Sodium-Based Osmotherapy in Continuous Renal Replacement Therapy: a Mathematical Approach

Abstract

Cerebral edema, in a variety of circumstances, may be accompanied by states of hyponatremia. The threat of brain injury from hypotonic stress-induced astrocyte demyelination is more common when vulnerable patients with hyponatremia who have end stage liver disease, traumatic brain injury, heart failure, or other conditions undergo overly rapid correction of hyponatremia. These scenarios, in the context of declining urinary output from CKD and/or AKI, may require controlled elevations of plasma tonicity vis-à-vis increases of the plasma sodium concentration. We offer a strategic solution to this problem via sodium-based osmotherapy applied through a conventional continuous RRT modality: predilution continuous venovenous hemofiltration.

Introduction

Generally, sodium-based osmotherapy (SBO) is tonicity therapy with the aim of reducing cerebral edema during states of hypotonic hyponatremia. Depending on the circumstance, plasma tonicity may be increased or decreased. Because the sodium concentration ([Na]) in the plasma at any time (t), P_Na(t), and accompanying anions constitute the bulk of plasma tonicity, SBO is predicated on gradual alteration of P_Na, in contrast to the relatively rapid P_Na increases imposed by steep dialysate-to-plasma [Na] gradients associated with conventional hemodialysis. Generally, osmotherapy is carried out when there is severe hyponatremia, oligo-anuria, and inability to excrete sufficient electrolyte-free water to maintain isotonicity (^1–3). Thus, SBO has played a role in patients with end stage liver disease and advanced heart failure.

Osmotic demyelination syndrome may transpire in patients who are hyponatremic with end stage liver disease after abrupt P_Na elevations during orthotopic liver transplantation (⁴,⁵). Correspondingly, presurgical elevation of P_Na among individuals prone to osmotic demyelination may be prophylactic. Less commonly, supranormal P_Na elevations have been imposed during traumatic brain injury or intracerebral hemorrhage to reduce brain swelling (⁶,⁷).

To rectify severe plasma hypotonicity, a relatively hypertonic/hypernatric solution is administered in a controlled fashion during continuous renal replacement therapy (CRRT), and P_Na is increased at rates consistent with consensus guidelines (⁸). Controlled P_Na elevations can be achieved by hemodialysis, but special device- and protocol-specific modifications are required to avoid dialysis disequilibrium syndrome (⁹). Sustained low-efficiency dialysis or slow continuous ultrafiltration with simultaneous infusion of a solution relatively hypernatric to P_Na is also feasible (¹⁰). In terms of CRRT, SBO has been conducted with continuous venovenous hemofiltration (CVVH) (¹¹,¹²), continuous venovenous hemodialysis (¹³), or continuous venovenous hemodiafiltration (¹⁴).

General Principles of SBO

SBO can be implemented as a stepwise approach based on established biophysical principles governing sodium transit via predilution CVVH. The following urea- and sodium-based kinetic methodology involves six steps: (1) establishing a time-dependent [Na] gradient [∇Na(t)] between the plasma and a replacement fluid (RF) based on a sodium concentration adjustment ratio (NaAR) (Figure 1), (2) estimation of total body water (TBW), (3) determination of sodium ion dialysance (D_Na) that approximates the urea hemofilter transfer rate, (4) on-treatment prediction of P_Na(t), (5) determination of sodium balance, and (6) troubleshooting.

Figure 1.: Plasma sodium concentration is exponentially changed by the replacement fluid sodium concentration and flow rates of plasma, replacement fluid, and ultrafiltration. The extracorporeal circuit is comprised of a hemofilter and replacement fluid. The plasma inflow rate (Q_P) is advected by a sodium concentration [Na]-adjusted replacement fluid (Na_RF2). The sodium concentration [Na] gradient, ∇Na(t), equals the [Na] difference between Na_RF2 and plasma sodium concentration at any time (t), P_Na(t). The sodium concentration adjustment ratio (NaAR) is defined by sodium ion dialysance (D_Na), time, and total body water volume (Watson volume, V). Hemofilter effluent equals the sum of RF2 flow rate (Q_RF2) and net ultrafiltration flow rate (Q_UF). ∇Na(t), [Na] gradient at time (t) or P_Na(t)-to-Na_RF2 difference; RF2, [Na]-adjusted replacement fluid 2.

Predilution CVVH

RF is infused postblood pump and prehemofilter at a specified rate (Q_RF) into the plasma flow (Q_P) to raise (or lower) P_Na from its pretreatment level, Na_Pre or P_Na(0), to its post-treatment level, Na_Post or P_Na(t) (Figure 1). Employing a fixed-volume model where TBW volume is constant and analogizing to established urea kinetic principles, the rate change of P_Na can be computed over a specified time interval (¹⁵,¹⁶). Thus, sodium advected from the RF gradually increases Na_Pre to Na_Post, with their difference equaling ΔNa (Equation 1).

