Review Article

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

Jerry Yee ,1 Naushaba Mohiuddin,2 Tudor Gradinariu,1 Junior Uduman,1 and Stanley Frinak1

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-a`-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. KIDNEY360 1: 281–291, 2020. doi: https://doi.org/10.34067/KID.0000382019

Introduction continuous venovenous hemofiltration (CVVH) (11,12), Generally, sodium-based osmotherapy (SBO) is tonicity continuous venovenous hemodialysis (13), or con- therapy with the aim of reducing cerebral edema during tinuous venovenous hemodiafiltration (14). states of hypotonic hyponatremia. Depending on the circumstance, plasma tonicity may be increased or decreased. Because the sodium concentration ([Na]) General Principles of SBO in the plasma at any time (t), PNa(t), and accompa- SBO can be implemented as a stepwise approach nying anions constitute the bulk of plasma tonicity, based on established biophysical principles govern- SBOispredicatedongradualalterationofPNa,in ing sodium transit via predilution CVVH. The follow- contrast to the relatively rapid PNa increases imposed ing urea- and sodium-based kinetic methodology by steep dialysate-to-plasma [Na] gradients associ- involves six steps: (1) establishing a time-dependent ∇ ated with conventional hemodialysis. Generally, [Na] gradient [ Na(t)] between the plasma and a fl osmotherapy is carried out when there is severe hypo- replacement uid (RF) based on a sodium concentra- natremia, oligo-anuria, and inability to excrete sufficient tion adjustment ratio (NaAR) (Figure 1), (2)estima- electrolyte-free water to maintain isotonicity (1–3). Thus, tion of total body water (TBW), (3) determination of SBO has played a role in patients with end stage liver sodium ion dialysance (DNa)thatapproximatesthe fi disease and advanced heart failure. urea hemo lter transfer rate, (4) on-treatment predic- Osmotic demyelination syndrome may transpire in tion of PNa(t), (5) determination of sodium balance, and patients who are hyponatremic with end stage liver (6)troubleshooting. disease after abrupt PNa elevations during orthotopic liver transplantation (4,5). Correspondingly, presurgical Predilution CVVH fi elevation of PNa among individuals prone to osmotic RF is infused postblood pump and prehemo lter at a fi fl demyelination may be prophylactic. Less commonly, speci ed rate (QRF)intotheplasma ow (QP)toraise supranormal PNa elevations have been imposed during (or lower) PNa from its pretreatment level, NaPre or traumatic brain injury or intracerebral hemorrhage to PNa(0), to its post-treatment level, NaPost or PNa(t) reduce brain swelling (6,7). (Figure 1). Employing a fixed-volume model where To rectify severe plasma hypotonicity, a relatively TBW volume is constant and analogizing to estab- hypertonic/hypernatric solution is administered in a lished urea kinetic principles, the rate change of PNa controlled fashion during continuous renal replacement can be computed over a specified time interval therapy (CRRT), and PNa is increased at rates consis- (15,16). Thus, sodium advected from the RF gradually tent with consensus guidelines (8). Controlled PNa increases NaPre to NaPost, with their difference equal- elevations can be achieved by hemodialysis, but spe- ing DNa (Equation 1). cial device- and protocol-specificmodifications are To produce an [Na] gradient, a stock RF (RF1) of required to avoid dialysis disequilibrium syndrome nominal [Na] NaRF1 is adjusted to NaRF2, thereby (9). Sustained low-efficiency dialysis or slow contin- establishing ∇Na(0), the maximal [Na] gradient at time uous ultrafiltration with simultaneous infusion of a (0) (Equation 2). DNa is also the product of ∇Na(0) and D ∇ solution relatively hypernatric to PNa is also feasible NaAR, and NaAR is the ratio of Na to Na(0) (Equa- (10). In terms of CRRT, SBO has been conducted with tion 3).

1Division of Nephrology and Hypertension, Henry Ford Hospital, Detroit, Michigan; and 2St. Clair Specialty Physicians, Roseville, Michigan

Correspondence: Dr. Jerry Yee, Division of Nephrology and Hypertension, Henry Ford Hospital, 2799 West Grand Boulevard, CFP-514, Detroit, MI 48202. Email: [email protected] www.kidney360.org Vol 1 April, 2020 Copyright © 2020 by the American Society of Nephrology 281 282 KIDNEY360

Replacement RF2 Fluid

∇Na(t) NaRF2

Q QP RF2

PNa(t) Hemofilter

Blood Pump

DNa·t DNa – NaAR=1–e V

QP – QUF

QRF2 + QUF

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 (QP) ∇ is advected by a sodium concentration [Na]-adjusted replacement fluid (NaRF2). The sodium concentration [Na] gradient, Na(t), equals the [Na] difference between NaRF2 and plasma sodium concentration at any time (t), PNa(t). The sodium concentration adjustment ratio (NaAR) is defined by sodium ion dialysance (DNa), time, and total body water volume (Watson volume, V). Hemofilter effluent equals the sum of RF2 flow rate ∇ (QRF2) and net ultrafiltration flow rate (QUF). Na(t), [Na] gradient at time (t) or PNa(t)-to-NaRF2 difference; RF2, [Na]-adjusted replacement fluid 2.

