Hemodialysis Dose

Abstract

Adequate dialysis requires a measure of the dose, which includes the extent and intensity of each treatment as well as the frequency of treatments. To measure the dose, attention should be directed to the primary goal of dialysis, which is to remove toxins normally eliminated by the patient’s native kidneys, with the ultimate goal of reducing their concentrations in body tissue to sub-toxic levels. Since we have not identified all of the toxins and cannot measure their levels, the focus of measurement should be on clearance of measurable solutes using an easily dialyzed representative such as urea or sodium. Allowances must be made for the self-limiting nature of intermittent hemodialysis, which reduces the treatment efficiency. The dose measurement must include the influences of convection, solute generation, and residual native kidney function, and consideration must be given to the effects of flow and red cell mass within the dialyzer as well as hollow-fiber permeability expressed as a mass transfer coefficient for each solute of interest. Additional attention must be given to sequestration of toxic solutes within the patient, protein binding of toxins, and the residual risk factors that remain after the dialysis treatment has been optimized. This chapter reviews the expressions of hemodialysis dose that have evolved over the past 50 years, such as Kt/V, and provides detailed methods for assessing dialyzer function and for measuring small solute clearances using single- and multi-compartment models of urea kinetics.

1 Historical Perspective

Evidence that equilibration of the blood with an isotonic salt solution across a semipermeable membrane as a potential method for removing unwanted substances from the body including drugs and uremic toxins dates back many years [1–3]. However, it was not until Dr. Willem J. Kolff successfully applied hemodialysis (HD) to treat a patient with acute kidney failure that the hypothesized benefit for patients suffering from uremia was proven [4]. This landmark event also confirmed the previous logical hypothesis that the cause of the immediate life-threatening aspect of uremia is from accumulation of small (dialyzable) solutes that normally appear in the urine. The reversal of a previously fatal disease was considered miraculous (patients sometimes awakened from uremic coma during the procedure), so little thought was given to measuring the treatment or determining its adequacy. Perhaps because of its complexity, physicians at the time, including its inventor, also felt that its application should be limited to management of reversible acute kidney disease, serving to allow time for the native kidneys to recover. Not until 1960, with the development of a permanent vascular access device, was management of chronic kidney disease accepted, and a quest for measurement of the dose and its adequacy begun [5, 6].

2 Measuring Diffusion, the Basic Principle of Dialysis

How does the patient and family know that he/she had a good dialysis? Probably after a poor dialysis the patient might feel better, having avoided the symptoms of clinical disequilibrium that often follow significant solute and fluid removal. How does one measure the effect of dialysis? Simply keeping the patient alive is not enough, and one can argue further that even if the patient reports feeling well, the caregiver should not be satisfied. Measuring the dialysis dose and assessment of its adequacy should be anticipatory, identifying inadequacies at an early stage to allow corrections before the symptomatic stage. To answer the patient’s question, the focus should be on the dialysis objective: removal of solute by simple diffusion across a semipermeable membrane.

Since the pioneering work of Thomas Graham [7] and Adolph Fick [8] in the mid to late 1800s, the driving force for diffusion of solutes and gases has been recognized as the concentration of the gas or solute. Most importantly, the rate of diffusion (e.g., bulk movement of solute) is directly proportional to the concentration gradient. Fick’s first law of diffusion has been adapted to dialysis [8]:

$$\text{Js}=\text{KoA}(\Delta \text{C}),$$

(3.1)

Js is the rate of solute movement or flux (e.g., mg/min), Ko is a membrane-specific and solute-specific constant (e.g., cm/min), A is the membrane area (e.g., cm²), ΔC is the solute concentration gradient across the membrane (e.g., mg/mL).

The proportionality constant KoA in Eq. 3.1 is defined as the ratio of flux (Js) to the concentration gradient (ΔC) across the membrane, which is essentially the definition of dialysance: a measurement similar to clearance that takes into consideration solute concentrations on both sides of the membrane. For a hollow-fiber kidney, KoA can be considered the initial clearance at the proximal end of the fibers before any buildup of solute on the dialysate side. When the dialysate concentration is zero, the denominator is simply the blood concentration, and clearance is then equal to dialysance. KoA can also be considered the dialyzer’s maximum clearance at infinite blood and dialysate flow rates. It is a dialyzer-specific measure used to compare the effectiveness of different hollow-fiber dialyzers, but it is also solute-specific (e.g., KoA values for urea and creatinine are different for the same dialyzer). Similar to clearance, which is determined by, but independent of either solute concentrations or flux, KoA is also independent of blood and dialysate flow rates. Its value can be determined by measuring the cross-dialyzer clearance at specified blood and dialysate flow rates [9]:

$${{K}_{0}}A=\frac{{{Q}_{b}}{{Q}_{d}}}{{{Q}_{b}}-{{Q}_{d}}}\ ln\left( \frac{{{Q}_{d}}\left( {{Q}_{b}}-{{K}_{d}} \right)}{{{Q}_{b}}\left( {{Q}_{d}}-{{K}_{d}} \right)} \right),$$

(3.2)

Q_b and Q_d are effective blood and dialysate flow rates respectively, and K_d is the dialyzer solute clearance. Equation 3.2, known as the Michael’s equation after its developer [9], is based on an exponential decline in solute concentration along the membrane as blood and dialysate flow in opposite directions for maximum efficiency.