To produce an [Na] gradient, a stock RF (RF1) of nominal [Na] Na_RF1 is adjusted to Na_RF2, thereby establishing ∇Na(0), the maximal [Na] gradient at time (0) (Equation 2). ΔNa is also the product of ∇Na(0) and NaAR, and NaAR is the ratio of ΔNa to ∇Na(0) (Equation 3).

Sodium Kinetic Principles

The NaAR is a function of treatment time (t), TBW (V, Watson volume), and D_Na. The NaAR is similar to the urea reduction ratio (URR, Equation 4), with equivalence of D_Na to the urea clearance constant, K_Urea (Equation 4, A and B).

Step 1: Establishing the Sodium Concentration Gradient

Replacement Fluids

To generate ∇Na(0), the sodium-adjusted RF [Na], Na_RF2, is often simply assigned an [Na] that is 6–10 mM greater than Na_Pre. However, Na_RF2 can be more rationally determined from intrinsic parameters of predilution CVVH (Tables 1 and 2). First, by predetermining a target Na_Post, ΔNa is defined. Second, estimation of NaAR from URR (Equations 3 and 4) and rearrangement of Equation 3 yields Na_RF2 as Equation 5.In summary, urea kinetics function to approximate NaAR. These principles are illustrated by the following example.

Table 1. - Sodium-based osmotherapy parameters

Row	Parameter	Definition	Units
1	ΔNa	Post-treatment [Na] minus pretreatment [Na]	mmol/l, mM
2	∇Na(0)	[Na] gradient at time (t)=0	mmol/l, mM
3	[Na]	Sodium concentration	mmol/l, mM
4	ΣNa	Sodium balance	mmol
5	DNa	Dialysance of sodium ion	ml/min
6	Eff-NaRF	Effective replacement fluid [Na] from combined infusions of NaRF1 and NaH	mmol/l, mM
7	NaAR	Sodium concentration adjustment ratio	Dimensionless
8	NaH	[Na] of a defined hypo-, iso-, hypertonic solution H	mmol/l, mM
9	NaPre	Pretreatment PNa, i.e., PNa(0)	mmol/l, mM
10	NaPost	End treatment PNa	mmol/l, mM
11	NaRF1	RF1 [Na], unadjusted replacement fluid	mmol/l, mM
12	NaRF2	RF2 [Na], sodium-adjusted replacement fluid	mmol/l, mM
13	PNa(t)	Plasma [Na] at time (t)	mmol/l, mM
14	QH	Solution H flow rate	ml/min
15	QB, QP	Respective blood and plasma fluid flow rates	ml/min
16	QRF	Replacement fluid flow rate	ml/min
17	QUF	Net ultrafiltration flow rate	ml/min
18.	QEff	Combined flow rate of QRF1 and QH	ml/min
19	RF1	Replacement fluid 1	—
20	RF2	Replacement fluid 2	—
21	t	Time	min
22	URR	Urea reduction ratio	Dimensionless
23	V	Total body water, i.e., Watson volume	ml, L
24	V4M	Volume of added hypertonic saline (23.4%, 4 M)	ml, L
25	VRF1	Volume of RF1	ml, L
26	VRF2	Volume of RF2	ml, L
27	VW	Volume of added sterile water	ml, L

Variables and abbreviations used in text and equations.