DNa 5 NaPost 2 NaPre (Equation 1) Step 1: Establishing the Sodium Concentration Gradient ∇ ð0Þ 5 2 Na NaRF2 NaPre (Equation 2) Replacement Fluids ∇ To generate Na(0), the sodium-adjusted RF [Na], NaRF2, NaAR5 DNa=∇Nað0Þ 5 ðNaPost 2 NaPreÞ=ðNaRF2 2 NaPreÞ is often simply assigned an [Na] that is 6–10 mM greater than (Equation 3) NaPre.However,NaRF2 can be more rationally determined from intrinsic parameters of predilution CVVH (Tables 1 and D fi 2). First, by predetermining a target NaPost, Na is de ned. Sodium Kinetic Principles Second, estimation of NaAR from URR (Equations 3 and 4) The NaAR is a function of treatment time (t), TBW (V, and rearrangement of Equation 3 yields NaRF2 as Equation 5. Watson volume), and D . The NaAR is similar to the urea Na 5 1 ðD = Þ reduction ratio (URR, Equation 4), with equivalence of NaRF2 NaPre Na NaAR (Equation 5) DNa to the urea clearance constant, KUrea (Equation 4, A and B). 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 URR 5 ðBUNð0Þ 2 BUNðtÞÞ=ðBUNð0Þ 2 BUN Þ Dialysate with stage 3 AKI. He has no peripheral edema. Laboratory 2 z = 5 5 2 KUrea t V ð Þ URR 1 e Equation 4A data: NaPre, 116 mM; BUN(0), 80 mg/dl; hematocrit, 0.25. The target BUN and PNa after 24 hours of CVVH are 48 mg/dl and 124 mM, respectively. First, NaAR approximating URR 2 z = 5 2 DNa t V “ ” NaAR 1 e (Equation 4B) is calculated, with BUNDialysate as zero. KIDNEY360 1: 281–291, April, 2020 Sodium-Based Osmotherapy, Yee et al. 283

Table 1. Sodium-based osmotherapy parameters

Row Parameter Definition Units

1 DNa Post-treatment [Na] minus mmol/l, mM pretreatment [Na] 2 ∇Na(0) [Na] gradient at time (t)50 mmol/l, mM 3 [Na] Sodium concentration mmol/l, mM 4 SNa Sodium balance mmol 5DNa Dialysance of sodium ion ml/min fl 6 Eff-NaRF Effective replacement uid [Na] from mmol/l, mM combined infusions of NaRF1 and NaH 7 NaAR Sodium concentration adjustment Dimensionless ratio fi 8NaH [Na] of a de ned hypo-, iso-, mmol/l, mM hypertonic solution H 9NaPre Pretreatment PNa, i.e., PNa(0) mmol/l, mM 10 NaPost End treatment PNa mmol/l, mM 11 NaRF1 RF1 [Na], unadjusted replacement mmol/l, mM fluid 12 NaRF2 RF2 [Na], sodium-adjusted mmol/l, mM replacement fluid 13 PNa(t) Plasma [Na] at time (t) mmol/l, mM fl 14 QH Solution H ow rate ml/min fl 15 QB,QP Respective blood and plasma uid ml/min flow rates fl fl 16 QRF Replacement uid ow rate ml/min fi fl 17 QUF Net ultra ltration ow rate ml/min fl 18. QEff Combined ow 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 ml, L (23.4%, 4 M) 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.

