Kidney360 Publish Ahead of Print, published on February 26, 2020 as doi:10.34067/KID.0000382019
Sodium-Based Osmotherapy
Title: Sodium-Based Osmotherapy in Continuous Renal Replacement Therapy: A Mathematical Approach
Short title: Sodium-based osmotherapy
Keywords: advection, dialysance of sodium (DNa), osmotherapy, sodium concentration adjustment ratio (NaAR), sodium concentration gradient (∇Na)
Authors: Jerry Yee, M.D., Naushaba Mohiuddin, M.D., Tudor Gradinariu, D.O., Junior Uduman, M.D., and Stanley Frinak, MSEE
Relevant Conflicts of Interest/Disclosures: Author Jerry Yee discloses honoraria from the American Society of Nephrology. Authors Naushaba Mohiuddin, Tudor Gradinariu, Junior Uduman, and Stanley Frinak have nothing to disclose.
Acknowledgements: None
Author Contributions: JY, JU, and SF conceptualized, wrote, and edited the manuscript. NM and TG contributed to writing and editing of the manuscript.
Corresponding Author:
Jerry Yee, MD, MACP, FASN, FNKF
Henry Ford Hospital
Division of Nephrology and Hypertension
2799 West Grand Blvd., CFP-514
Detroit, MI 48202
Phone: (313) 916–9405
Fax: (313) 916–2554
Email: [email protected]
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Copyright 2020 by American Society of Nephrology. Sodium-Based Osmotherapy
Author List
Naushaba Mohiuddin, MD
5120 Hollow Ct.
Bloomfield Hills, MI 48302
Phone: (313) 574–1136
Email: [email protected]
Tudor Gradinariu, DO
Henry Ford Hospital
Division of Nephrology and Hypertension
2799 West Grand Blvd., CFP-5
Detroit, MI 48202
Phone: (313) 916–7134
Fax: (313) 916–2554
Email: [email protected]
Junior Uduman, MD
Henry Ford Hospital
Division of Nephrology and Hypertension
2799 West Grand Blvd., CFP-5
Detroit, MI 48202
Phone: (313) 916–7138
Fax: (313) 916–2554
Email: [email protected]
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Stanley Frinak, MSEE
Henry Ford Hospital
Division of Nephrology and Hypertension
2799 West Grand Blvd., CFP-5
Detroit, MI 48202
Phone: (313) 916–2706
Fax: (313) 916–2554
Email: [email protected]
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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, hyponatremic patients with 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 chronic kidney disease and/or acute kidney injury, 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 renal replacement therapy modality, pre-dilution continuous venovenous hemofiltration.
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Introduction
Generally, sodium-based osmotherapy 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. As plasma sodium
concentration ([Na]) at any time (t), PNa(t), and accompanying anions constitute the bulk of plasma tonicity, sodium-based osmotherapy (SBO) is predicated on gradual alteration
of PNa, in contrast to the relatively rapid PNa 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 (ODS) may transpire in hyponatremic end-stage liver disease patients after abrupt PNa elevations during orthotopic liver transplantation (4,
5). Correspondingly, pre-surgical elevation of PNa among individuals prone to ODS
may be prophylactic. Less commonly, supranormal PNa 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 controlled fashion during continuous renal replacement therapy (CRRT),
and PNa is increased at rates consistent with consensus guidelines (8). Controlled PNa 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
relatively hypernatric solution to PNa 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 SODIUM-BASED OSMOTHERAPY
SBO can be implemented as a stepwise approach based on established biophysical principles governing sodium transit via pre-dilution CVVH. The following urea- and sodium-based kinetic methodology involves 6 steps: (1) establishing a time-dependent [Na]-gradient [∇Na(t)] between the plasma and a replacement fluid based on a sodium concentration adjustment ratio (Figure 1), (2) estimation of total body water (TBW), (3) determination of sodium ion dialysance (DNa) that approximates the urea hemofilter
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transfer rate, (4) on-treatment prediction of PNa(t), (5) determination of sodium balance, and (6) troubleshooting.