More importantly, once the dialyzer KoA has been determined, a rearrangement of Eq. 3.2 can be used to predict the clearance for any blood and dialysate flow rate:

$${{K}_{d}}={{Q}_{bw}}\left[ \frac{{{e}^{{{K}_{0}}A\left( \frac{{{Q}_{d}}-{{Q}_{b}}}{{{Q}_{d}}{{Q}_{b}}} \right)}}-1}{{{e}^{{{K}_{0}}A\left( \frac{{{Q}_{d}}-{{Q}_{b}}}{{{Q}_{d}}{{Q}_{b}}} \right)}}-\frac{{{Q}_{b}}}{{{Q}_{d}}}} \right].$$

(3.3)

3 Intermittent Dialysis is Self-Limiting

Despite the constant nature of KoA and the constancy of clearance during a single HD at fixed Q_b and Q_d, intermittent dialysis is intrinsically self-limiting. For peritoneal dialysis (PD), the clearance (but not the dialysance) gradually falls with time and will eventually extinguish during a single exchange of fluid as solute concentrations in the dialysate completely equilibrate with the patient’s blood concentrations. For intermittent HD, clearances remain constant during the treatment because fresh dialysate is constantly supplied, but the treatment’s effectiveness falls as concentrations in the patient’s blood fall. In the absence of replenishment (G), removal of solute during HD would also extinguish with time (despite a constant Kt/V). This self-limiting feature of dialysis results both from solute buildup on the dialysate side (PD) and from reduction in solute concentrations on the blood side. In other words, for intermittent dialysis, the more one dialyzes the less solute is removed. Fortunately, uremic toxicity is also concentration-dependent, such that dialysis is more effective for the more toxic patient .

4 Diffusion in a Flowing Circuit

Figure 3.1 shows what happens inside the dialyzer as blood flows from inlet to outlet and dialysate flows in the countercurrent direction. Solute transfer from blood to dialysate depends on both flow rates and the membrane permeability to each solute. The gradient across the membrane diminishes with time and with distance along the membrane. For solutes with high membrane permeability, the gradient diminished more rapidly with distance as shown in Fig. 3.1a. The downstream dissipation of the gradient is correctable by increasing the blood flow, which explains the flow dependency of clearance. For solutes with low permeability, distance along the membrane has less impact, so solute removal is more dependent on membrane permeability and less dependent on flow as shown in Fig. 3.1b. For patients dialyzed intermittently (e.g., three times weekly) the gradient also diminishes with time and would eventually extinguish in the absence of new solute generation. This accounts in part for the inefficiency of intermittent dialysis as discussed below.

Fig. 3.1

Hollow-fiber solute gradients. a An easily dialyzed solute with blood flow-dependent clearance. b Solutes less well dialyzed; clearance is membrane-dependent, less dependent on blood flow

Within the hollow fiber, solutes diffuse across the membrane only from the water fraction of the blood. Because macromolecules like serum lipids and proteins occupy space that excludes water-soluble molecules, they reduce the effective blood flow to about 93 % of the whole blood flow. The role of larger blood components such as erythrocytes depends on the solute. For solutes like urea that diffuse rapidly across red cell membranes the patient’s hematocrit has little influence on clearance, so solute delivery to the membrane is essentially a function of blood water flow, including erythrocyte water [10, 11]. For solutes like creatinine, phosphorus, and uric acid with negligible diffusion from red cells during the 10–20 s transit through the dialyzer, effective flow is restricted to plasma water, which must be used to measure clearances (Table 3.1) [12, 13]. However, red cells contain significant amounts of these solutes that eventually equilibrate with the plasma after leaving the dialyzer. This phenomenon explains in part why creatinine clearances have not been popular as a measure of dialysis adequacy ; the post-dialyzer plasma creatinine concentration is spuriously low and may require several hours to equilibrate with red cells in the same blood sample.

Table 3.1 Effective dialyzer blood compartment flow [12, 13]

Between dialyses, in addition to solutes, the patient accumulates water. Removal is easily accomplished during dialysis by applying hydrostatic pressure across the dialysis membrane. Since the resulting convective loss of fluid and solute is in the same direction as diffusive solute movement, it adds to the effectiveness of the dialysis. However, the augmenting effect of filtration is less than might be expected because convective transfer of solute across the membrane diminishes the gradient for diffusion, and in contrast to diffusive loss of easily dialyzed solutes like urea, convective losses occur along the entire length of the hollow fiber [14]. At the distal end where urea concentrations may be reduced by 70–80 %, convective transfer of solute is greatly diminished. Equation 3.4 is used to quantify instantaneous solute removal by convection, and illustrates the dilution effect.

$${{K}_{d}}={{Q}_{b}}\left( \frac{Cin-Cout}{Cin} \right)+{{Q}_{f}}\left( \frac{Cout}{Cin} \right),$$

(3.4)

K_d is the dialyzer clearance, Q_b is the dialyzer blood outflow, C_in and C_out are the inflow and outflow solute concentrations respectively, and Q_f is the ultrafiltration flow rate. Note that if C_out is zero, that is, solute removal is complete, Q_f adds nothing to dialyzer clearance .