Table 2. - Sodium-based osmotherapy equations

Row	Description	Equation
1	Dialysance of sodium ion	DNa = –(V/t) × LN(1 – NaAR)
		DNa = QP × [(QUF + QRF)/(QP + QRF)]
2	Method 1 calculation of added water volume	VRF2 = VRF1 × (NaRF1/NaRF2)
		VW = VRF1 × [(NaRF1 – NaRF2)/NaRF2]
3	Method 2 calculation of water exchange volume	VX = VRF1 × (NaRF1 – NaRF2)/NaRF1]
4	Method 3 volume calculation of added 4 M hypertonic saline volume (23.4%)	V4M = VRF1 × (NaRF2 – NaRF1)/(Na4m – NaRF2)
5	Method 4 calculation of solution H fluid flow rate	QH = QEff × (NaRF1 – Eff-NaRF)/(NaRF1 – NaH)
6	Method 4 replacement fluid 1 (RF1) flow rate	QRF1 = QEff × (Eff-NaRF – NaH)/(NaRF1 – NaH)
7	Plasma flow rate calculation	QP = QB × (1 – hematocrit)
8	Sodium concentration at treatment time (t)	PNa(t) = PNa(0) + ∇Na(0) × (1 – e–DNa ·t/V); PNa(0) = NaPre
		PNa(t) = PNa(0) + (NaRF2 − NaPre) × (1 – e–DNa ·t/V)
		PNa(t) = NaPre + ([NaRF2 − NaPre] × NaAR)
9	Replacement fluid flow rate	QRF = QP × (DNa − QUF)/(QP − DNa); QUF = 0
10	Sodium balance at time (t)	ΣNa(t) = PNa(t) × (V − QUF × t) − (NaPre × V)
		ΣNa(t) = PNa(t) × (V − QUF × t) − (PNa(0) × V)
11	Sodium concentration adjustment ratio	NaAR = 1 – e–DNa ·t/V
		NaAR = ΔNa/∇Na(0) = (NaPost – NaPre)/(NaRF2 − NaPre)
12	Sodium concentration change at end-treatment time (t)	ΔNa = ∇Na(0) × NaAR
		ΔNa = NaPost – NaPre
13	Sodium concentration gradient, initial	∇Na(0) = NaRF2 – NaPre
14	Sodium concentration of RF2	NaRF2 = NaPre + (ΔNa/NaAR)
		NaRF2 = NaPre + [ΔNa/(1 – e–DNa ⋅t/V)]
15	Time at which specified PNa occurs (tX)	tX = –(V/DNa) × LN[(NaRF2 – PNa(tX))/(NaRF2 – NaPre)]
16	Ultrafiltration rate to achieve net zero sodium balance at time (t)	QUF(t) = ([NaPost × V] – [NaPre × V])/(NaPost × t)
		QUF(t) = (ΔNa × V)/(NaPost × t)
17	Urea reduction ratio	URR = 1 – e–KUrea ·t/V
		URR = (BUN(0) – BUN(t))/(BUN(0) – BUNDialysate)
18	Watson volume	VMan = 2.447 – 0.09156 × (age, yr)
		+0.1074 × (height, cm) + 0.3362 × (weight, kg)
		VWoman = –2.097 + 0.1069 × (height, cm) + 0.2466 × (weight, kg)

See Table 1 for definitions of variables.

Case 1.

A 42-year-old man, 178 cm and 90 kg, is anuric with stage 3 AKI. He has no peripheral edema. Laboratory data: Na_Pre, 116 mM; BUN(0), 80 mg/dl; hematocrit, 0.25. The target BUN and P_Na after 24 hours of CVVH are 48 mg/dl and 124 mM, respectively. First, NaAR approximating URR is calculated, with BUN_Dialysate as “zero.”Second, after NaAR is determined, ΔNa, ∇Na(0), and Na_RF2 are calculated.The time dependencies of Na_Post, NaAR, and ΔNa during prolonged SBO are tabulated in Table 3. Figure 2 demonstrates the effect of increasing ∇Na(0) on P_Na at NaAR of 0.4 over 1440 minutes of treatment. The random assignment of a 6–10 mM ∇Na(0) would have suboptimally elevated P_Na, underscoring this approach of using NaAR to determine Na_RF2. Note the relatively low NaAR complements the large ∇Na(0). Importantly, a low URR of 0.4 provides a therapeutic advantage by mitigating the risk of inducing cerebral edema by lowering overall urea flux.

Table 3. - Time-dependencies of plasma sodium concentration and sodium concentration adjustment ratio during sodium-based osmotherapy

Time (t, min)	PNa(0)	NaAR	ΔNa(t) (mM)	PNa(t) (mM)
0	116.0	0.0 (0.0)	0.0 (0.0)	116.0 (116.0)
360	116.0	0.12 (0.14)	2.4 (2.9)	118.4 (118.9)
720	116.0	0.23 (0.27)	4.5 (5.4)	120.5 (121.4)
1080	116.0	0.32 (0.37)	6.4 (7.5)	122.4 (123.5)
1440	116.0	0.40 (0.47)	8.0 (9.3)	124.0 (125.3)
2880	116.0	0.64 (0.71)	12.8 (14.3)	128.8 (130.3)
4320	116.0	0.78 (0.85)	15.7 (16.9)	131.7 (132.9)

Predilution continuous venovenous hemofiltration is carried out on a hypothetical 42-year-old, 178-cm, 90-kg man with P_Na(0) 116 mM and Watson volume 48.0 L for times shown. The replacement fluid is adjusted from a nominal [Na] of 140 mM to 136 mM to achieve a 20 mM [Na] gradient. Values in parentheses are those of a 42-year-old woman with a Watson volume of 39.1 L, treated with the same parameters. P_Na, plasma sodium concentration; NaAR, sodium concentration adjustment ratio; ΔNa(t), P_Na(t) minus P_Na(0); P_Na(t), P_Na at time (t); [Na], sodium concentration; P_Na(0), P_Na at time (t) = 0.