Pre-dilution Continuous Venovenous Hemofiltration
A replacement fluid (RF) is advected post-blood pump and pre-hemofilter at a specified rate (QRF) into the plasma flow (QP) to raise (or lower) PNa from its pre-treatment level,
NaPre or PNa(0), to its post-treatment level, NaPost or PNa(t) (Figure 1). Employing a fixed- volume model where total body water volume is constant and analogizing to established
urea kinetic principles, the rate-change of PNa can be computed over a specified time- interval (15, 16). Sodium flux advected from the RF gradually increases NaPre to the post-
treatment level (NaPost). NaPost minus NaPre equals ΔNa (Eq. 1). To produce a [Na]-
gradient, a stock RF (RF1) of nominal [Na] NaRF1 is adjusted to NaRF2, thereby establishing ∇Na(0), the maximal [Na]-gradient at time (0) (Eq. 2). ΔNa is also the product of ∇Na(0) and the sodium concentration adjustment ratio (NaAR), and NaAR is the ratio of ΔNa- to-∇Na(0) (Eq. 3).
(Eq. 1) ∆Na = NaPost – NaPre
(Eq. 2) ∇Na(0) = NaRF2 − NaPre
(Eq. 3) NaAR = ΔNa/∇Na(0) = (NaPost – NaPre)/(NaRF2 − NaPre)
Sodium Kinetic Principles
The NaAR is a function of treatment-time (t), total body water (V, Watson volume), and
dialysance of sodium (DNa). The NaAR is similar to the urea reduction ratio (URR, Eq. 4),
with equivalence of DNa to the urea clearance constant, KUrea (Eq. 4a and 4b).
(Eq. 4a) URR = [(BUN(0) – BUN(t)]/[BUN(0) – BUNDialysate] = URR = 1 – e–KUrea∙t/V
(Eq. 4b) NaAR = 1 – e–DNa∙t/V
STEP 1: ESTABLISHING THE SODIUM CONCENTRATION GRADIENT
Replacement Fluids
To generate ∇Na(0), the sodium adjusted-replacement fluid [Na], NaRF2, is often simply
assigned a [Na] that is 6–10 mM greater than NaPre. However, NaRF2 can be more rationally determined from intrinsic parameters of pre-dilution CVVH. First, by
predetermining a target NaPost, ΔNa is defined. Second, estimation of NaAR from URR
(Eqs. 3 and 4) and rearrangement of Eq. 3 yields NaRF2 as Eq. 5.
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(Eq. 5) NaRF2 = NaPre + (ΔNa/NaAR)
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 from hypovolemic shock.
He has no peripheral edema, and V of 48.0 L. Laboratory data: NaPre 116 mM, BUN(0) 80
mg/dl, and hematocrit 0.25. The target BUN and PNa after 24 h of CVVH are 48 mg/dl and
124 mM, respectively. First, NaAR is calculated, with BUNDialysate as “0.”
NaAR ≈ URR = [BUN(0) – BUN(1440)]/BUN(0)
= (80 – 48) mg/dl/80 mg/dl = 0.4
Second, after NaAR is determined, ΔNa, ∇Na(0), and NaRF2 are calculated.
∆Na = NaPost – NaPre = 124 mM – 116 mM = 8 mM
∇Na(0) = ΔNa/NaAR = 8 mM/0.4 = 20 mM
NaRF2 = NaPre + (∆Na/NaAR) = 116 mM + 8 mM/0.4 = 116 mM + 20 mM = 136 mM
NB: ∇Na(0) = NaRF2 – NaPre = 136 mM – 116 mM = 20 mM
The time-dependencies of NaPost, NaAR, and ∆Na during prolonged SBO are tabulated
in Table 2. Figure 2 demonstrates the effect of increasing ∇Na(0) on PNa at NaAR of 0.4 over 1440 min treatment. The random assignment of a 6–10 mM ∇Na(0) would have
suboptimally elevated PNa, underscoring this approach of utilizing NaAR to determine
NaRF2. 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 inducing cerebral edema through lower overall urea flux.
