2.1 Development of Formulas Determining the Flow Rate Ratio W:S:B:A

Table 1 specifies the concentrations of the ingredients in the concentrates S , B and A . Figure 1 shows a scheme of the proposed system. The flow rates of stream B for any desired concentration of bicarbonate and of stream S for any desired concentration of sodium in the final dialysis fluid at the ratio W:S:B:A of 45 (45X) are calculated using the formulas presented subsequently. The flow rate of stream A remains constant at 1.0. Finally, the flow rate of stream W is adjusted so that the ratio W:S:B:A remains constant at 45 (45X).

In addition to supplying several of the dialysis fluid ingredients, stream A allows adjustment of the pH of the dialysis fluid, which would be dangerously high if only streams W , S, and B were operating [13]. Dialysis fluid pH values higher than 7.8 cause precipitation of ingredients of the dialysis fluid (e.g., calcium) [4, 9, 13]. Low levels of dialysis fluid pH have been associated with blood clotting in the dialyzer [14]. To optimize safety, the pH of the dialysis fluid should ideally be between 6.8 and 7.2 [12]. Chemical reaction between the sodium bicarbonate in stream B and any of the three acids in stream A lowers the final concentration of bicarbonate and adds dissolved carbon dioxide—and carbonic acid—to the dialysis fluid, thereby maintaining the pH within the safe range [7, 12]. After transfer into the blood and metabolism of the acid anion of stream A to carbon dioxide and water, the sodium ion gained as sodium acetate or sodium citrate reconstitutes the buffer base lost in the dialysis fluid with the titration in the dialysis fluid of sodium bicarbonate by the acid component in stream A [10].

Table 2 shows the concentrations of electrolytes delivered by streams S , B, and A to the final dialysis fluid, plus the concentrations of dextrose and acid delivered to this fluid by stream A when the ratio W:S:B:A is 42:1:1:1. In this case, the concentrations of sodium and chloride delivered to the final dialysis fluid through stream S plus the concentrations of sodium and bicarbonate delivered through stream B are all 21.5 mmol/L. These concentrations of 21.5 mmol/L are used to calculate the required flow rates of streams W , S , and B for any desired concentrations of sodium and bicarbonate and for the corresponding concentration of chloride in the dialysis fluid.

The concentration of sodium delivered to the final 45X dialysis fluid by stream A does not change with different W : S : B : A ratios because the flow rate of stream A is constant. Calculation of the flow rate ratio W : S : B : A for any desired value of [Na]_df requires accounting for the dialysis fluid concentration of sodium provided by stream A . The flow rates for streams B , S , and W for any desired bicarbonate and sodium dialysis fluid concentrations are calculated using the formulas contained in Table 3. Bicarbonate is contained in stream B . The desired bicarbonate concentration is the product of the concentration of bicarbonate delivered to a dialysis fluid volume of 45 L by a flow rate B equal to 1 (21.5 mmol/L) times the unknown flow rate B (formula 1). The desired flow rate B for any specific value of dialysis fluid bicarbonate concentration is obtained by solving formula 1 for B (formula 2).

Sodium is present in streams S , B , and A . Flow rates of all three streams must be included in the calculation of the flow rate ratio W : S : B : A for any desired dialysis fluid sodium concentration. The sodium concentration delivered to the dialysis fluid by stream A is 63 mmol/L (Table 2). Any flow rate of stream B will contain equal concentrations of bicarbonate and sodium (Tables 1 and 2). Therefore, the numerical value of the desired bicarbonate concentration can be used in the calculation of the flow rate of stream S as the concentration of sodium provided by stream B to the final dialysis fluid. Formula 3 calculates the desired dialysis fluid sodium concentration. The desired flow rate S for any specific concentration of sodium in the dialysis fluid is obtained by solving formula 3 for S (formula 4). When stream A contains sodium diacetate instead of acetic acid or citric acid, 67 should be substituted for “63” in formula 4.