NaAR URR 5 ðBUNð0Þ 2 BUNð1440ÞÞ=BUNð0Þ Replacement Fluid Manipulation 5 ð80 2 48Þmg=dl=80mg=dl 5 0:4 In predilution CVVH SBO, the NaRF1 is frequently low- ered from a nominal level of 130 or 140 mM. For Case 1, D ∇ Na can be adjusted to an Na of 136 mM by several Second, after NaAR is determined, Na, Na(0), and NaRF2 RF1 RF2 are calculated. methods (Figure 3) (11,12): method 1, diluting RF1 (NaRF1 140 mM) with 147 ml sterile water; method 2, exchanging 143 ml of RF1 (Na 140 mM) for sterile water; and method D 5 2 5 2 5 RF1 Na NaPost NaPre 124 mM 116 mM 8 mM 3, addition of 7.8 ml of 4 M saline (23.4%) to 5 L of RF1 ∇Nað0Þ 5 DNa=NaAR 5 8 mM=0:4 5 20 mM solution (NaRF1 130 mM). NaRF2 5 NaPre 1 ðDNa=NaARÞ 5 116 mM 1 8 mM=0:4 5 116 mM 1 20 mM 5 136 mM Effective Replacement Fluid Sodium Concentrations NB: ∇Nað0Þ 5 NaRF2 2 NaPre 5 136 mM 2 116 mM 5 20 mM If institutional policy prohibits RF manipulations, an effec- tive RF [Na] (Eff-NaRF) equal to the desired NaRF2 must be generated via flow-rate adjustments of an unadjusted RF1 and The time dependencies of Na , NaAR, and DNa during Post a separate solution (H; Figure 3,method4)(14,17–19). Periph- prolonged SBO are tabulated in Table 3. Figure 2 demon- eral infusion of 5% dextrose in water (D W) or sterile water by ∇ 5 strates the effect of increasing Na(0) on PNa at NaAR of 0.4 central vein may be used as “0” mM [Na] solutions (20). over 1440 minutes of treatment. The random assignment of a 6–10 mM ∇Na(0) would have suboptimally elevated P , Na Step 2: Estimating TBW as Watson Volume underscoring this approach of using NaAR to determine Watson Volume Na . Note the relatively low NaAR complements the large RF2 NaAR is a function of time, DNa, and TBW (V, Watson ∇Na(0). Importantly, a low URR of 0.4 provides a ther- volume). Hence, accurate determination of V is critical. apeutic advantage by mitigating the risk of inducing cere- Consequently, the Watson volume, representing TBW as bral edema by lowering overall urea flux. urea space, is used in subsequent calculations because it is a 284 KIDNEY360

Table 2. Sodium-based osmotherapy equations

Row Description Equation 5 – 3 – 1 Dialysance of sodium ion DNa (V/t) LN(1 NaAR) 5 3 1 1 DNa QP [(QUF QRF)/(QP QRF)] 5 3 2 Method 1 calculation of added water VRF2 VRF1 (NaRF1/NaRF2) 5 3 – volume VW VRF1 [(NaRF1 NaRF2)/NaRF2] 5 3 – 3 Method 2 calculation of water VX VRF1 (NaRF1 NaRF2)/NaRF1] exchange volume 5 3 – – 4 Method 3 volume calculation of V4M VRF1 (NaRF2 NaRF1)/(Na4m NaRF2) added 4 M hypertonic saline volume (23.4%) 5 3 – – 5 Method 4 calculation of solution H QH QEff (NaRF1 Eff-NaRF)/(NaRF1 NaH) fluid flow rate fl 5 3 – – 6 Method 4 replacement uid 1 (RF1) QRF1 QEff (Eff-NaRF NaH)/(NaRF1 NaH) flow rate 7 Plasma flow rate calculation Q 5 Q 3 (1 – hematocrit) P B – z 8 Sodium concentration at treatment P (t) 5 P (0) 1 ∇Na(0) 3 (1 – e DNa t/V); P (0) 5 Na Na Na – Naz Pre 5 1 2 3 – DNa t/V time (t) PNa(t) PNa(0) (NaRF2 NaPre) (1 e ) 5 1 2 3 PNa(t) NaPre ([NaRF2 NaPre] NaAR) fl fl 5 3 2 2 5 9 Replacement uid ow rate QRF QP (DNa QUF)/(QP DNa); QUF 0 S 5 3 2 3 2 3 10 Sodium balance at time (t) Na(t) PNa(t) (V QUF t) (NaPre V) SNa(t) 5 P (t) 3 (V 2 Q 3 t) 2 (P (0) 3 V) Na – z UF Na 11 Sodium concentration adjustment NaAR 5 1 – e DNa t/V 5 D ∇ 5 – 2 ratio NaAR Na/ Na(0) (NaPost NaPre)/(NaRF2 NaPre) 12 Sodium concentration change at end- DNa 5 ∇Na(0) 3 NaAR D 5 – treatment time (t) Na NaPost NaPre ∇ 5 – 13 Sodium concentration gradient, initial Na(0) NaRF2 NaPre 14 Sodium concentration of RF2 Na 5 Na 1 (DNa/NaAR) RF2 Pre – z 5 1 D – DNa t/V NaRF2 NaPre [ Na/(1 e )] fi 5 – 3 – – 15 Time at which speci ed PNa occurs tX (V/DNa) LN[(NaRF2 PNa(tX))/(NaRF2 NaPre)] (tX) fi 5 3 – 3 3 16 Ultra ltration rate to achieve net zero QUF(t) ([NaPost V] [NaPre V])/(NaPost t) sodium balance at time (t) Q (t) 5 (DNa 3 V)/(Na 3 t) UF – z Post 17 Urea reduction ratio URR 5 1 – e KUrea t/V 5 – – URR (BUN(0) BUN(t))/(BUN(0) BUNDialysate) 5 – 3 18 Watson volume VMan 2.447 0.09156 (age, yr) 10.1074 3 (height, cm) 1 0.3362 3 (weight, kg) 5 – 1 3 1 3 VWoman 2.097 0.1069 (height, cm) 0.2466 (weight, kg)

See Table 1 for definitions of variables.

