Urea Kinetic Modeling for Guiding Hemodialysis Therapy in Adults

Introduction

Dialysis is arguably a successful life-sustaining therapy. This unique, extracorporeal therapy has granted millions of people years of life after kidney failure. Hemodialysis (HD) is presently the most utilized form of renal replacement therapy around the globe. Even as technology improves, the method through which HD provides its therapy remains little changed over the last few decades. The removal of low-molecular-weight, water- soluble, and minimally protein-bound substances primarily by diffusion is still what dialysis does best.

Clinicians order HD as a prescription. Like any medication prescription, the timing, frequency, and dose are all important to the efficacy of the treatment. Nephrologists should assess the dose of HD they are prescribing by periodically measuring it. The dose of HD is the fractional clearance of urea, often referred to as the adequacy of HD. Meeting a minimum threshold for urea clearance cannot be the only metric for an adequate HD treatment. Thorough consideration of other objective and subjective factors also becomes important in the care of these vulnerable patients. Nonetheless, nephrologists should understand the background, history, and methods used in determining dialysis dosing based on the dynamics of urea.

Modeling of any system is an attempt to better understand complex processes by using mathematical approximations. This chapter focuses on urea kinetic modeling (UKM) in determining the dose of HD in adults. We will discuss why urea has been the molecule of choice, describe the modeling techniques in nontechnical terms, outline some simplified equations to approximate the results of UKM, and give some practical troubleshooting tips. For those interested in computer programming or a practical online tool to explore the possibilities of UKM, we include additional references at the end of this chapter.

Why Model Urea?

In stages of chronic kidney disease not requiring dialysis, serum creatinine concentrations are used to estimate kidney glomerular filtration rate. Since the generation of creatinine, which roughly correlates with muscle mass, is relatively constant over time and minimally influenced by dietary variations, it serves well in this role. In measuring HD clearance, creatinine could also conceivably be used as a representative molecule. However, since a reliable method for determining muscle mass and hence creatinine generation rate is not readily available, we shift away from using creatinine as a marker for monitoring HD adequacy. Urea instead was chosen as the marker for HD adequacy as its generation rate is easier to assess ( Fig. 4.1 ). Urea is also inexpensively and readily measured in most clinical laboratories by way of blood urea nitrogen (BUN).

Nitrogen-containing waste products, derived from amino acid breakdown in protein catabolism, are excreted almost exclusively by the kidneys. In humans, nitrogenous waste comes mainly in the form of ammonia, urea, creatinine, and uric acid. Ammonia is toxic at higher concentrations. Many animals, especially terrestrial species, spend valuable energy to transform ammonia to urea, a much less toxic compound. Urea is by far the most plentiful of the nitrogen-containing waste molecules primarily produced by the liver via the Krebs ornithine–urea cycle in a zero-order kinetic fashion (its rate of production is not affected by concentration). Even prior to the advent of dialysis, it was observed that limiting protein intake in patients with advanced kidney failure lessened the signs and symptoms of the condition. So, does this imply that urea is the main toxin of renal failure?

It is evident from prior human and animal studies that the toxicity of kidney failure is not due to urea. However, elevation of the blood urea level loosely correlates with the hundreds of other substances that accumulate in advanced kidney failure, leading to the clinical syndrome of uremia. Similarly, while HD removes urea, it is likely the concomitant clearance of a myriad of other retained toxins that leads to patient improvement. Most importantly, large-scale clinical studies on HD dosing have used the fractional removal of urea to help us understand how the dose of HD relates to morbidity and mortality.

In summary, the attributes of an ideal marker for monitoring HD adequacy would likely embody the following characteristics: (1) it would increase in kidney failure, (2) it would correlate with clinical signs and symptoms of the disease, (3) it would be removable by dialysis, (4) it would be easy and reproducibly measurable, and (5) its degree of removal would be associated with important clinical outcomes. While not a perfect marker, urea serves as an easily accessible and reproducible marker for dialysis adequacy.

The Kinetics of Urea

The word “kinetic” has its root in the Greek term for motion. The BUN at any given moment provides minimal information regarding the condition of the HD patient nor the adequacy of dialysis. For example, a low pre-HD BUN may reflect either a patient who has been receiving excellent routine dialysis clearance or a patient who has poor protein intake and this singular value provides no information on the dynamics of urea. Understanding how the concentration of urea changes over time in the context of urea generation and dialysis removal is the value of UKM.

Nephrologists owe much of the understanding of UKM, the concepts and the mathematics behind it, to Gotch and Sargent, as well as to numerous other scientists and investigators who have further defined and refined the concepts. This section will outline the broad concepts, differing methods, assumptions, and required data for UKM.

Balance Between Urea Production and Removal

The urea concentration in serum, most commonly assessed as BUN, is the balance of urea production from protein breakdown and the removal of urea. In patients with kidney failure on HD, serum urea concentration is constantly changing since its removal by HD is an intermittent process. Urea generation rate ( G ), expressed in units of mass per unit time (g/day or mg/min), for the purpose of UKM, is assumed to be constant both during and between dialysis treatments. Removal of urea ( K ) is the sum of dialyzer and native kidney clearances ( K _D and K _R , respectively). So, the concentration of urea ( C ) is a function of its generation rate within the body ( G ), the body water in which urea is distributed ( V ), and the clearance of urea by K _D and K _R . The rate of change in the amount of urea (volume × concentration) over time ( t ) can be written as:

$\frac{d\left(V\times C\right)}{dt}=G-K\times C$

Urea generation ( G ), predominantly by the liver, is a zero- order kinetic process, meaning that its rate of production is not affected by the surrounding concentration. Urea removal by dialysis and native kidneys are first-order elimination processes. In other words, the urea removal rate is dependent on its concentration. The rate of urea elimination declines over time for both diffusive and convective clearances since the concentration of the urea in the plasma declines. Therefore, urea concentration in the patient during HD decreases in a logarithmic fashion, and removal becomes less “efficient” over time. Fig. 4.2 illustrates the typical removal and gain of urea. In the process of UKM, two mathematical expressions, one for the rise in urea from generation and the other for the fall of urea from dialysis and any native kidney function, need to be created and solved simultaneously to describe the rise and fall of urea over the course of a week. Fig. 4.3 shows a typical thrice-weekly HD profile for BUN. Note the linear rise in urea between HD treatments (we are assuming no residual kidney function in this example) by zero-order generation of urea, with the curvilinear first-order kinetic decline of BUN during intermittent HD treatments.