Author – Matthew Wolf
Professor Emeritus 
University of South Carolina, School of Medicine

Summary

Modeling and simulation of Peritoneal Dialysis therapy plays an important role in understanding body fluid management. Instead of experimentation, using a simulation to establish a precise relationship between peritoneal volume and dwell time after infusion leads to a safer and more efficient dialysis.  Optimization based on the simulated relationship provides further information on key clinically-important parameters.  The Altair Embed product was used for all simulation and optimization tasks in this paper.  It’s power, ease of use, and numerical accuracy were key considerations for its selection.  In addition, the ability to freely share the Peritoneal Dialysis model with simulation capability to colleagues using the free Embed Viewer provides an excellent way to collaborate with other experts. 

 

Introduction

Fluid management is one of the principal objectives in renal (kidney) failure patients to obtain long term survival.  Their lack of the ability to produce sufficient urine, if not treated, leads to death.  If a transplant is not available, the standard treatment is periodic or continuous dialysis, where sufficient water and various dissolved solutes are removed from the patient’s body fluids.

Peritoneal dialysis (PD) is one of the commonly used therapies, where the peritoneal cavity, which encloses the gastro-intestinal organs, is used as a fluid reservoir whose bounding vascular membranes can exchange water and solutes between the contained peritoneal fluid and the blood plasma.  The plasma is in chemical communication with the rest of the body fluids.

Hemodialysis is another commonly used therapies.  In this therapy, arterial blood is removed from the patient and passed through a membrane device.  The blood leaving the device has a more normal chemical composition because of removal of water, excess waste products and other substances through transport into a specialized fluid on the other side of the membrane.  This blood is then returned to the body, eventually restoring more normal chemical composition.

Computer simulation has long played an important role in understanding the physicochemical processes involved in transport of materials among the body fluids, as well as across the peritoneal-capillary membrane during peritoneal dialysis, as these processes have been controversial.  A central simulation concept has been that the various body-fluids can be lumped into discrete, chemically homogenous, individual volumes called compartments, which are in in chemical communication.

 

Model Description

The body fluid compartmental system is usually assumed to be in a chemical steady-state, where the volumes of the various compartments and the concentrations of their many chemical species remain constant from minute to minute unless perturbed.  Figure 1 shows the important perturbing factors considered as inputs to the chemical system and some of the chemical entities (outputs) affected by these factors.

Figure 1

 

Indicated in Fig. 1 is that the steady-state distribution of water and solutes among the various body fluid compartments and the resulting volumes, acid-base status and individual species chemical concentrations are regulated by a number of physicochemical processes.  Food and water inputs and various excretions perturb the chemical composition outputs stimulating the kidney (renal system) controller to excrete urine of a specific volume and chemical composition, which will return the system to normal.  If renal failure occurs, some other means, such as dialysis, is used to approximate normal renal function to maintain the steady-state and keep the patient alive and functioning.

As seen in Fig. 2, in the PD procedure, typically, a large volume of a specially designed (very high glucose concentration) dialysis solution is infused through a catheter inserted into the peritoneum, which bathes the organs contained in the abdominal cavity.  This procedure greatly enlarges the normally small peritoneal volume and changes its chemical composition, in particular, greatly increasing its glucose concentration, which osmotically draws water and its dissolved solutes from the blood plasma (see below).

 

Figure 2

 

Peritoneal fluid is considered to be part of the interstitial fluid, which separates the great majority of cells in the body from the plasma part of the blood.  This relationship is diagramed in Figure 3.  As depicted, water (H2O) and various dissolved solutes exchange between plasma and cells via the interstitial fluid.  The solute, urea, and other nitrogenous molecules are formed in cells as proteins are metabolized.  These molecules are toxic and must be eliminated from the body fluids, normally in the urine, but when renal failure occurs, the therapeutic PD procedure transports them into the peritoneal fluid along with H2O and other substances, due to the physicochemical forces acting across the peritoneal membrane.  The chemically altered peritoneal fluid is emptied every 4 to 6 hours and the entire filling, dwelling, emptying and fresh fluid refilling PD procedure is continually repeated as shown in Fig. 3, approximating the lost normal kidney function in the patient. 

The loss of water and solutes from the plasma sets up a situation where its water and contained solutes are partially restored from the other body fluids, due to changes in the physicochemical forces acting across their bounding membranes, resulting in all of the body fluids changing as shown in Fig. 3; most of this peritoneal fluid volume increase comes from the extracellular compartments, interstitial and plasma.  During the PD-dwell time, the limiting water-transport situation is approached as the peritoneal glucose concentration decreases substantially, due to its continual diffusion across the peritoneal membrane into the plasma.