For high-flux dialyzers where filtration rates are typically an order of magnitude greater than for conventional-flux dialyzers, convective fluid removal at the proximal end of the hollow fiber is much greater than at the distal end where oncotic effects may cause filtration to move in the opposite direction, so-called back-filtration [15]. This effect counteracts the negative effect of filtration on diffusion and may contribute to the higher clearances achieved by high-flux dialyzers [16, 17]. For all modes of dialysis, contraction of blood and extracellular fluid volume due to solute-deprived fluid removal helps to maintain the concentration at the blood inlet for a longer time, and thereby increases the effectiveness of the dialysis. This phenomenon highlights the importance of including fluid volume shifts in the mathematical models of dialysis urea kinetics (see below).

5 Origin of Kt/V

The concentration of solute is the driving force for diffusion, and the rate of diffusion is directly proportional to the concentration as noted in Eq. 3.1. Ignoring the effects of volume changes and solute generation, the change in concentration (C) with time (t) can be simplified and expressed mathematically as:

$$\text{dC/dt}\,\text{=}\,-\text{kC}\text{.}$$

(3.5)

The symbol k is the elimination constant, similar to that of an injected drug, and indicates that the fractional change in concentration (dC/C)/dt is constant during the treatment. When expressed as a fraction of the distribution volume (V), k × V is the clearance (K), which is also constant, since in this overly simplified example we assume that V does not change. Integration of Eq. 3.5 and substituting K/V for k yields:

$$\text{C}={{\text{C}}_{0}}{{\text{e}}^{\text{-Kt/V}}},$$

(3.6)

C₀ is the initial concentration and C is the concentration at time (t). Logarithmic transformation of Eq. 3.6 yields:

$$\text{Kt/V}=\ln \left( {{\text{C}}_{0}}/\text{C} \right).$$

(3.7)

The left side of the overly simplified Eq. 3.7 (Kt/V) is the fractional clearance expressed per dialysis and normalized to body size (V). The denominator (V) adds value as a correlate to lean body mass, which is usually more desirable than body weight as a normalizing factor for body size. Equation 3.7 helps to illustrate the strong dependence of the clearance (expressed as Kt/V) on the ratio of solute concentrations in two blood samples, one at the beginning (C₀), and one at the end of the treatment (C). Note that the ratio is used, not the absolute concentrations, and also note that none of the components of the Kt/V expression need to be measured independently, including the treatment time (t).

If urea is the solute, and its generation (G) and volume changes (ΔV) during the dialysis are included, Eq. 3.8 (see below) must be substituted for Eq. 3.7, but the fundamental strong dependence of Kt/V on pre/post-urea concentrations remains .

6 Modeling Urea Kinetics

Regardless of what we think is going on within the hollow-fiber membranes during dialysis, it is possible to precisely model solute flux, including the effect of ultrafiltration , using a mass balance approach where input equals output. Figure 3.2 depicts the elements contributing to urea mass balance within the patient during and between dialyses. Equation 3.8 is the solution to the mass balance equations in Fig. 3.2 and provides a practical estimate of fluctuating serum urea concentrations while the patient’s urea volume varies usually by several kilograms during and between treatments. Equation 3.8 also incorporates residual native kidney function and urea generation, and is used as the fundamental tool for modeling urea kinetics.

Fig. 3.2

Single-compartment model of urea mass balance. Equation 3.8 is the explicit solution to the differential equation in this figure, which is used to resolve Kt/V and G from a single pre-dialysis BUN and a single post-dialysis BUN. V is the urea distribution volume, C is the urea concentration, K_d is the dialyzer clearance, K_r is the kidney clearance, and G is the urea generation rate. K is the sum of K_d and K_r during dialysis, and is equal to K_r between dialyses

$$\begin{aligned}&C={{C}_{0}}{{\left[ \frac{V-\Delta V\bullet t}{V}\right]}^{\left( \frac{{{K}_{r}}+{{K}_{d}}+\Delta V}{\Delta V}\right)}}\\&\;+\frac{G}{{{K}_{r}}+{{K}_{d}}+\Delta V}\left[1-{{\left[ \frac{V-\Delta V\bullet t}{V} \right]}^{\left(\frac{{{K}_{r}}+{{K}_{d}}+\Delta V}{\Delta V} \right)}}\right],\end{aligned}$$

(3.8)

C is the solute concentration at any time (t), C₀ is the initial concentration, V is the solute distribution volume, ΔV is the rate of fluid removal, G is the solute generation rate, K_r is the patient’s native kidney solute clearance, and K_d is the dialyzer clearance.