Figure 2.: Plasma sodium concentration increases are time- and sodium concentration gradient-dependent. Data are modeled from a hypothetical 42-year-old, 178-cm, 90-kg man with Watson volume 48.0 L (see text, Case 1). Plasma sodium concentration (P_Na) is 116 mM before predilution continuous venovenous hemofiltration is carried out at four different [Na] gradients. NaAR equals 0.4 after 1440 minutes of sodium-based osmotherapy. At end treatment, P_Na increases in direct proportion to ∇Na(0). ∇Na(0), [Na] gradient between plasma and replacement fluid at time (0).

Replacement Fluid Manipulation

In predilution CVVH SBO, the Na_RF1 is frequently lowered from a nominal level of 130 or 140 mM. For Case 1, Na_RF1 can be adjusted to an Na_RF2 of 136 mM by several methods (Figure 3) (¹¹,¹²): method 1, diluting RF1 (Na_RF1 140 mM) with 147 ml sterile water; method 2, exchanging 143 ml of RF1 (Na_RF1 140 mM) for sterile water; and method 3, addition of 7.8 ml of 4 M saline (23.4%) to 5 L of RF1 solution (Na_RF1 130 mM).

Figure 3.: Replacement fluid sodium concentration adjustment. Method 1: Sterile water is added to replacement fluid 1 (RF1) of volume V_RF1 and sodium concentration Na_RF1 to produce replacement fluid 2 (RF2) of volume V_RF2 and sodium concentration Na_RF2. Method 2: A volume from RF1 (V_X) is exchanged with sterile water to produce Na_RF2. Method 3: A volume of 4 M sodium chloride solution (V_4M) is added to RF1 to produce RF2 volume V_RF2 and Na_RF2. Method 4: Solution H is infused postblood pump and prehemofilter at flow rate Q_H in parallel with RF1 at flow rate Q_RF1 to produce a blended solution with an effective [Na] (Eff-Na_RF) at flow rate Q_Eff. H, solution of defined [Na]; Eff-Na_RF, effective-[Na] of RF1 and solution H; Na_H, solution H [Na]; Q_Eff, additive flow rate of Q_RF1 and Q_H; Q_H, solution H flow rate; Q_RF1, RF1 flow rate; Q_RF2, RF2 flow rate; V_4M, 4 M saline volume; V_W, water volume added to RF1; V_X, RF1 exchange volume.

Effective Replacement Fluid Sodium Concentrations

If institutional policy prohibits RF manipulations, an effective RF [Na] (Eff-Na_RF) equal to the desired Na_RF2 must be generated via flow-rate adjustments of an unadjusted RF1 and a separate solution (H; Figure 3, method 4) (¹⁴,^17–19). Peripheral infusion of 5% dextrose in water (D₅W) or sterile water by central vein may be used as “0” mM [Na] solutions (²⁰).

Step 2: Estimating TBW as Watson Volume

Watson Volume

NaAR is a function of time, D_Na, and TBW (V, Watson volume). Hence, accurate determination of V is critical. Consequently, the Watson volume, representing TBW as urea space, is used in subsequent calculations because it is a superior estimate of TBW compared to multiplication of body weight by an arbitrary factor, i.e., 0.5–0.6 (²,²¹). For Case 1, initial estimates of V for a 178-cm, 90-kg man and woman are 48.0 L and 39.1 L, respectively. For initial estimates of V, considerations of edema and third spacing of extracellular fluid are excluded, but accommodations for these factors can be made (see Additional Considerations).

Step 3: Dialysance of Sodium Ion

Sodium Ion Dialysance

Dialysance of sodium ion (D_Na) comprises three flow rates: plasma (Q_P), RF (Q_RF), and net ultrafiltration (Q_UF) (²²). Q_P has the greatest influence on D_Na by virtue of its greater magnitude. D_Na is also the product of Q_P and the filtration fraction as follows.We recommend a blood flow (Q_B) of 250–300 ml/min to promote clearance and prevent filter clotting (²³). As shown, at a Q_B of 300 ml/min and hematocrit (Hct) of 0.25, Q_P is 225 ml/min (Equation 7).

Application

In Case 1, NaAR at 1440 minutes equals 0.4. Thus, D_Na is resolved by specifying V and t and rearranging Equation 4B as Equation 8.