The flow rate of stream W required for keeping the total W : S : B : A flow rate at 45 is calculated by formula 5. Chloride is present in streams S and A . The concentration of chloride provided to the final dialysis fluid by stream A is 68.3 mmol/L (Table 2). The concentration of chloride in the dialysis fluid is calculated by formula 6.

3.1 Calculations of W:S:B:A Flow Rates by This Method

An EXCEL spread sheet allowing calculation of the W : S : B : A flow rates and of dialysis fluid chloride for any desired combination of sodium and bicarbonate concentrations in the dialysis fluid by formulas 2, 4,5, and 6 is provided. The results presented in this section contain only calculations in hypothetical patients. Application of the proposed method in actual patients and measurements of electrolyte concentrations have not been performed. Table 4 shows representative W : S : B : A ratios for a wide range of combinations of desired dialysis fluid sodium and bicarbonate concentrations and the corresponding dialysis fluid chloride values.

3.2 Ranges of Dialysis Fluid Sodium and Bicarbonate Concentrations Allowed

The ranges of sodium and bicarbonate concentrations in the dialysis fluid that can be obtained with any hemodialysis system dictate the ranges of dysnatremias and metabolic acid–base disorders that can be treated by this system. Commercially available four-stream hemodialysis systems can obtain a 130–160 mmol/L sodium concentration range [11, 15]. The upper limit of the sodium range in the four-stream system presented in this report is considerably higher than any clinical requirement might demand. The lower limit of this range represents the major advantage offered by this new system. With this system the sodium concentration reaches its lower limit when the flow rate of stream S becomes zero. From formula 4, the flow rate of stream S becomes zero when sodium concentration is equal to bicarbonate concentration plus 63. Thus, the lower limit of sodium concentration is determined by the desired bicarbonate concentration. For example, the lower limit of sodium concentration is 100 mmol/L when bicarbonate is 37 and 90 mmol/L when bicarbonate concentration is 27 mmol/L.

The upper limit of bicarbonate concentration is reached when the flow rate of stream S becomes zero and is therefore dependent on the desired concentration of sodium. For example, the upper limit of the range of bicarbonate concentration is 74 mmol/L at a sodium concentration of 137 mmol/L, 37 mmol/L at a sodium of 100 mmol/L, and 27 mmol/L at a sodium of 90 mmol/L. The lower value of bicarbonate concentration that can be obtained by this system is zero when the flow rate of stream B is zero.

3.3 Safe Range of Dialysis Fluid Bicarbonate Concentration

The safe range of the bicarbonate concentrations corresponding to a dialysis fluid pH range of 6.8–7.2 is calculated as follows: When stream A contains acetic acid with a concentration of 4 mmol/L in the dialysis fluid (Table 2), titration of this acetic acid by bicarbonate will result in a sum of concentrations of carbonic acid and dissolved carbon dioxide very close to 4 mmol/L. [7, 16] Conversion of 4 mmol/L of carbonic acid plus dissolved carbon dioxide, which represents by far the greatest part of the 4 mmol/L, to partial pressure of carbon dioxide (P _CO2) using a conversion coefficient of 0.0301 mmHg per mmol/L [17] results in a P _CO2 of 4/0.0301 = 133 mmHg. For a temperature of 37°C, the dissociation constant (pK) of carbonic acid is 6.108 at a pH of 7.2 [17], and 6.199 at a pH of 6.8 [18]. The bicarbonate values that correspond to pH values of 7.2 and 6.8 at a P _CO2 of 133 mmol/L, calculated by the formula 0.0301 × P _CO2 × 10^(pH–pK) which is derived by solving the Henderson–Hasselbalch formula for bicarbonate [17], are 4 × 10^{(7.2–6.108)} = 49.4 mmol/L for a pH of 7.2 and 4 × 10^{(6.8–6.199)} = 16.0 mmol/L for a pH of 6.8. One point of caution for choosing the low value of the range of dialysis fluid bicarbonate concentration consists of the fact that the carbonic acid pK of 6.199 for a pH of 6.8 was obtained from a linear regression of the pK on pH at pH values between 7.0 and 7.6 on pK at 37°C [18], not from experimental data. Measuring the pH of the dialysis fluid after each change in its composition is required.

