Abstract
Background and Aims
Experimental studies and computational modeling show increased hydration of peritoneal tissue close to peritoneal surface after intraperitoneal (ip) administration of hypertonic dialysis fluid. This overhydration - due to fluid inflow from peritoneal cavity (driven by increased intraperitoneal pressure) and from blood (due to high interstitial concentration of osmotic agent diffusing from the cavity) - may lead to tissue swelling, as observed in experiments and in disturbed physiological conditions. We estimated the degree of swelling using linear poroelastic theory with fluid and solute transport parameters obtained from clinical studies.
Method
The spatially distributed model of peritoneal transport was extended by equations for tissue deformation and stress derived from linear poroelastic theory. The model describes also fluid and osmotic agent flows across tissue and capillary wall. We assumed that transport and deformation occur across a layer of tissue with initial intact width L0 and deformed width L; the deformation is described as the ratio L/L0. Transport parameters are assumed as average values estimated for intact tissue by Stachowska-Pietka (2019). As tissue stiffness (Lame coefficient) for muscle is not known, we examined stiffness ranging from 110 mmHg (connective tissue; interstitium) to 700 mmHg (solid tumor). We assumed that for initial periods of peritoneal dialysis when osmotic pressure of dialysis fluid is high: 1) osmotic pressure gradient across the capillary wall prevails over the combined Starling forces, 2) spatial profile of osmotic agent concentration in tissue (interstitial fluid) can be approximated by exponential function with the penetration depth ΛS. The model yields an equation for L/L0 to be solved numerically, but an approximated closed formula also works well for typical dialysis conditions.
Results
The model predicts that swelling of peritoneal tissue depends on factors such as tissue stiffness, tissue width, solute penetration depth, and transport parameters for tissue and capillary wall, and on the forces that induce fluid transport: intraperitoneal pressure and the increment of osmolality of dialysis fluid over plasma osmolality. Examples of L/L0 yielded by the model - with use of glucose 1.36% dialysis fluid and for two levels of ip hydrostatic pressure (Pip) - are shown. In Figure, left panel, for L0 = 1 cm representing human abdominal muscle, and solute diffusional penetration ΛS=ΛD=0.055 cm, or lower, as due to diffusion against fluid flow, ΛS=ΛD/2=0.027 cm, is plotted versus the tissue stiffness; the dialysis fluid with glucose 1.36% is applied (osmolality increment of 60 mmol/L at the beginning of peritoneal dwell, Waniewski et al, 1996) and Pip is 15 mmHg. As stiffness of abdominal and bowel muscles may be expected around 300 mm Hg, swelling might be up to 15%; it decreases with lower ip hydrostatic and osmotic pressures. Hypothetical dialysis at Pip = 0 (isobaric with interstitial fluid) would reduce swelling by factor 2, see Figure, right panel. The depth of osmotic agent penetration into the tissue impacts tissue hydration and swelling, see Figure 1 for L/L0 with twice reduced ΛS. The model and its approximation by the closed formula provide practically the same outcomes for clinical peritoneal dialysis, see Figure 1, but some discrepancy between them may occur for thin tissue, as rat abdominal wall. The approximate formula for L/L0 works well if ΛS is much shorter than L0. Nevertheless, for high degree of swelling a nonlinear theory should be constructed.
Conclusion
In peritoneal dialysis, exposure of peritoneal tissue to hypertonic dialysis fluid at increased hydrostatic pressure contributes to overhydration and swelling (by 5-15% after fluid infusion) of the tissue. The extent by which this swelling may contribute to changes in peritoneal tissue structure and function warrants further studies.
A Mathematical Model for Transport in Poroelastic Materials with Variable Volume: Derivation, Lie Symmetry Analysis and Examples. Part 2