With D_Na known, Q_RF is determined by rearranging Equation 6 as Equation 9.

In summary, steps 1–3 determine an NaAR of 0.4 and a ∇Na(0) of 20 mM that yield a ΔNa of 8 mM. Similar results are obtained by increasing D_Na (i.e., greater NaAR) and proportionally decreasing ∇Na(0). For example, if NaAR is 0.6, ∇Na(0) becomes 13.3 mM and Na_RF2 becomes 129.3 mM. Also, the Na_RF2 that produces a specified ΔNa at time (t) is calculated from Equations 4B and 5 (Equation 10).

Step 4: Plasma Sodium Concentration during Osmotherapy

Targeting the Plasma Sodium Concentration

Because D_Na and TBW are constants within the constraints of a fixed-volume model, P_Na(t) can be projected over a specified treatment interval (t) (Equation 11).This concept is depicted in Figure 4 where time- and volume-dependencies of P_Na(t) are displayed for a man and woman of equal height and weight. The greater P_Na(t) of the woman throughout treatment is attributable to a lesser Watson volume. The time (t_X) when a specified P_Na(t_X) occurs is ascertained by substituting t_X into Equation 11 and solving for it.

Figure 4.: Plasma sodium concentration increases are time- and volume-dependent. Data are derived from a hypothetical 42-year-old, 178-cm, 90-kg man (M; see text, Case 1) with Watson volume 48.0 L and a 42-year-old woman (W) with Watson volume 39.1 L. The baseline plasma and replacement fluid sodium concentrations of both patients are 116 mM and 136 mM, respectively. Continuous venovenous hemofiltration treatment parameters are as follows: Q_P, 225 ml/min; Q_RF, 18.3 ml/min; Q_UF, 0 ml/min; and treatment time, 4320 minutes. The P_Na of the woman is greater at all time points due to her smaller Watson volume. Q_P, plasma flow rate; Q_RF, replacement fluid rate; Q_UF, net ultrafiltration fluid rate; P_Na, plasma sodium concentration.

Step 5: Sodium Balance during Osmotherapy

In a fixed-volume model of SBO, sodium accrual is inevitable as P_Na increases. If patient vulnerability to volume overload is present, net ultrafiltration is advised. Consequently, real-time net sodium balance (ΣNa) monitoring is critical and computed by Equation 13.In Case 1, ΣNa(1440) is +384 mmol if Q_UF = 0 but –62.4 mmol if Q_UF is 0.15 L/h or 3.6 L per day.The Q_UF that “zeroes” the sodium load at time (t) is calculated as 3.1 L per 24 hours by Equation 14.

Modeling Sodium Balance

For patients vulnerable to volume excess/overload, ΣNa should be modeled a priori, and we demonstrate this concept as follows.

Case 2.

A 30-year-old man with heart failure and stage 3B CKD develops AKI and dyspnea. The admission weight is 2 kg more than his last-reported hospital discharge weight. His vital signs are as follows: height, 170 cm; weight, 80 kg; temperature, 36.5°C; heart rate, 118 bpm; blood pressure 130/80 mm Hg; respiratory rate, 18 per minute; and Watson volume, 44.85 L. His laboratory data are as follows: Na_Pre, 120 mM; BUN, 50 mg/dl; serum creatinine, 4.2 mg/dl; and hematocrit, 0.33. Urine output is <0.05 ml/kg·h. A 24-hour Na_Post target of 126 mM is planned. Predilution CVVH is begun with parameters of Q_P 200 ml/min, Q_RF 50 ml/min, Q_UF 2.5 ml/min, and NaAR 0.74. An NaRF2 of 128 mM is formulated by adding 79 ml sterile water to an RF1 of 130 mM. To achieve net sodium balance of zero after 24 hours, net ultrafiltration of 2.14 L per 24 hours is required, as shown below. Ultrafiltration beyond 24 hours produces net total body sodium loss. Figure 5 depicts the evolution of P_Na(t) and ΣNa(1440) if Q_UF is 3.6 L per 24 hours.

Figure 5.: Plasma sodium concentration elevation without sodium accumulation is achieved by net ultrafiltration during predilution continuous venovenous hemofiltration. Treatment parameters during predilution continuous venovenous hemofiltration of a hyponatremic, 170-cm, 80-kg, 30-year-old man with Watson volume 44.85 L are as follows (see text, Case 2): Na_RF2, 128 mM; Q_P, 200 ml/min; Q_RF2, 50 ml/min; Q_UF, 2.5 ml/min; and treatment time, 1440 minutes. At end treatment, NaAR is 0.74 and P_Na increases from 120 mM to 126 mM (top plot). Negative sodium balance begins at t = 240 minutes. Cumulative sodium loss is 185 mmol at end treatment (bottom plot).