Urea modeling uses Eq. 3.8 in a reverse manner. The modeler measures C and C₀ (analogous to Eq. 3.7) then solves for G and Kt/V using computerized iterations of Eq. 3.8. The modeler must also have knowledge of volume fluxes (ΔV), K_r, and t, although these are less critical. Equation 3.8 yields a profile of the BUN during and between treatments and repeats itself weekly because the interdialysis treatment intervals are asymmetric during the week. Each treatment is assumed to be identical, but the patient begins the treatment differently because of the time asymmetry. For example, if dialysis is performed three times per week, the patient will have accumulated solute for 2 or 3 days depending on the day of the week. Equation 3.8 is solved (by iteration) twice, once during dialysis , and again between dialyses when K_d is zero. Note that the results are expressed in relative terms, as a fraction of the patient’s urea volume. For example, to resolve V, knowledge of K_d is necessary and vice versa. Ordinarily, the user provides an estimate of K_d, which is assumed to be constant throughout the treatment as noted above; K_d and KoA can be measured using samples collected simultaneously from the blood inflow and outflow ports or estimated using Eqs. 3.2 and 3.3.

During dialysis, K_d has the major influence; between dialyses G dominates. This means that Kt/V is primarily determined by the pre-dialysis and post-dialysis BUN values (see Eq. 3.7), and G is determined by the post-dialysis and subsequent pre-dialysis BUN values. Because the primary modeling outcome is Kt/V, an independent measure of K_d is not required, and errors in estimates of K_d have little influence on the resulting Kt/V dose measurement. Similar to Eq. 3.7, the ratio of post- to pre-BUN values determines Kt/V; absolute values are not considered. Absolute values, however, can be used to measure G using an iterative method as depicted in Fig. 3.3, eliminating the need to sample blood again at the next dialysis [18]. Since urea is an end product of protein metabolism, G can be converted to a protein equivalent, a net protein catabolic rate normalized to V (PCRn), as shown in Eq. 3.9 [19]. PCRn can be useful as an adjunct to dietary counseling :

$$\text{PCRn}=5420\left( \text{G/V} \right)+0.17.$$

(3.9)

Fig. 3.3

Measuring G with only 2 BUN values. The upper graph shows a weekly BUN profile generated by Eq. 3.8 that uses an excessively high value for G. In the middle graph the value is too low. By repeated iteration, a value for G is found (lower graph) that matches the pre-dialysis BUN with the end-week BUN. [18]

7 More Refined Modeling

The single-compartment (single V) model diagramed in Fig. 3.2 predicts BUN concentrations during and between dialyses, but the results do not coincide precisely with measured values, especially for short intense dialysis as shown in Fig. 3.4. BUN values are overestimated during dialysis and underestimated between dialyses, especially in the immediate post-dialysis period. The cause of these discrepancies is delayed diffusion among the patient’s body compartments, most notably intracellular versus extracellular, which reduces the effective volume of distribution during dialysis and causes a rebound in concentration as the two compartments re-equilibrate post dialysis. Despite the unique and rapid diffusibility of urea across red cell membranes as noted above, urea kinetics in the remainder of the body are better described by a two-compartment model, as shown in Fig. 3.5. This model is similar to the single-compartment model depicted in Fig. 3.2 with an added remote compartment volume (V₂) and concentration (C₂). Unfortunately, the addition of a second compartment complicates the mathematics such that the equations depicted in Fig. 3.5 are not easily resolved explicitly and require more complex mathematical manipulations for a solution [20]. A method using numerical analysis has been implemented and made available on an Internet site devoted to dialysis dosing [21].

Fig. 3.4

Modeled and measured BUN values compared. The single-compartment prediction of BUN values during and following a short, high-efficiency dialysis is shown as the dashed line. Actual values measured every 15 min are shown as open circles. The solid line shows the prediction of a two-compartment model

Fig. 3.5

Two-compartment diffusion model. Fast iterative resolution of the two differential equations shown in this figure yield values for V₁, V₂, K_C, and G. V₁ is the dialyzed compartment volume, V₂ is the remote compartment volume, and K_C is the inter-compartment mass transfer coefficient. Other symbols are the same as defined in Fig. 3.2

The single-compartment assumption causes the errors in predicted concentrations as shown in Fig. 3.4 but when used to calculate the dialysis dose as Kt/V, the two errors during and after the end of dialysis tend to cancel each other; the resulting values for Kt/V (and K_d) calculated by each model are similar, justifying clinical use of the simpler model [22]. Despite this minimization of the single-compartment error, some authorities have objected to using the immediate post-dialysis BUN as an indicator of the dialysis dose, since it is falsely low if compared to the equilibrated value shown in Fig. 3.6. The latter is determined by extrapolating the late inter-dialysis concentration curve back to the immediate post-dialysis time, which essentially converts the patient’s urea kinetics to a single compartment but with an equilibrated clearance (eK). The resulting eK and eKt/V are always lower than the dialyzer instantaneous clearance and single pool Kt/V (spKt/V). The lowered clearance is an effective whole body clearance defined as the removal rate divided by the average urea concentration in the patient’s body compartments at the time the removal rate is measured. eKt/V was used in the HEMO Study (see below) as the target for randomization [23], and by the European Best Practice Guideline Expert Group as a target for HD adequacy in general [24]. Fortunately, a two-compartment model is not needed to calculate eKt/V; approximations based on the intensity of dialysis have been developed [25–27], one of which is shown here [26]:

$$\text{eKt/V}=\text{spKt/V}\left( \text{t}/\left( \text{t}+30 \right) \right).$$

