## 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.

- Acid/Base and Electrolyte Disorders
- Advection
- Dialysance of sodium
- osmotherapy
- Replacement fluid
- sodium concentration adjustment ratio
- Sodium-gradient
- Urea reduction ratio

## 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.

### 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.

#### 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.

### 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).

### 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 (D_{5}W) 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.

## 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 (*Σ*Na) 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.

### 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.

### 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 D_{5}W 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 D_{5}W 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 D_{5}W infusions have minimal potential for generating severely elevated P_{Glu} due to rapid glucose sieving through the hemofilter. If D_{5}W or sterile water infusion rates are eschewed, less hypotonic solutions can be used, *e.g*., 0.225% or 0.45% saline solution.

### 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).

## 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 hoursΔNa = 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 hoursNaAR ≈ 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 tD

_{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.

## Author Contributions

S. Frinak was responsible for methodology; S. Frinak, T. Gradinariu, N. Mohiuddin, and J. Yee were responsible for formal analysis; S. Frinak, J. Uduman, and J. Yee conceptualized the manuscript S. Frinak and J. Yee were responsible for supervision and validation; N. Mohiuddin and J. Yee were responsible for visualization; all authors wrote the original draft of the manuscript, and reviewed and edited the manuscript.

- Copyright © 2020 by the American Society of Nephrology