Joanna Stachowska-Pietka

Computational models of peritoneal dialysis (PD) are increasingly useful for optimizing treatment in patients with kidney disease requiring dialysis (KDRD). However, although several mathematical models have been developed in the past few decades, a direct comparison of the models’ accuracy with respect to predicting in vivo data is needed to further create robust personalized models. Here, we used a dataset obtained in a previous in vivo experimental model of PD in pigs (23 sessions of 4 h 2 L dwells in four pigs) and humans (20 sessions in 20 patients) to compare six computational models of PD: the Graff model (UGM), the three-pore model (TPM), the Garred model (GM), and the Waniewski model (WM), as well as two variations of these (UGM-18, SWM). We conducted this comparison to predict the dialysate concentrations of key uremic toxins and electrolytes (four in humans) throughout a 4 h dwell. The model predictions can provide insight into inter-individual differences in ultrafiltration, which are critical for tailoring PD regimens in KDRD. While TPM offered improved physiological reality, its computational cost suggests a trade-off between model complexity and clinical applicability for real-time or portable kidney support systems. In future applications, such models could provide adaptive PD regimens for tailored care based on patient-specific toxin kinetics and fluid dynamics.

In peritoneal dialysis, ultrafiltration is achieved by adding an osmotic agent into the dialysis fluid. During an exchange with icodextrin-based solution, polysaccharide chains are degraded by α-amylase activity in dialysate, influencing its osmotic properties. We modelled water and solute removal taking into account degradation by α-amylase and absorption of icodextrin from the peritoneal cavity. Data from 16 h dwells with icodextrin-based solution in 11 patients (3 icodextrin-exposed, 8 icodextrin-naïve at the start of the study) on dialysate volume, dialysate concentrations of glucose, urea, creatinine and α-amylase, and dialysate and blood concentrations of seven molecular weight fractions of icodextrin were analysed. The three-pore model was extended to describe hydrolysis of icodextrin by α-amylase. The extended model accurately predicted kinetics of ultrafiltration, small solutes and icodextrin fractions in dialysate, indicating differences in degradation kinetics between icodextrin-naïve and icodextrin-exposed patients. In addition, the model provided information on the patterns of icodextrin degradation caused by α-amylase. Modelling of icodextrin kinetics using an extended three-pore model that takes into account absorption of icodextrin and changes in α-amylase activity in the dialysate provided accurate description of peritoneal transport and information on patterns of icodextrin hydrolysis during long icodextrin dwells.

In peritoneal dialysis, ultrafiltration is achieved by adding an osmotic agent into the dialysis fluid. During an exchange with icodextrin-based solution, polysaccharide chains are degraded by α-amylase activity in dialysate, influencing its osmotic properties. We modelled water and solute removal taking into account degradation by α-amylase and absorption of icodextrin from the peritoneal cavity. We analysed data from 16-hour dwells with icodextrin-based solution in 11 patients (8 icodextrin-naïve, 3 icodextrin-exposed) on dialysate volume, dialysate concentrations of glucose, urea, creatinine and α-amylase, and dialysate and blood concentrations of 7 icodextrin molecular weight fractions. The three-pore model was extended to describe hydrolysis of icodextrin by α-amylase. The extended model accurately predicted kinetics of ultrafiltration, small solutes and icodextrin fractions in dialysate, indicating differences in degradation kinetics between icodextrin-naïve and icodextrin-exposed patients. In addition, the model provided information on the patterns of icodextrin degradation caused by α-amylase. Modelling of icodextrin kinetics using a modified three-pore model that takes into account absorption of icodextrin and changes in α-amylase activity in the dialysate provided accurate description of peritoneal transport and information on patterns of icodextrin hydrolysis during long icodextrin dwells.

The model for perfused tissue undergoing deformation taking into account the local exchange between tissue and blood and lymphatic systems is presented. The Lie symmetry analysis in order to identify its symmetry properties is applied. Several families of steady-state solutions in closed formulae are derived. An analysis of the impact of the parameter values and boundary conditions on the distribution of hydrostatic pressure, osmotic agent concentration and deformation of perfused tissue is provided applying the solutions obtained in examples describing real-world processes.