5 3 ð 2 Þ 5 = 3 ð 2 : Þ 5 = superior estimate of TBW compared to multiplication of QP QB 1 Hct 300 ml min 1 0 25 225 ml min i.e – body weight by an arbitrary factor, ., 0.5 0.6 (2,21). For (Equation 7) 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 esti- Application mates of V, considerations of edema and third spacing of fl In Case 1, NaAR at 1440 minutes equals 0.4. Thus, DNa is extracellular uid are excluded, but accommodations for resolved by specifying V and t and rearranging Equation 4B these factors can be made (see Additional Considerations). as Equation 8.

DNa 52ðV=tÞ 3 LNð1 2 NaARÞ 52ð48; 000 ml=1440 minÞ Step 3: Dialysance of Sodium Ion 3 LNð1 2 0:4Þ Sodium Ion Dialysance 52 : = 32 : 5 : = ð Þ fl 33 3 ml min 0 51 17 0 ml min Equation 8 Dialysance of sodium ion (DNa) comprises three ow fi rates: plasma (QP), RF (QRF), and net ultra ltration (QUF) With D known, Q is determined by rearranging Equa- fl Na RF (22). QP has the greatest in uence on DNa by virtue of its tion 6 as Equation 9. greater magnitude. DNa is also the product of QP and the fi 5 3 ð 2 Þ=ð 2 Þ; 5 ltration fraction as follows. QRF QP DNa QUF QP DNa QUF 0 5 ð225 ml=min 3 17 ml=minÞ=ð225 ml=min 2 17 ml=minÞ 518:4 ml=min51:1 L=h ðEquation 9Þ 5 3 ½ð 1 Þ=ð 1 Þ DNa QP QUF QRF QP QRF (Equation 6) In summary, steps 1–3 determine an NaAR of 0.4 and a fl – ∇ D We recommend a blood ow (QB) of 250 300 ml/min to Na(0) of 20 mM that yield a Na of 8 mM. Similar results fi promote clearance and prevent lter clotting (23). As shown, are obtained by increasing DNa (i.e., greater NaAR) and ∇ at a QB of 300 ml/min and hematocrit (Hct) of 0.25, QP is proportionally decreasing Na(0). For example, if NaAR is ∇ 225 ml/min (Equation 7). 0.6, Na(0) becomes 13.3 mM and NaRF2 becomes 129.3 KIDNEY360 1: 281–291, April, 2020 Sodium-Based Osmotherapy, Yee et al. 285

Table 3. Time-dependencies of plasma sodium concentration and sodium concentration adjustment ratio during sodium-based osmotherapy D Time (t, min) PNa(0) NaAR Na(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)

fi Predilution continuous venovenous hemo ltration is carried out on a hypothetical 42-year-old, 178-cm, 90-kg man with PNa(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 D parameters. PNa, plasma sodium concentration; NaAR, sodium concentration adjustment ratio; Na(t), PNa(t) minus PNa(0); PNa(t), PNa 5 at time (t); [Na], sodium concentration; PNa(0), PNa at time (t) 0.

fi D mM. Also, the NaRF2 that produces a speci ed Na at time ascertained by substituting tX into Equation 11 and solving (t) is calculated from Equations 4B and 5 (Equation 10). for it. h . i 2 z = DNa t V tX 52ðV=DNaÞ 3 LN½ðNaRF2 2 PNaðtXÞÞ= ðNaRF2 2 NaPreÞ NaRF2 5 NaPre 1 DNa 1 2 e (Equation 10) (Equation 12) Step 4: Plasma Sodium Concentration during Osmotherapy Targeting the Plasma Sodium Concentration Step 5: Sodium Balance during Osmotherapy Because DNa and TBW are constants within the con- fi In a fixed-volume model of SBO, sodium accrual is inevi- straints of a xed-volume model, PNa(t) can be projected over a specified treatment interval (t) (Equation 11). table as PNa increases. If patient vulnerability to volume overload is present, net ultrafiltration is advised. Conse- h i 2 z = quently, real-time net sodium balance (SNa) monitoring is P ðtÞ 5 Na 1 ðNa 2 Na Þ 3 1 2 e DNa t V Na Pre RF2 Pre critical and computed by Equation 13. (Equation 11) S ð Þ 5 ð Þ 3 ð 2 3 Þ 2 ð 3 Þ Na t PNa t V QUF t NaPre V S ð Þ 5 ð Þ 3 ð 2 3 Þ 2 ð ð Þ 3 Þ This concept is depicted in Figure 4 where time- and Na t PNa t V QUF t PNa 0 V volume-dependencies of PNa(t) are displayed for a man and (Equation 13) woman of equal height and weight. The greater PNa(t)ofthe S 1 5 – woman throughout treatment is attributable to a lesser Watson In Case 1, Na(1440) is 384 mmol if QUF 0 but 62.4 fi volume. The time (tX)whenaspecied PNa(tX)occursis mmol if QUF is 0.15 L/h or 3.6 L per day.