Sodium Balance with Edema

If the entire 2-kg excess weight is assumed isotonic to plasma, total body sodium balance must be recalculated. The Watson volume of the 78-kg man was 44.18 L and increased to 46.18 L from 2 L of edema. Achieving zero sodium balance requires just 0.06 L more net ultrafiltration. However, there is a 160-mmol sodium excess if edema is considered isotonic plasma (Equation 15). To shed the sodium surfeit, an additional 1.27 L of net ultrafiltration is required. Overall, net ultrafiltration of 3.47 L attains a P_Na(1440) of 126 mM at 76.53 kg.

Influence of Exogenous Fluids and Urine Output on Replacement Fluid Sodium Concentration

During SBO, the influence of exogenous cation (sodium and potassium)-containing fluids on P_Na and ΣNa must be tallied. Only cationic effects require analysis as anions follow pari passu. The RF [Na] is altered by infusions of exogenous fluids and/or urine output and produces a blended solution with an effective [Na] (Eff-Na_RF). Table 4 illustrates the 4-hour effects on Eff-Na_RF in a patient who receives three intravenous fluids, 0.45% saline and hypothetical solutions A and B. By evaluating a short time interval, the singular and collective effects of each fluid on Eff-Na_RF are exposed early on. In aggregate, with consideration of all inputs and outputs, the 4-hour effects on Eff-Na_RF and extracellular fluid volume are +0.8 mM and +0.05 L, respectively. Extrapolation of this analysis to a 24-hour interval may obligate readjustments of Na_RF1 and/or Q_UF. Lastly, elaboration of hypotonic urine increases Eff-Na_RF minimally, unless urine output is copious, i.e., >4 L per day.

Table 4. - Effects of intravenous solutions and urine output on the effective replacement fluid sodium concentration

Solution	RF	0.45%	Solution A	Solution B	UO	4-Hour Results a
Flow rate, L/h	2.0	Single dose	Single dose	Single dose	−0.1	—
Time, h	4.0	4.0	—	—	4.0	—
[Na], mM	130.0	77.0	154.0	40.0	50.0	—
Volume, L	8.0	0.10	0.10	0.25	−0.40	8.05
Cation, mmol	1040.0	7.7	15.4	10.0	−20.0	1053.1
Eff-NaRF, mM b	130.0	129.3	130.3	127.3	134.2	130.8

The replacement fluid is infused simultaneously with three separate solutions as shown, with ongoing urine output. To simplify calculations, the RF-potassium concentration is assumed equal to plasma potassium concentration and not described. RF, replacement fluid with [Na] 130 mM; UO, urine output; [Na], sodium concentration; Eff-Na_RF, effective [Na] of RF and one of the solutions listed and/or UO.

^aAggregate effect of solutions and urine output on Eff-Na_RF.

^bIsolated effect of each solution or urine output on Eff-Na_RF.

Acute Sodium Loading

Sodium loading can benefit individuals who are normonatremic with acute brain swelling. In patients who are hyponatremic and hypovolemic, sodium loading may be carried out abruptly by delivery of several small-volume, hypertonic saline boluses (e.g., 100-ml boluses of 23.4% saline) (⁷,²³). Subsequent maintenance of the hypertonic state can be achieved with CRRT modalities. Importantly, the gradual sodium loading of SBO should not supplant urgent volume resuscitation where indicated. In brief, the associated risk of sodium loading must be weighed at the outset of SBO, particularly in patients who are volume overloaded or edematous.

Step 6: Troubleshooting

Slow or No Plasma Sodium Concentration Elevation

If P_Na fails to increase during SBO, the osmotherapy prescription must be reexamined. Equipment and extracorporeal circuit integrity must be checked, and the effects of all fluid inputs and outputs must be reevaluated. If V is underestimated, the rise of P_Na is mathematically inhibited by an NaAR that is lower than calculated. A Q_UF increase will not remedy the situation because D_Na and NaAR are essentially unchanged. NaAR must be augmented by increasing Q_P and/or Q_RF. In parallel, ∇Na(0) can be increased to rectify suboptimal P_Na elevations. When P_Na increases more rapidly than expected per se >1 mM per hour for 4–6 hours, the aforementioned maneuvers should be attenuated, stopped, or even reversed.