(3.10)

Fig. 3.6

Source of eKt/V. The equilibrated post-dialysis BUN shown here as the large circle is obtained by extrapolating measured post-dialysis BUN values. It is always higher than the BUN measured immediately post dialysis (shown just below it). Whole body eKt/V, which is derived from the equilibrated BUN, is always lower than spKt/V, which is derived from the immediate post-dialysis BUN

To complicate the model further, the immediate rebound in urea concentration post dialysis is not entirely due to delayed diffusion. Disequilibrium within the blood compartment is caused by multiple parallel circuits with markedly different blood flow rates [28]. The most rapidly flowing circuit is the route through the patient’s arteriovenous fistula , heart and lungs, and back [29]; this cardiopulmonary (CP) circuit has a round-trip circulation time of 5–15 s depending on the patency of the fistula and the patient’s cardiac output. The CP circuit also happens to be the dialyzed circuit, all others feeding into it from venous return. As a result the urea concentration falls to a lower level in the CP circuit during dialysis, as much as 20 mg/dl lower than in the periphery, and it rebounds within about 2 min when the blood pump is stopped [28]. This flow-related disequilibrium differs from the diffusion -related disequilibrium (Fig. 3.6) with respect to several factors listed in Table 3.2.

Table 3.2 Flow limited versus diffusion limited clearance; both contribute to rebound

In addition to reducing solute clearance, disequilibrium has a significant impact on the method for drawing the post-dialysis BUN. A method that yields a modeled dialyzer clearance equivalent to the actual cross-dialyzer clearance is shown in Table 3.3. If the sample is drawn too soon, before potential access recirculation has dissipated, the dialysis dose , expressed as a delivered clearance, will be overestimated, putting the patient in jeopardy from under-dialysis. If drawn too late, the dose will be inconsistent from treatment to treatment.

Table 3.3 Blood sampling technique to measure the post-dialysis BUN

8 Intermittent Versus Continuous Dialysis

Solute disequilibrium is a consequence of high clearances applied intermittently. This phenomenon together with the self-limiting nature of intermittent dialysis as described above reduces the treatment efficiency, which means that more dialysis (clearance × time) must be applied to achieve the same concentration-lowering effect as continuous dialysis . When dialysis is applied continuously (e.g., continuous PD) or for native kidney function, constant replenishment of solute on the blood side (G) eliminates this inefficiency, and solute disequilibrium is essentially nonexistent. When minimum standards for PD and HD are compared, it appears that patients maintained with continuous PD require approximately half of the weekly clearance × time required by HD patients. Two theories have been put forth to explain this observation. One is based on peak urea concentrations, claiming that peak concentrations correlate better with overall uremic toxicity than mean levels, and the other is based on solute disequilibrium, claiming that toxic solutes are sequestered in remote compartments that equilibrate more slowly with the dialyzed compartment, essentially preventing the dialyzer from completing its job. Slow continuous treatments eliminate peaks and allow time for equilibration. Both theories have a basis in mathematical modeling and both produce similar solute concentration profiles under a variety of conditions as discussed below under “Dosing Frequent Dialysis” [30].

Although less efficient than continuous treatment, intermittent treatments are much easier to measure. Continuous clearances such as PD or native kidney function require collections of urine and/or dialysate during a defined time period. Intermittent hemodialysis clearances only require measuring the change in blood concentrations from beginning to end of the treatment and applying a model of solute kinetics as described above. Blood sampling alone is required; collection of dialysate is not necessary.

9 Practical Differences Between Hemodialysis Kt/V and Native Kidney Glomerular Filtration Rate (GFR)

In comparison with the native kidney, the clearance concept and definition are the same but the methods for measuring and expressing clearance differ, as shown in Table 3.4. For HD, urea is the preferred marker solute instead of creatinine because of the red cell creatinine disequilibrium discussed above, the additional patient-specific information obtained about protein nutrition, and the sensitivity of urea clearances to dialyzer effectiveness. Urea is not favored as a measure of native kidney clearance because tubular urea reabsorption is variable and unpredictable. Most current incenter dialysis treatments are intermittent, so the expression of dose must take into account the time during which the patient is not dialyzed. Expressing the dose as a clearance per dialysis satisfies this requirement as long as the frequency is specified as part of the dose. Instead of body surface area, the denominator for the dialysis dose is the volume of urea distribution, an automatic result of urea kinetic modeling as noted above and a mathematical convenience. Lastly, the fluctuations in urea concentration between and during intermittent dialyses allow measuring the dose by mathematical modeling without need for dialysate collection.