124 123 122

) 121 120 ( mM Na

P 119 118 117 116 0 120 240 360 480 600 720 840 960 1080 1200 1320 1440 Time (min)

∇Na(0) 20 mM ∇Na(0) 15 mM ∇Na(0) 10 mM ∇Na(0) 6 mM

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 (PNa) 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, PNa increases in direct proportion to Na(0). Na(0), [Na] gradient between plasma and replacement fluid at time (0). 286 KIDNEY360

V Method 1. w Method 3. V4M

NaRF1 NaRF2 NaRF1 NaRF2 + Vw + V4M VRF1 VRF2 VRF1 VRF2

VRF2 = VRF1 × (NaRF1/NaRF2) V4M = VRF1 × (NaRF2 – NaRF1)/ Vw = VRF1 × (NaRF1 – NaRF2)/NaRF2 (Na4M – NaRF2)

Method 2. Method 4. Vx QH = QEff × [(NaRF1 – Eff-NaRF)/ (NaRF1 – NaH)] Vx NaH

NaRF1 NaRF2 QRF1 + QH = Eff-NaRF VRF1 VRF2 QEff NaRF1 V = V × (Na – Na )/Na x RF1 RF1 RF2 RF1 QRF1 = QEff × [(Eff-NaRF – NaH)/ (NaRF1 – NaH)]

Figure 3. | Replacement fluid sodium concentration adjustment. Method 1: Sterile water is added to replacement fluid 1 (RF1) of volume VRF1 and sodium concentration NaRF1 to produce replacement fluid 2 (RF2) of volume VRF2 and sodium concentration NaRF2. Method 2: A volume from RF1 (VX) is exchanged with sterile water to produce NaRF2. Method 3: A volume of 4 M sodium chloride solution (V4M) is added to RF1 to produce RF2 volume VRF2 and NaRF2. Method 4: Solution H is infused postblood pump and prehemofilter at flow rate QH in parallel with RF1 at flow rate QRF1 to produce a blended solution with an effective [Na] (Eff-NaRF) at flow rate QEff. H, solution of defined [Na]; Eff-NaRF, effective- [Na] of RF1 and solution H; NaH, solution H [Na]; QEff, additive flow rate of QRF1 and QH;QH, solution H flow rate; QRF1, RF1 flow rate; QRF2, RF2 flow rate; V4M, 4 M saline volume; VW, water volume added to RF1; VX, RF1 exchange volume.

S ð Þ 5 ð ð Þ 3 Þ 2 ð 3 Þ; 5 = ð Þ 5 ½ð 3 Þ 2 ð 3 Þ=ð 3 Þ Na t PNa t V NaPre V QUF 0 ml min QUF t NaPost V NaPre V NaPost t

SNað1440Þ 5 ð124 mM 3 48:0 LÞ 2 ð116 mM 3 48:0 LÞ 5 ðV 3 DNaÞ=ðNaPost 3 tÞ ð Þ 5 ð 3 D Þ=ð 3 Þ 51384 mmol QUF t V Na NaPost t S ð Þ 5 ð Þ 3 ð 2 3 Þ 2 ð 3 Þ 5 ð48 L 3 8 mMÞ=ð124 mM 3 1440 minÞ Na t PNa t V QUF t NaPre V : = 5 : SNað1440Þ 5 124 mM 3 ð48:0 L 2 0:15 L=h 3 24 hÞ 0 00215 L min 3 1 L per 24 hours 2 ð116 mM 3 48:0 LÞ 5262:4 mmol (Equation 14) Modeling Sodium Balance For patients vulnerable to volume excess/overload, SNa “ ” The QUF that zeroes the sodium load at time (t) is calcu- should be modeled a priori, and we demonstrate this concept lated as 3.1 L per 24 hours by Equation 14. as follows.

134 132 130 128 ) 126 124 ( mM

Na 122 P 120 118 116 114 0 360 720 1080 1440 1800 2160 2520 2880 3240 3600 3960 4320 Time (min)

W M

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: QP, 225 ml/min; QRF, 18.3 ml/min; QUF, 0 ml/min; and treatment time, 4320 minutes. The PNa of the woman is greater at all time points due to her smaller Watson volume. QP, plasma flow rate; QRF, replacement fluid rate; QUF, net ultrafiltration fluid rate; PNa, plasma sodium concentration. KIDNEY360 1: 281–291, April, 2020 Sodium-Based Osmotherapy, Yee et al. 287

127 126 125

) 124 123 ( mM Na

P 122 121 120 119 0 120 240 360 480 600 720 840 960 1080 1200 1320 1440 Time (min)

50

0 )

-50

-100

-150

-200

Sodium Balance ( mmol -250

-300 0 120 240 360 480 600 720 840 960 1080 1200 1320 1440 Time (min)

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): NaRF2,128mM;QP, 200 ml/min; QRF2,50 ml/min; QUF, 2.5 ml/min; and treatment time, 1440 minutes. At end treatment, NaAR is 0.74 and PNa increases from 120 mM to 126 mM (top plot). Negative sodium balance begins at t 5 240 minutes. Cumulative sodium loss is 185 mmol at end treatment (bottom plot).