 

Figure 3

 

Shown in Fig. 4 is a more detailed description of the processes acting across the peritoneal membrane during the PD dwell.

 

Figure 4

 

The very high glucose concentration in the dialysis-fluid fill (214 mmol/liter, abbreviated as mM) osmotically drives H2O from plasma in blood flowing through peritoneal capillaries into the peritoneal fluid, thereby transiently increasing its volume to 2.7 liters in this example.  Convectively transported with H2O are solutes, such as urea and various ions.  Although glucose also moves convectively, its high diffusion gradient drives glucose transport from peritoneum to blood plasma, whose glucose concentration is relatively low (5 mM) due to entry into cells and subsequent metabolism.  Convective urea transport, along with its high concentration gradient in these patients, drives urea into peritoneal fluid.  At the end of the dialysis dwell, 4 to 6 hours, the high amounts of urea (70 mmol), H2O and excess ions in the peritoneal fluid are emptied and then this process continues.

The model simulation of the kinetic changes described above and the forces leading to these changes were programmed in Altair Embed as illustrated in Fig.5.  As seen, the major simulation blocks consist of simulating the: 1) dialysis fluid infusion kinetics, 2) peritoneal fluid volume and chemical composition kinetics due to the infusion and 3) changes in the steady-state, body-fluid volumes and chemical composition due to kinetic exchanges across the peritoneal membrane between peritoneal fluid and plasma, as described above.

 

Figure 5

 

Each of these major blocks can be drilled into to see the multitude of sub-blocks and mathematical processes contained in the major blocks shown.  Figure 6 shows a screenshot example. The current PD model has over 5000 of these units.

 

 

Figure 6

 

Figure’s 7 and 8 show the model predictions (solid lines) during the PD procedure for the kinetics of peritoneal volume and the mass and concentration of urea, one of the many solutes simulated in the model.  These data were taken from Wolf1, 2.  As seen, the graphical model results closely describe experimental measurements (open circles with SD error bars), which demonstrates that the hypothesized physicochemical forces simulated in the model are the ones producing the kinetic changes.

 

Figure 7

Figure 8

 

Conclusions

           Altair Embed is a useful tool for visualizing, constructing and solving the various differential equations simulating the dialysis procedure in patients without normal kidney function.

           The Altair Embed optimization feature gives a powerful way of identifying key, unknown, clinically important parameter values.

           Embed has proven to be a powerful tool in increasing understanding of the critical physicochemical processes governing body-fluid chemistry in health and disease.

 

References

  1. Wolf MB. Are transient changes in capillary surface area required to explain peritoneal transport in renal-failure patients? Perit Dial Intl. 2020;40:587-92.
  2. Wolf MB. Peritoneal physicochemical transport mechanisms: hypotheses, models and controversies. Perit Dial Intl. 2021.
  3. Wolf MB, DeLand EC. A mathematical model of blood-interstitial acid-base balance: application to dilution acidosis and acid-base status. J Appl Physiol. 2011;110:988-1002.
  4. Wolf MB. Whole body acid-base and fluid-electrolyte balance: a mathematical model. Am J Physiol: Renal Physiol. 2013;305:F1118-F31.
  5. Wolf MB. Physicochemical models of acid-base. Sem Neph. 2019;39:328-39.
  6. Wolf MB. Mechanisms of Acid-Base Kinetics During Hemodialysis: a Mathematical-Model Study. ASAIO J. 2021.

 

About the author 

Matthew Wolf 

He has used computer simulation for over fifty years to study the physiology of living systems.  His prior use of electronic analog computers in the aerospace industry, after receiving a B.Sc. and M.Sc. in engineering at UCLA, led him to choose VisSim, now Altair Embed as his simulation tool in his physiological careers at the Universities of Southern California and South Carolina, after graduating UCLA with a Ph.D. in physiology.

His 2011 paper3, using VisSim to simulate the acid-base status of some of the body fluids with his co-author Edward DeLand, stemmed from Dr. DeLand’s much earlier seminal work at Air Force’s Project RAND Corp. and UCLA on using digital computers to simulate body-fluid chemistry.  Dr. Wolf’s more recent work has been using his body-fluid chemistry model simulated with Altair Embed to study physiologically relevant, clinical issues in critically ill patients4, 5 and studying extracorporeal therapies6.

 

About Rahul Ponginan

Technical Manager - Academic Program
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