Table 3.4 Hemodialysis Kt/V versus native kidney glomerular filtration rate (GFR)

10 Dosing Frequent Dialysis

As noted above, the efficiency of HD depends on the frequency, increasing with more frequent treatments and eventually reaching maximum efficiency with continuous treatment. To include frequency in the dose, the peak concentration hypothesis [31] has been applied, which redefines the clearance as the removal rate divided by the average peak concentration [32]. This newly defined continuous equivalent clearance , called “standard Kt/V” (stdKt/V) is expressed as a fractional clearance similar to spKt/V, but as a weekly clearance similar to PD. The target is slightly higher than the target for continuous PD (2.0 per week) and is independent of dialysis frequency. Figure 3.7 shows the relationship between spKt/V and stdKt/V for different frequencies of dialysis. Of note, the current minimum standard for spKt/V is 1.2 per dialysis 3×/week, which corresponds to a stdKt/V of 2.0/week as shown in Fig. 3.7.

Fig. 3.7

Single pool versus continuous equivalent (standard) Kt/V. The single-pool dose per dialysis on the horizontal axis is compared to the equivalent (standard) weekly dose on the vertical axis. When given three times weekly, the currently accepted minimum dose is 1.2 per dialysis, which closely matches the minimum dose in the USA for continuous PD (large circle)

An explicit simplified equation, based on a fixed volume urea kinetic model has been developed for converting eKt/V to stdKt/V [27]:

$$_{\text{std}}{\rm Kt}/{\rm V}=\frac{10080\frac{1-{{\rm e}^{-{\text{eKt/V}}}}}{\rm t}}{\frac{1-{{e}^{-{\text{eKt/V}}}}}{\text{eKt}/{\rm V}}+\frac{10080}{\rm Nt}-1}.$$

(3.11)

A recent modification of Eq. 3.11 allows variations in urea volume and K_r [33]:

$$_{\text{std}}{\rm Kt}/{\rm V}\ \ =\ \ \tfrac{S}{1\,\ -\ \frac{0.74{\rm U}{{\rm f}_{\rm W}}}{\rm F\cdot V}}\ \ +\ \ {\rm Kr}\frac{10080}{\rm V},$$

(3.12)

S is the patient’s stdKt/V from Eq. 3.11; Uf_w is the patient’s weekly fluid removal in ml; F is the dialysis weekly frequency; V is the patient’s urea distribution volume in ml; K_r is the patient’s native kidney urea clearance in ml/min; 10080 is the number of minutes in a week.

11 Adequacy of the Dose

The question of adequacy relates to native kidney function as well as dialysis. We have a vague sense that GFRs > 20 ml/min are adequate, but some patients are able to tolerate GFRs as low as 5–10 ml/min for sustained periods of time [34]. The established minimum dose for PD patients is a weekly urea clearance index (Kt/V) of 1.7 [35]. The latter translates, for an average size patient with a urea volume of 30 L, to about 5 ml/min. Recall that GFR overestimates urea clearance because urea is reabsorbed by the native kidney, and it underestimates creatinine clearance because creatinine is secreted. Since the dialyzer has neither reabsorptive nor secretive functions, urea clearance should correspond to native kidney GFR on average. This reasoning leads to a conclusion that the minimum level of dialysis for continuous PD is equivalent to a barely acceptable level of native kidney function; hence the word “minimum” should be emphasized. For HD patients, standard Kt/V (see above) has been introduced to allow comparisons among more frequent and continuous clearances, including native kidney function. Published USA guidelines specify a minimum stdKt/V 2.0/week, which translates to about 7 ml/min for an average size patient. These surprisingly low levels of replacement function are based on outcomes studies such as the HEMO and ADEMEX studies that failed to show improvement in mortality and various secondary outcomes including hospitalization rates when the dose was increased [23, 35].

Reports of improved outcomes in patients dialyzed more frequently led investigators to suggest that intermittent treatments have intrinsic limitations that can only be overcome by increasing the frequency of treatments to 4–6 sessions per week. Solute kinetic analysis also suggested that increasing the treatment time would be more effective when applied more than 3×/week (see Fig. 3.7). In keeping with these theoretical considerations and marked benefits reported from uncontrolled studies, controlled clinical trials showed significant improvements in patient outcomes but somewhat less impressive than anticipated. The US National Institutes of Health-sponsored Frequent Hemodialysis Network study found that short daily incenter dialysis for 1 year improved the primary composite outcome of survival + reduction in left ventricular (LV) mass [36], the latter mainly in patients with ventricular hypertrophy. Quality of life was also improved. A similar improvement in LV mass was noted in a smaller Canadian study that compared frequent nocturnal HD with standard treatments given three times per week [37]. Together with findings of a significant reduction in pre-dialysis blood pressure, the data suggest that accumulation of fluid between dialyses is detrimental, but correctable by an increase in dialysis frequency. Phosphorus control was also improved as evidenced by lower pre-dialysis serum concentrations and a reduced requirement for oral phosphate binders. Whether the predictable increase in removal of other small solutes contributed to the clinical improvements is not possible to dissect from the data. For the present, more frequent dialysis is recommended for patients who prefer it and for patients with poor control of BP, volume, or serum phosphorus.