Case 2. A 30-year-old man with heart failure and stage 3B mM; BUN, 50 mg/dl; serum creatinine, 4.2 mg/dl; and CKD develops AKI and dyspnea. The admission weight is hematocrit, 0.33. Urine output is ,0.05 ml/kgzh. A 24-hour 2 kg more than his last-reported hospital discharge weight. NaPost target of 126 mM is planned. Predilution CVVH is His vital signs are as follows: height, 170 cm; weight, 80 kg; begun with parameters of QP 200 ml/min, QRF 50 ml/min, temperature, 36.5°C; heart rate, 118 bpm; blood pressure QUF 2.5 ml/min, and NaAR 0.74. An NaRF2 of 128 mM is 130/80 mm Hg; respiratory rate, 18 per minute; and Watson formulated by adding 79 ml sterile water to an RF1 of 130 volume, 44.85 L. His laboratory data are as follows: NaPre,120 mM. To achieve net sodium balance of zero after 24 hours, net

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 Resultsa

Flow rate, L/h 2.0 Single dose Single dose Single dose 20.1 — 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 20.40 8.05 Cation, mmol 1040.0 7.7 15.4 10.0 220.0 1053.1 b Eff-NaRF,mM 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 fl uid with [Na] 130 mM; UO, urine output; [Na], sodium concentration; Eff-NaRF, effective [Na] of RF and one of the solutions listed and/or UO. a Aggregate effect of solutions and urine output on Eff-NaRF. b Isolated effect of each solution or urine output on Eff-NaRF. 288 KIDNEY360