Inaccurate NaAR

When BUN is relatively low, e.g., 30–40 mg/dl, calculation of NaAR may be inaccurate. This may transpire when sodium ion and urea clearance are discordant, i.e., abnormal rate of urea metabolism. Accordingly, a D_Na of 25–40 ml/min can be prespecified by empirically establishing ∇Na, Q_P, Q_RF, and, optionally, Q_UF.

Additional Considerations

Hyperglycemia from Dextrose-Containing Solutions

If RF solutions cannot be altered, delivery of a parallel, posthemofilter D₅W infusion in pre-/postdilution CVVH may provoke concern for induction of hyperglycemia. However, this concern is unwarranted. A maximal rate of carbohydrate infusion of 4 mg/kg⋅min has been suggested to prevent lipogenesis (²⁴). At this metabolic threshold, the patient of Case 1 can tolerate a posthemofilter D₅W infusion of 300 ml/h, without hyperglycemia (Table 5). Absent carbohydrate metabolism, this infusion rate, in an extracellular volume of 16 L, increases plasma glucose (P_Glu) from 100 to 2150 mg/dl. However, at a submaximal rate of glucose metabolism of 2.65 mg/kg⋅min, P_Glu remains stable at 100 mg/dl. Notably, the effective P_Na entering the hemofilter is changed minimally. Prefilter D₅W infusions have minimal potential for generating severely elevated P_Glu due to rapid glucose sieving through the hemofilter. If D₅W or sterile water infusion rates are eschewed, less hypotonic solutions can be used, e.g., 0.225% or 0.45% saline solution.

Table 5. - Theoretical effects of a posthemofilter 5% dextrose infusion on glucose metabolism during pre-/post-dilution continuous venovenous hemofiltration

Parameter	Value
D5W infusion, ml/h	30	80	160	240	300
CHO load, mg/kg·min	0.28	0.74	1.48	2.22	2.78
PGlu, without carbohydrate metabolism for 24-h, mg/dl	125	500	1100	1700	2150
Maintenance metabolic rate, mg/kg·min	0.15	0.62	1.36	2.10	2.65
Prehemofilter PNa, mM	117.0	117.0	116.9	116.8	116.8

The effects of a 5% dextrose infusion on glucose metabolism in a hypothetical, nondiabetic, 42-year-old, 178-cm, 90-kg man with Watson volume 48 L and P_Na(0) 116 mM (see text, Case 1) after 24 hours of CVVH are displayed. CVVH parameters are: Na_RF, 130 mM; Q_P, 225 ml/min; combined prehemofilter RF and posthemofilter D₅W flow rate, 1.1 L/h (18.3 ml/min); and net ultrafiltration rate, 0 ml/min. Calculations are based on an extracellular fluid volume of 16 L (48 L × 0.33), without expansion of the extracellular fluid space from glucose accumulation. All CHO metabolism is assumed to originate from the D₅W infusion. With no CHO metabolism, increasing the CHO load (row 2) by increasing the D₅W infusion rate from 0 to 300 ml/h rapidly increases P_Glu (row 3). The respective glucose metabolic rates required to maintain P_Glu at 100 mg/dl for increasing D₅W infusion rates are shown (row 4). The minimal dilutional effect of the increasing D₅W infusion rate on hemofilter inlet P_Na is shown (row 5). CVVH, continuous venovenous hemofiltration; D₅W, 5% dextrose solution; CHO, carbohydrate; P_Glu, plasma glucose concentration; P_Na(0), plasma [Na] at time (t) = 0; Na_RF, RF [Na]; Q_P, plasma flow rate; RF, unadjusted replacement fluid; [Na], sodium concentration.

Regional Citrate Anticoagulation

Regional citrate anticoagulation with trisodium citrate (TSC) solutions of 4% ([Na], 408 mM) or 2.2% ([Na], 224 mM) have been used during SBO (^25–27). Nevertheless, hypertonic TSC infusions can greatly increase plasma tonicity, necessitating reduction of RF [Na] and/or dialysate [Na] to prevent untoward elevations of P_Na. If TSC is used during SBO, a priori sodium modeling is advised with appropriate laboratory monitoring at 4- to 8-hour intervals, including ionized calcium levels that will decline with untoward P_Na elevations if hypercitratemia occurs.

SBO by Other CRRT Modalities

Aside from predilution CVVH, other CRRT modalities and protocols are available, and some employ pre- and posthemofilter RF delivery (¹⁹). When Q_RF is partitioned pre- and postfilter versus prefilter alone, there is an incremental postfilter P_Na elevation. Table 6 represents a quantitative analysis for pre- and posthemofilter CVVH and reveals only a 0.5-mM increment with a 30/70 division of Q_RF between pre- and postfilter fractions. TSC has been exploited to increase P_Na from normal to supranormal levels in patients with cerebral edema (⁶). However, in acute cerebral edema, rapid induction of hypertonicity via hypertonic saline boluses (4 M) is favored when prompt elevation of plasma tonicity is critical (⁷).