It is important to distinguish between adequate dialysis and adequate care of the patient. These distinct concepts are sometimes confused. Dialysis is the major focus of the nephrologist, but it is only a subset of the latter. Care certainly would be considered inadequate if it consisted only of dialysis and assessment of the dialysis dose . Measures of the adequacy of care in other spheres are also required. Patients approaching the need for dialysis usually bring with them a legacy of medical problems some of which may have contributed to the decline in kidney function. These problems are not necessarily alleviated or even improved by dialysis, and usually require attention, sometimes more attention than the dialysis itself.

12 Influence of Native Kidney Function on the Dose

Considered precious and frequently measured in the months and years prior to starting dialysis, residual native kidney function (K_r) is largely ignored once dialysis has begun. Perhaps use of terminology such as “replacement therapy” gives the impression that it no longer matters. The fallacy of this concept was well shown by the Netherlands Cooperative study where the mortality rate in patients with no K_r exceeded that of patients even with a K_r of 1–3 ml/min by an order of magnitude [38, 39]. For patients managed with PD, K_r is measured with each assessment of dialysis adequacy but the practice of collecting the patient’s urine to measure K_r in HD patients is unusual. Several factors may explain this seemingly strange behavior: (1) PD patients are schooled in self-care and tend to be more self-directed. (2) Adequacy of dialysis is more difficult to measure in PD patients so it is done only 3 or 4 times/year instead of monthly in HD patients. (3) Combining K_r with K_d is conceptually easier in PD patients where simple addition suffices (see below).

Once the dialysis dose is reduced, K_r must be monitored carefully to guard against under-dialysis when kidney function deteriorates further. Opponents of K_r measurements point to the negative psychological impact on patients whose treatment time requires an increase when K_r diminishes or is lost. Caregivers must then struggle to convince the patient that a higher dose of dialysis is necessary. Financial providers might also object to equal pay for reduced and full (anuric) doses of dialysis (Table 3.5) [38, 40–48].

Table 3.5 Clinical consequences due to loss of K_r

Regardless of efforts to measure K_r, efforts to preserve native kidney function in patients prior to initiating dialysis should be continued after dialysis is started. Table 3.6 lists recommended precautions and practices to preserve K_r.

Table 3.6 To preserve native kidney function

Combining native kidney urea clearance with continuous dialysis clearance is a simple matter of addition, but combining with intermittent (HD) urea clearance requires manipulation of the data to account for their non-simultaneous occurrences. As noted above, intermittent dialysis is less efficient than continuous dialysis, so adjustments for differences in efficiency must be made as well. The first method listed in Table 3.7 was also the first used and continues to be applied:

$${\rm Kt}/{\rm V}=\frac{{{\rm K}_{\rm d}}\times {{\rm T}_{\rm d}}+{{\rm K}_{\rm r}}\times {{\rm T}_{\rm r}}}{\rm V},$$

(3.13)

K_d is the dialyzer clearance , T_d is the treatment time, K_r is the patient’s native kidney clearance, T_r is the inter-dialysis interval, and V is the urea distribution volume. Since K_r has its major impact between dialyses, it is reasonable to use the inter-dialysis time interval (first column in Table 3.8) as a multiplier when calculating K_r × T_r. To account for differences in efficiency, T_r can be inflated, as shown in the second column of Table 3.8.

Table 3.7 How to incorporate K_r into Kt/V and stdKt/V

Table 3.8 Inflation of the inter-dialysis interval to account for the greater efficiency of K_r

The second method listed in Table 3.7 involves reducing the dialyzer component to a continuous equivalent clearance (e.g., standard K or stdKt/V as described above), followed by simple addition. Care must be taken to avoid including K_r in the method for downsizing K_d [33].

Alternatives to Urea Modeling

The urea reduction ratio (URR), defined as (C₀ − C)/C₀ where C₀ is the pre-dialysis BUN and C is the post-dialysis BUN, is a crude measure of urea extraction during a single dialysis. Its strength is simplicity, and it involves little or no manipulation of the raw data, two advantages that are perhaps the reasons it was chosen by the US Centers for Medicare and Medicaid Services (CMS) for monitoring its constituent dialysis clinics. The URR cannot be used to measure continuous clearances, does not include residual kidney function , and fails to incorporate the additional clearance afforded by ultrafiltration, sometimes as much as 20–30 % of the total Kt/V . Urea generation during dialysis is also not accounted for, an especially important factor during prolonged dialysis sessions.