Water removal which is a key treatment goal of automated peritoneal dialysis (APD) can be assessed cycle-by-cycle using remote patient monitoring (RPM). We analysed ultrafiltration patterns during night APD following a dry day (APD_DD; no daytime fluid exchange) or wet day (APD_WD; daytime exchange). Ultrafiltration for each APD exchange were recorded for 16 days using RPM in 14 patients. The distributed model of fluid and solute transport was applied to simulate APD and to explore the impact of changes in peritoneal tissue hydration on ultrafiltration. We found lower ultrafiltration (mL, median [first quartile, third quartile]) during first and second vs. consecutive exchanges in APD_DD(−61 [−148, 27], 170 [78, 228] vs. 213 [126, 275] mL; p < 0.001), but not in APD_WD(81 [−8, 176], 81 [−4, 192] vs. 115 [4, 219] mL; NS). Simulations in a virtual patient showed that lower ultrafiltration (by 114 mL) was related to increased peritoneal tissue hydration caused by inflow of 187 mL of water during the first APD_DDexchange. The observed phenomenon of lower ultrafiltration during initial exchanges of dialysis fluid in patients undergoing APD_DDappears to be due to water inflow into the peritoneal tissue, re-establishing a state of increased hydration typical for peritoneal dialysis.

Water removal which is a key treatment goal of automated peritoneal dialysis (APD) can be assessed cycle-by-cycle using remote patient monitoring (RPM). We analysed ultrafiltration patterns during night APD following a dry day (APD_DD; no daytime fluid exchange) or wet day (APD_WD; daytime exchange). Ultrafiltration for each APD exchange were recorded for 16 days using RPM in 14 patients. The distributed model of fluid and solute transport was applied to simulate APD and to explore the impact of changes in peritoneal tissue hydration on ultrafiltration. We found lower ultrafiltration (mL, median [first quartile-third quartile]) during first and second vs. consecutive exchanges in APD_DD (-61 [-148—27], 170 [78—228] vs. 213 [126—275] mL; pWD (81 [-8—176], 81 [-4—192] and 115 [4—219] mL; NS). Simulations in a virtual patient showed that lower ultrafiltration (by 114 mL) was related to increased peritoneal tissue hydration caused by inflow of 187 mL of water during the first APD_DD exchange. The observed phenomenon of lower ultrafiltration during initial exchanges of dialysis fluid in patients undergoing APD_DD appears to be due to water inflow into the peritoneal tissue, re-establishing a state of increased hydration typical for peritoneal dialysis.