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/kgzmin 0.28 0.74 1.48 2.22 2.78 PGlu, without carbohydrate metabolism for 125 500 1100 1700 2150 24-h, mg/dl Maintenance metabolic rate, mg/kgzmin 0.15 0.62 1.36 2.10 2.65 fi Prehemo lter 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 PNa(0) 116 mM (see text, Case 1) after 24 hours of CVVH are displayed. CVVH parameters are: NaRF, 130 mM; QP, 225 fi fi fl fi ml/min; combined prehemo lter RF and posthemo lter D5W ow rate, 1.1 L/h (18.3 ml/min); and net ultra ltration rate, 0 ml/min. Calculations are based on an extracellular fluid volume of 16 L (48 L 3 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 PGlu (row 3). The respective glucose metabolic rates required to maintain PGlu at 100 mg/dl for increasing D5W infusion rates are shown (row 4). The minimal dilutional fi fi effect of the increasing D5Winfusionrateonhemo lter inlet PNa is shown (row 5). CVVH, continuous venovenous hemo ltration; 5 D5W,5%dextrosesolution;CHO,carbohydrate;PGlu, plasma glucose concentration; PNa(0), plasma [Na] at time (t) 0; NaRF,RF fl fl [Na]; QP,plasma ow rate; RF, unadjusted replacement uid; [Na], sodium concentration. ultrafiltration of 2.14 L per 24 hours is required, as shown tallied. Only cationic effects require analysis as anions fol- below. Ultrafiltration beyond 24 hours produces net total low pari passu. The RF [Na] is altered by infusions of exog- fl body sodium loss. Figure 5 depicts the evolution of PNa(t) and enous uids and/or urine output and produces a blended S Na(1440) if QUF is 3.6 L per 24 hours. solution with an effective [Na] (Eff-NaRF). Table 4 illustrates the 4-hour effects on Eff-NaRF in a patient who receives three ð Þ 5 ð 3 D Þ=ð 3 Þ QUF 1440 V Na NaPost t intravenous fluids, 0.45% saline and hypothetical solutions A 5 ð44:85 L 3 6 mMÞ=ð126 mM 3 1440 minÞ and B. By evaluating a short time interval, the singular and fl 5 0:00148 L=min 5 2:14 L per 24 hours collective effects of each uid on Eff-NaRF are exposed early on. In aggregate, with consideration of all inputs and out- fl puts, the 4-hour effects on Eff-NaRF and extracellular uid volume are 10.8 mM and 10.05 L, respectively. Extrapola- Sodium Balance with Edema tion of this analysis to a 24-hour interval may obligate If the entire 2-kg excess weight is assumed isotonic to readjustments of Na and/or Q . Lastly, elaboration of plasma, total body sodium balance must be recalculated. RF1 UF hypotonic urine increases Eff-Na minimally, unless urine The Watson volume of the 78-kg man was 44.18 L and RF output is copious, i.e., .4 L per day. increasedto46.18Lfrom2Lofedema.Achievingzero sodium balance requires just 0.06 L more net ultrafiltration. However, there is a 160-mmol sodium excess if edema is Acute Sodium Loading considered isotonic plasma (Equation 15). To shed the sodium Sodium loading can benefit individuals who are normo- surfeit, an additional 1.27 L of net ultrafiltration is required. natremic with acute brain swelling. In patients who are fi Overall, net ultra ltration of 3.47 L attains a PNa(1440) of hyponatremic and hypovolemic, sodium loading may be 126 mM at 76.53 kg. carried out abruptly by delivery of several small-volume, hypertonic saline boluses (e.g., 100-ml boluses of 23.4% ð Þ 5 ð 3 D Þ=ð 3 Þ QUF 1440 V Na NaPost t saline) (7,23). Subsequent maintenance of the hypertonic 5 ð46:18 L 3 6 mMÞ=ð126 mM 3 1440 minÞ state can be achieved with CRRT modalities. Importantly, 5 0:00153 ml=min52:2 L per 24 h the gradual sodium loading of SBO should not supplant urgent volume resuscitation where indicated. In brief, the (Equation 15) associated risk of sodium loading must be weighed at the SNað0Þ 5 PNað0Þ 3 ðadjusted V 1 edema ½kgÞ outset of SBO, particularly in patients who are volume 5 120 mM 3 ð44:18 1 2ÞL 5 5542 mmol overloaded or edematous. SNað0Þ 5 PNað0Þ 3 ðunadjusted VÞ 5 120 mM 3 44:85 L 5 5382 mmol DTotal body sodium5 5542 mmol 2 5382 mmol 5 160 mmol Step 6: Troubleshooting Additional ultrafiltration volume 5 160 mmol=126 mM Slow or No Plasma Sodium Concentration Elevation 5 1:27 L If PNa fails to increase during SBO, the osmotherapy prescription must be reexamined. Equipment and extracor- poreal circuit integrity must be checked, and the effects of all Influence of Exogenous Fluids and Urine Output on fluid inputs and outputs must be reevaluated. If V is under- Replacement Fluid Sodium Concentration estimated, the rise of PNa is mathematically inhibited by an fl During SBO, the in uence of exogenous cation (sodium NaAR that is lower than calculated. A QUF increase will not fl S and potassium)-containing uids on PNa and Na must be remedy the situation because DNa and NaAR are essentially KIDNEY360 1: 281–291, April, 2020 Sodium-Based Osmotherapy, Yee et al. 289

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

fi A hypothetical patient with Watson volume 40 L and PNa(0) 120 mM undergoes 24 hours of continuous venovenous hemo ltration with the following parameters: NaRF, 130 mM; QP, 200 ml/min, and QRF, 3 L/h. Three simulations are shown: predilution only and pre- and postdilution with QRF pre- and postdilution ratios of 0.5/0.5 and 0.3/0.7. DNa, NaAR, and PNa(1440) increase with an increasing fi proportion of postdilution QRF. The maximal PNa(1440) difference among the three pre-/posthemo lter combinations is 0.5 mM. QP, fl fl fl plasma ow rate; QRF, replacement uid ow rate; DNa, dialysance of sodium; NaAR, sodium concentration adjustment ratio; PNa(0), 5 fl PNa at t (0); PNa(1440), PNa at t 1440 minutes; NaRF, replacement uid [Na].

