. 4

(A) V_isf, V_isf,L, and Π_isf change and (B) pressure-balance diagram in Model 1 in experiment changing P_pl,v.

Fig. 5

(A) V_isf, V_isf,L, P_isf, and Π_isf change and (B) pressure-balance diagram in Model 2 in experiment changing P_plv.

Fig. 6

(A) V_isf, V_isf,L, P_isf, and Π_isf change and (B) pressure-balance diagram in Model 3 in experiment changing P_pl,v.

Fig. 7

(A) V_isf, V_isf,L, Q_isf, P_isf, and Π_isf change and (B) pressure-balance diagram in Model 4 in experiment changing P_pl,v.

Fig. 8

(A) V_isf, V_isf,L, Q_isf, Q_isf,L, P_isf, and Π_isf change and (B) pressure-balance diagram in Model 4 in lymphatic obstruction experiment.

Fig. 9

(A) Phase-plane diagram in steady state at $P_{pl,v}=15$ mmHg and (B, C) instantaneous equilibrium point for $J_v$ and J_q. Arrows in A and B represent the trajectories for V_isf and Q_isf. $J_v$ and J_q were multiplied by 3.0 × 10³ and 6.0 × 10⁴, respectively, to visualize vectors in the diagram in A. Red and blue circles in A, Ba, and Bb indicate V_isf and Q_isf values obtained when $P_{pl,v}$ was switched back to 15 mmHg from 17 mmHg and 13 mmHg, respectively. Green circles in panels A, Ba, and Bb indicate values obtained at steady state at $P_{pl,v}=15$ mmHg. Red, green, and blue squares indicate equilibrium points, to which the circles with corresponding colours tended to approach at a given time.