Table 6. - Effect of pre- and posthemofilter replacement fluid infusion on end treatment plasma sodium concentration

Variable	Units	Predilution Only	Pre-/Postdilution	Pre-/Postdilution
QP	ml/min	200.0	200.0	200.0
QRF	ml/min	50.0	50.0	50.0
Replacement fluid	—	1.0/0.0	0.5/0.5	0.3/0.7
Pre-/postdilution ratio
DNa	ml/min	40.0	44.4	46.5
NaAR	—	0.76	0.80	0.81
PNa(1440)	mM	127.6	128.0	128.1

A hypothetical patient with Watson volume 40 L and P_Na(0) 120 mM undergoes 24 hours of continuous venovenous hemofiltration with the following parameters: Na_RF, 130 mM; Q_P, 200 ml/min, and Q_RF, 3 L/h. Three simulations are shown: predilution only and pre- and postdilution with Q_RF pre- and postdilution ratios of 0.5/0.5 and 0.3/0.7. D_Na, NaAR, and P_Na(1440) increase with an increasing proportion of postdilution Q_RF. The maximal P_Na(1440) difference among the three pre-/posthemofilter combinations is 0.5 mM. Q_P, plasma flow rate; Q_RF, replacement fluid flow rate; D_Na, dialysance of sodium; NaAR, sodium concentration adjustment ratio; P_Na(0), P_Na at t (0); P_Na(1440), P_Na at t = 1440 minutes; Na_RF, replacement fluid [Na].

Summary

In conclusion, advective SBO by predilution CVVH may be therapeutically exploited in hypotonic conditions with hyponatremia and oligo-anuria. We recommend a six-step protocol based on calculation of NaAR to achieve a time-targeted P_Na. A failure of SBO signifies potential miscalculation(s) and/or the influences of external input and output solutions. Recurrent laboratory monitoring and quantitative analysis of these variables is imperative for safe and successful implementation of SBO. Modeling the plasma sodium concentration, sodium balance, and ultrafiltration with our mise en place approach prevents treatment-based sodium loading (Box 1).

Box 1. Osmotherapy by Predilution Continuous Venovenous Hemofiltration

• (1) Define ΔNa from time (0) to time (t) by defining Na_Post, e.g., 8 mM after 24 hours
• ΔNa = Na_Post – Na_Pre; Na_Pre = P_Na(0); t = end treatment time
• (2) Define sodium concentration adjustment ratio (NaAR) from time (0) to t via urea reduction ratio (URR), e.g., 30%–70% over 24 hours
• NaAR ≈ URR = (BUN(0) − BUN(t))/(BUN(0) − BUN_Dialysate)
• (3) Define ∇Na(0)
• ∇Na(0) = ΔNa/NaAR = (Na_Post – Na_Pre)/NaAR = Na_RF2 – Na_Pre
• (4) Calculate Na_RF2
• Na_RF2 = Na_Pre + ∇Na(0)
• (5) Adjust Na_RF1 to Na_RF2 by methods 1–4 (Figure 3)
• (6) Calculate dialysance of sodium (D_Na) from NaAR, Watson volume (V), and t
• D_Na = −(V/t) × LN(1 − NaAR)
• (7) Calculate plasma flow rate (Q_P) from blood flow rate (Q_B) and hematocrit (Hct)
• Q_P = Q_B × (1–Hct)
• (8) Calculate Q_RF from D_Na and Q_P
• Q_RF = Q_P × (D_Na − Q_UF)/(Q_P − D_Na); Q_UF = 0
• (9) Model predilution continuous venovenous hemofiltration at specified Q_P and Q_RF to determine Q_UF(t) (see below)
• Monitor P_Na at 4- to 6-hour intervals
• (10) Calculate sodium balance ΣNa from time (0) to (t)
• ΣNa(t) = P_Na(t) × (V − Q_UF × t) − (Na_Pre × V)
• Note: Adjust for additional inputs and outputs and edema (see text)
• (11) Calculate Q_UF(t) for zero sodium balance at time (t)
• Q_UF(t) = [(Na_Post × V) – (Na_Pre × V)]/(Na_Post × t) = (ΔNa × V)/(Na_Post × t)

Disclosures

J. Yee discloses honoraria from the American Society of Nephrology. S. Frinak, T. Gradinariu, N. Mohiuddin, and J. Uduman have nothing to disclose.

Funding

None.