unchanged. NaAR must be augmented by increasing QP SBO, a priori sodium modeling is advised with appropriate ∇ and/or QRF. In parallel, Na(0) can be increased to rectify laboratory monitoring at 4- to 8-hour intervals, including suboptimal PNa elevations. When PNa increases more rap- ionized calcium levels that will decline with untoward PNa idly than expected per se .1 mM per hour for 4–6 hours, the elevations if hypercitratemia occurs. aforementioned maneuvers should be attenuated, stopped, or even reversed. SBO by Other CRRT Modalities Aside from predilution CVVH, other CRRT modalities Inaccurate NaAR and protocols are available, and some employ pre- and When BUN is relatively low, e.g., 30–40 mg/dl, calcula- fi posthemo lter RF delivery (19). When QRF is partitioned tion of NaAR may be inaccurate. This may transpire when pre- and postfilter versus prefilter alone, there is an incre- sodium ion and urea clearance are discordant, i.e., abnormal mental postfilter P elevation. Table 6 represents a quan- – Na rate of urea metabolism. Accordingly, a DNa of 25 40 ml/ titative analysis for pre- and posthemofilter CVVH and fi ∇ min can be prespeci ed by empirically establishing Na, reveals only a 0.5-mM increment with a 30/70 division of fi QP,QRF, and, optionally, QUF. QRF between pre- and post lter fractions. TSC has been exploited to increase PNa from normal to supranormal levels in patients with cerebral edema (6). However, in acute Additional Considerations cerebral edema, rapid induction of hypertonicity via hyper- Hyperglycemia from Dextrose-Containing Solutions tonic saline boluses (4 M) is favored when prompt elevation If RF solutions cannot be altered, delivery of a parallel, fi of plasma tonicity is critical (7). posthemo lter D5W infusion in pre-/postdilution CVVH may provoke concern for induction of hyperglycemia. How- ever, this concern is unwarranted. A maximal rate of car- Summary bohydrate infusion of 4 mg/kgzmin has been suggested to In conclusion, advective SBO by predilution CVVH may prevent lipogenesis (24). At this metabolic threshold, the be therapeutically exploited in hypotonic conditions with patient of Case 1 can tolerate a posthemofilter D W infusion 5 hyponatremia and oligo-anuria. We recommend a six-step of 300 ml/h, without hyperglycemia (Table 5). Absent car- protocol based on calculation of NaAR to achieve a time- bohydrate metabolism, this infusion rate, in an extracellular targeted P . A failure of SBO signifies potential miscalcu- volume of 16 L, increases plasma glucose (P ) from 100 to Na Glu lation(s) and/or the influences of external input and output 2150 mg/dl. However, at a submaximal rate of glucose solutions. Recurrent laboratory monitoring and quantitative metabolism of 2.65 mg/kgzmin, P remains stable at Glu analysis of these variables is imperative for safe and suc- 100 mg/dl. Notably, the effective P entering the hemo- Na cessful implementation of SBO. Modeling the plasma filter is changed minimally. Prefilter D W infusions have 5 sodium concentration, sodium balance, and ultrafiltration minimal potential for generating severely elevated P due Glu with our mise en place approach prevents treatment-based to rapid glucose sieving through the hemofilter. If D Wor 5 sodium loading (Box 1). sterile water infusion rates are eschewed, less hypotonic solutions can be used, e.g., 0.225% or 0.45% saline solution. Author Contributions Regional Citrate Anticoagulation S. Frinak was responsible for methodology; S. Frinak, T. Gradinariu, Regional citrate anticoagulation with trisodium citrate N. Mohiuddin, and J. Yee were responsible for formal analysis; (TSC) solutions of 4% ([Na], 408 mM) or 2.2% ([Na], 224 S. Frinak, J. Uduman, and J. Yee conceptualized the manuscript mM) have been used during SBO (25–27). Nevertheless, S. Frinak and J. Yee were responsible for supervision and val- hypertonic TSC infusions can greatly increase plasma tonic- idation; N. Mohiuddin and J. Yee were responsible for visual- ity, necessitating reduction of RF [Na] and/or dialysate [Na] ization; all authors wrote the original draft of the manuscript, to prevent untoward elevations of PNa. If TSC is used during and reviewed and edited the manuscript. 290 KIDNEY360

Box 1. Osmotherapy by Predilution Continuous Venovenous Hemofiltration

D (1) Define Na from time (0) to time (t) by defining NaPost, e.g., 8 mM after 24 hours D 5 5 5 Na NaPost –NaPre;NaPre PNa(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 5 2 2 NaAR URR (BUN(0) BUN(t))/(BUN(0) BUNDialysate) (3) Define ∇Na(0) ∇ 5 D 5 5 Na(0) Na/NaAR (NaPost –NaPre)/NaAR NaRF2 –NaPre (4) Calculate NaRF2 5 1 ∇ NaRF2 NaPre Na(0) (5) Adjust NaRF1 to NaRF2 by methods 1–4 (Figure 3) (6) Calculate dialysance of sodium (DNa) from NaAR, Watson volume (V), and t 52 3 2 DNa (V/t) LN(1 NaAR) (7) Calculate plasma flow rate (QP) from blood flow rate (QB) and hematocrit (Hct) 5 3 QP QB (1–Hct) (8) Calculate QRF from DNa and QP 5 3 2 2 5 QRF QP (DNa QUF)/(QP DNa); QUF 0 (9) Model predilution continuous venovenous hemofiltration at specified QP and QRF to determine QUF(t) (see below) Monitor PNa at 4- to 6-hour intervals (10) Calculate sodium balance SNa from time (0) to (t) S 5 3 2 3 2 3 Na(t) PNa(t) (V QUF t) (NaPre V) Note: Adjust for additional inputs and outputs and edema (see text) (11) Calculate QUF(t) for zero sodium balance at time (t) 5 3 3 3 5 D 3 3 QUF(t) [(NaPost V) – (NaPre V)]/(NaPost t) ( Na V)/(NaPost t)

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