3.4 Prescription of the Sodium and Bicarbonate Concentrations in the Dialysis Fluid

The prescription of sodium concentration in the dialysis fluid for correction of any dysnatremia requires the following steps: (a) Pseudohyponatremia should be ruled out [19]. (b) Osmotic demyelination [20, 21] should be prevented by choosing the target dialysis fluid sodium concentration. The target rise in serum sodium concentration for treating hyponatremia with infusion of hypertonic saline was set at 4–6 mmol/L. [22] Larger increase in serum sodium, up to 12 mmol/L, in a hemodialysis session, appears to be safe [2, 23]. (c) The effects of the Gibbs–Donnan equilibrium principle on the sodium concentrations in serum, which contains polyanions, and in dialysis fluid, which does not, should be accounted for in the prescription of the dialysis fluid sodium concentration [24, 25]. (d) Changes in the external balances of sodium, water, and potassium which affect the change in serum sodium concentration during treatment of hyponatremia, other than the changes from a hemodialysis session, should be accounted for [26].

The prescription of the dialysis fluid bicarbonate concentration requires accurate diagnosis of the underlying acid–base disorder(s). Although metabolic acidosis represents the most common acid–base abnormality encountered pre-dialysis and has several adverse effects [27-29], respiratory disorders are also frequent [4], and metabolic alkalosis requiring correction by dialysis is also encountered [30, 31]. The serum total carbon dioxide (TCO ₂), which is routinely measured in serum along with other electrolytes, constitutes an inadequate indicator of the acid–base status pre-hemodialysis [32-35]. Metabolic alkalosis is encountered in uremic patients and can be treated by dialytic methods [33, 36]. Blood gas analysis should be performed [33, 36].

A hypothetical case requiring correction of both severe hyponatremia and metabolic acidosis using the four stream system of this report is presented. A patient having missed several sessions of hemodialysis presents with seizures, coma, serum sodium of 100 mmol/L, arterial blood pH of 7.21, arterial bicarbonate of 8 mmol/L and arterial P _CO2 of 20 mmHg. A slow hemodialysis session with this new method is planned with targets of 108 mmol/L for serum sodium and 25 mmol/L for arterial bicarbonate. Serum glucose, protein, and lipid concentrations are normal allowing an estimate of serum water content at 93% and of sodium concentration in serum water of 100/0.93 = 107.5 mmol/L. An interstitial fluid to-plasma water Gibbs–Donnan coefficient of 0.950 has been used for cation concentrations [37]. Using the same coefficient for dialysis fluid-to-plasma water sodium concentrations, the dialysis fluid sodium concentration value required for a serum sodium of 108 mmol/L (sodium concentration in serum water of 108/0.93 = 116.1 mmol/L) is 0.950 × 116.1 = 110.3 mmol/L. The W : S : B : A flow rate ratio of 41.80:1.04:1.16:1 is obtained by entering 25 for dialysis fluid bicarbonate concentration and 110.3 for dialysis fluid sodium concentration in the EXCEL flow sheet. Thus each 45 L of dialysis fluid consists of 41.80 L of product water, 1.04 L of concentrate S , 1.16 L of concentrate B , and 1 L of concentrate A .

Measurements in the dialysis fluid reveal a pH of 6.86, a dialysis fluid sodium of 110.5 mmol/L, and a dialysis fluid bicarbonate of 25 mmol/L. The relation between the sodium concentrations in serum and serum water used applies only when serum water content is 93%, the Gibbs–Donnan coefficient used represents an average estimate, and the change in serum bicarbonate concentration cannot always be predicted with accuracy. These reasons dictate the potential need of changing the dialysis fluid composition by monitoring the concentrations of sodium and bicarbonate (or TCO ₂) in serum during the hemodialysis session.