Simplified formulas for estimating Kt/V from formal urea modeling are available as well. The most popular was developed by Daugirdas and recently upgraded to include more frequent dialyses [49, 50]:

$$\frac{\rm K\cdot \rm t}{\rm V}=-\ln\left( \rm R-0.03 \right)+\left( 4-3.5\cdot \rm R \right)\frac{\Delta \rm BW}{\rm BW},$$

(3.14)

R is the ratio of post-dialysis BUN to pre-dialysis BUN. This measure is especially helpful in population studies where the opportunity for modeling individual patients is not available.

Cross-dialyzer solute clearance can be measured as a change in conductivity in response to a pulsed change in the inlet dialysate concentration [51, 52]. Most dialysis delivery systems monitor dilution of a dialysate concentrate using conductivity meters, so the machine is already poised to measure “conductivity clearance,” better termed “ionic dialysance.” Since sodium and its accompanying anion are responsible for > 90 % of the dialysate conductivity, conductivity changes simply reflect sodium dialysance, which is nearly identical to the clearance of urea (and other small solutes). Figure 3.8 shows the pulsed change in conductivity induced on the dialysate inlet side (ΔC_in) and the response (ΔC_out) on the outlet side recorded by conductivity electrodes placed in the inflow and outflow dialysate lines. The ionic dialysance is calculated as [51, 53]:

$${{\rm D}_{\text{ionic}}}={{\rm Q}_{\rm d}}\left[ \frac{\Delta {\rm C_{\rm in}}-\Delta {\rm C_{\rm out}}}{\Delta {\rm C_{\rm in}}} \right].$$

(3.15)

Fig. 3.8

Conductivity profiles illustrate the online clearance method. The upper graph shows conductivity in the dialysate inflow line during a 3-min increase in the dialysate concentration. The lower line records the conductivity response in the dialysate outflow line

Equation 3.15 provides an instantaneous measure of small solute clearance, equivalent to cross-dialyzer urea clearance. It must be measured several times during the dialysis to obtain an average for the entire treatment to generate a measure equivalent to urea Kt/V. Advantages to this method include real-time monitoring, no blood sampling or analysis, no disposables, and ready use of body surface area as the denominator. Disadvantages include the need for multiple measurements during each dialysis, and need for an independent measure of V to meet current standards, which are measured as Kt/V.

Some authorities have argued that urea is a poor surrogate for uremic toxins, suggesting that Kt/V urea is inappropriate as a measure of dose [54, 55]. This argument fails to consider that absolute levels of urea are not part of Kt/V and that urea is simply a marker for small solute clearance, as noted above. Comparison with PD, however, and the development of standard Kt/V suggest that a sequestered solute might be a better marker [56, 57]. Other solutes too, such as larger (or middle) molecules and protein-bound toxins might be more representative [58–60], especially for the residual syndrome. A comparison among these marker solutes is presented in Table 3.9.

Table 3.9 Solutes cleared less readily than urea

Removal of salt and water has been highlighted as an essential part of the dose or prescription [61]. Fluid accumulation between dialyses must be limited by dietary restriction, and the excess must be removed during dialysis to prevent states of fluid overload and its consequences, including hypertension, pulmonary edema, and death. Rapid removal of fluid, however, has been associated with hypotension and adverse cardiac consequences including arrhythmias and myocardial stunning [62]. Uncontrolled studies have shown that these adverse consequences are correlated with the treatment time, leading some to recommend that the patient’s treatment time be extended to a minimum of 4 h, regardless of Kt/V, and/or that a maximum rate of fluid removal be set at 10–15 ml/kg body weight [63–65]. These recommendations seem reasonable although they require more of the patient’s time, and their validity has not been established in controlled clinical studies.

Although fluid removal by ultrafiltration during dialysis is an essential requirement for most patients, it is not essential for some. In contrast to solute removal, some uremic patients require no fluid removal and conversely, removal of fluid alone will never reverse uremia. Fluid accumulation is therefore not an essential part of the uremic syndrome, and the ultrafiltration component of the dialysis dose must be considered adjunctive therapy.

13 The Future of Dosing

In view of continued high morbidity and mortality rates and failed attempts to improve the outcomes of dialysis patients including improved biocompatibility of dialyzer membranes, higher clearances, high-flux dialysis, increases in thrice weekly Kt/V, and more frequent or prolonged treatments, it is reasonable to look elsewhere for an explanation and question current methods for measuring the dialysis dose. Contributions of the native kidney to personal health may be subtle and yet to be discovered, perhaps analogous to erythropoietin support of red cell mass. Patient comorbidities, independent of the kidney failure, may contribute to the high mortality. Poorly dialyzed solutes such as those listed in Table 3.9 may be responsible. However, one must not lose sight of the remarkable ability of dialysis to prolong life that would end within a few days in an anuric patient. The prolongation of life is surely due to removal of small dialyzable (urinary) solutes, reducing their concentrations in the patient to sub-lethal levels. Dialysis does nothing more than remove small solutes by diffusion across a relatively tight semipermeable membrane. There is nothing complex or mysterious about therapeutic dialysis. Therefore, first and foremost in our responsibilities to the patient should be a measure of small solute clearance. After that, the field is open to further exploration and treatment of the residual syndrome, which should be encouraged.