Lay summary: Peritoneal dialysis (PD) uses the peritoneal membrane for dialysis. The peritoneal membrane is a thin layer of tissue that lines the abdomen. The lining is used as a filter to help remove extra fluid and poisonous waste from the blood. Everybody is unique. What is normal for one person’s membrane may be very different from another person’s. The kidney care team wants to provide each person with the best dialysis prescription for them and to do this they must evaluate the person’s peritoneal lining. Sometimes dialysis treatment itself can cause the membrane to change after some years. This means more assessments (evaluations) will be needed to determine whether the person’s peritoneal membrane has changed. Changes in the membrane may require changes to the dialysis prescription. This is needed to achieve the best dialysis outcomes. A key tool for these assessments is the peritoneal equilibration test (PET). It is a simple, standardized and reproducible tool. This tool is used to measure the peritoneal function soon after the start of dialysis. The goal is to understand how well the peritoneal membrane works at the start of dialysis. Later on in treatment, the PET helps to monitor changes in peritoneal function. If there are changes between assessments causing problems, the PET data may explain the cause of the dysfunction. This may be used to change the dialysis prescription to achieve the best outcomes. The most common problem with the peritoneal membrane occurs when fluid is not removed as well as it should be. This happens when toxins (poisons) in the blood cross the membrane more quickly than they should. This is referred to as a fast peritoneal solute transfer rate (PSTR). Since more efficient fluid removal is associated with better outcomes, developing a personal PD prescription based on the person’s PSTR is critically important. A less common problem happens when the membrane fails to work properly (also called membrane dysfunction) because the peritoneal membrane is less efficient, either at the start of treatment or developing after some years. If membrane dysfunction gets worse over time, then this is associated with progressive damage, scarring and thickening of the membrane. This problem can be identified through another change of the PET. It is called reduced ‘sodium dip’. Membrane dysfunction of this type is more difficult to treat and has many implications for the individual. If the damage is major, the person may need to stop PD. They would need to begin haemodialysis treatment (also spelled hemodialysis). This is a very important and emotional decision for individuals with kidney failure. Any decision that involves stopping PD therapy or transitioning to haemodialysis therapy should be made jointly between the clinical team, the person on dialysis and a caregiver, if requested. Although evidence is lacking about how often tests should be performed to determine peritoneal function, it seems reasonable to repeat them whenever there is difficulty in removing the amount of fluid necessary for maintaining the health and well-being of the individual. Whether routine evaluation of membrane function is associated with better outcomes has not been studied. Further research is needed to answer this important question as national policies in many parts of the world and the COVID-19 has placed a greater emphasis and new incentives encouraging the greater adoption of home dialysis therapies, especially PD. For Chinese and Spanish Translation of the Lay Summary, see Online Supplement Appendix 1. Key recommendations: Guideline 1: A pathophysiological taxonomy: A pathophysiological classification of membrane dysfunction, which provides mechanistic links to functional characteristics, should be used when prescribing individualized dialysis or when planning modality transfer (e.g. to automated peritoneal dialysis (PD) or haemodialysis) in the context of shared and informed decision-making with the person on PD, taking individual circumstances and treatment goals into account. ( practice point ) Guideline 2a: Identification of fast peritoneal solute transfer rate (PSTR): It is recommended that the PSTR is determined from a 4-h peritoneal equilibration test (PET), using either 2.5%/2.27% or 4.25%/3.86% dextrose/glucose concentration and creatinine as the index solute. ( practice point ) This should be done early in the course dialysis treatment (between 6 weeks and 12 weeks) ( GRADE 1A ) and subsequently when clinically indicated. ( practice point ) Guideline 2b: Clinical implications and mitigation of fast solute transfer: A faster PSTR is associated with lower survival on PD. ( GRADE 1A ) This risk is in part due to the lower ultrafiltration (UF) and increased net fluid reabsorption that occurs when the PSTR is above the average value. The resulting lower net UF can be avoided by shortening glucose-based exchanges, using a polyglucose solution (icodextrin), and/or prescribing higher glucose concentrations. ( GRADE 1A ) Compared to glucose, use of icodextrin can translate into improved fluid status and fewer episodes of fluid overload. ( GRADE 1A ) Use of automated PD and icodextrin may mitigate the mortality risk associated with fast PSTR. ( practice point ) Guideline 3: Recognizing low UF capacity: This is easy to measure and a valuable screening test. Insufficient UF should be suspected when either (a) the net UF from a 4-h PET is GRADE 1B ) and/or (b) the daily UF is insufficient to maintain adequate fluid status. ( practice point ) Besides membrane dysfunction, low UF capacity can also result from mechanical problems, leaks or increased fluid absorption across the peritoneal membrane not explained by fast PSTR. Guideline 4a: Diagnosing intrinsic membrane dysfunction (manifesting as low osmotic conductance to glucose) as a cause of UF insufficiency: When insufficient UF is suspected, the 4-h PET should be supplemented by measurement of the sodium dip at 1 h using a 3.86% glucose/4.25% dextrose exchange for diagnostic purposes. A sodium dip ≤5 mmol/L and/or a sodium sieving ratio ≤0.03 at 1 h indicates UF insufficiency. ( GRADE 2B ) Guideline 4b: Clinical implications of intrinsic membrane dysfunction (de novo or acquired): in the absence of residual kidney function, this is likely to necessitate the use of hypertonic glucose exchanges and possible transfer to haemodialysis. Acquired membrane injury, especially in the context of prolonged time on treatment, should prompt discussions about the risk of encapsulating peritoneal sclerosis. ( practice point ) Guideline 5: Additional membrane function tests: measures of peritoneal protein loss, intraperitoneal pressure and more complex tests that estimate osmotic conductance and ‘lymphatic’ reabsorption are not recommended for routine clinical practice but remain valuable research methods. ( practice point ) Guideline 6: Socioeconomic considerations: When resource constraints prevent the use of routine tests, consideration of membrane function should still be part of the clinical management and may be inferred from the daily UF in response to the prescription. ( practice point )

The transitory change of fluid and solute transport parameters occurring during the initial phase of a peritoneal dialysis dwell is a well-documented phenomenon; however, its physiological interpretation is rather hypothetical and has been disputed. Two different explanations were proposed: (1) the prevailing view—supported by several experimental and clinical studies—is that a vasodilatory effect of dialysis fluid affects the capillary surface area available for dialysis, and (2) a recently presented alternative explanation is that the molecular radius of glucose increases due to the high glucose concentration in fresh dialysis fluid and that this change affects peritoneal transport parameters. The experimental bases for both phenomena are discussed as well as the problem of the accuracy necessary for a satisfactory description of clinical data when the three-pore model of peritoneal transport is applied. We show that the correction for the change of transport parameters with dwell time provides a better fit with clinical data when applying the three-pore model. Our conclusion is in favor of the traditional interpretation namely that the transitory change of transport parameters with dwell time during peritoneal dialysis is primarily due to the vasodilatory effect of dialysis fluids.

Fluid and solute transport in poroelastic media is studied. Mathematical modeling of such transport is a complicated problem because of the volume change of the specimen due to swelling or shrinking and the transport processes are nonlinearly linked. The tensorial character of the variables adds also substantial complication in both theoretical and experimental investigations. The one-dimensional version of the theory is less complex and may serve as an approximation in some problems, and therefore, a one-dimensional (in space) model of fluid and solute transport through a poroelastic medium with variable volume is developed and analyzed. In order to obtain analytical results, the Lie symmetry method is applied. It is shown that the governing equations of the model admit a non-trivial Lie symmetry, which is used for construction of exact solutions. Some examples of the solutions are discussed in detail.