Manipulation of Replacement Fluids
In pre-dilution CVVH SBO, the NaRF1 is frequently lowered from a nominal level of 130
or 140 mM. For Case 1, NaRF1 can be adjusted to NaRF2 136 mM by several methods
(Figure 3) (11, 12): Method 1, diluting RF1 (NaRF1 140 mM) with 147 ml sterile water;
Method 2, exchanging 143 ml of RF1 (NaRF1 140 mM) for sterile water; and Method 3, addition of 7.8 ml of 4 M saline (23.4%) to a 5-L, 130 mM bag.
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Effective-Sodium Concentration Solutions
If institutional policy prohibits RF manipulations, an Effective-[Na] (Eff-[Na]) that equals the desired NaRF2 must be generated via flow rate adjustments of an unadjusted RF1 and a separate hypotonic 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 TOTAL BODY WATER AS WATSON VOLUME
Watson Volume
NaAR is a function of time, DNa, and total body water (V, Watson volume). Hence, accurate determination of V is critical. Consequently, the Watson volume, representing total body water (TBW) as urea space is used in subsequent calculations because it is a superior estimate of TBW compared to multiplication of bodyweight 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 Clearance
Dialysance of sodium ion (DNa) is comprised of 3 flow rates: plasma (QP), replacement
fluid (QRF), and net ultrafiltration rate (QUF) (22). QP has the greatest influence on DNa by virtue of its greater magnitude. DNa is also the product of QP and filtration fraction as follows.
(Eq. 6) DNa = QP × [(QRF + QUF)/(QRF + QP)]
We recommend QB of 250–300 ml/min to promote clearance and prevent filter clotting
(23). As shown, at QB 300 ml/min and hematocrit (Hct) 0.25, QP is 225 ml/min (Eq. 7).
(Eq. 7) QP = QB × (1 – Hct) = 300 ml/min × (1 – 0.25) = 225 ml/min
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Application
In Case 1, NaAR at 1440 min equals 0.4. Thus, DNa is resolved by specifying V and t and rearranging Eq. 3 as Eq. 8.
(Eq. 8) DNa = –(V/t) × LN(1 – NaAR) = –(48,000 ml/1440 min) × LN(1 – 0.4)
= –33.3 ml/min × –0.51 = 17 ml/min
With DNa known, QRF is determined by rearranging Eq. 6 as Eq. 9.
(Eq. 9) QRF = (QP × DNa)/(QP – DNa)
= (225 ml/min × 17 ml/min)/(225 ml/min – 17 ml/min) = 18.4 ml/min = 1.1 L/h
In summary, Steps 1 to 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 DNa (i.e., greater NaAR) and proportionally decreasing ∇Na(0). For example, if NaAR is 0.6, ∇Na(0) becomes 13.3 mM,
and NaRF2 129.3 mM. Also, the NaRF2 that produces a specified ∆Na at time (t) is calculated from Eqs. 4b and 5 (Eq. 10).
(Eq. 10) NaRF2 = NaPre + [∆Na(t)/(1 – e–DNa∙t/V)]
STEP 4. PLASMA SODIUM CONCENTRATION DURING OSMOTHERAPY
Targeting the Plasma Sodium Concentration
Since DNa and TBW are constants within the constraints of a fixed-volume model, PNa(t) can be projected over a specified treatment interval (t) (Eq. 11).
(Eq. 11) PNa(t) = NaPre + [(NaRF2 − NaPre) × (1 – e–DNa∙t/V)]
This concept is depicted in Figure 4 where time- and volume-dependencies of PNa(t) are
displayed for a man and woman of equal height and weight. The greater PNa(t) of the woman throughout treatment is attributable to a lesser Watson volume. Conversely, the
time (tX) when a specified PNa(tX) occurs is ascertained by combining Eqs. 8 and 11.
(Eq. 12) tX = –(V/DNa) × LN{[NaRF2 – PNa(tX)]/(NaRF2 – NaPre)}
STEP 5. SODIUM BALANCE DURING OSMOTHERAPY
In a fixed-volume SBO model of SBO, sodium accrual is inevitable as PNa increases. If patient vulnerability to volume overload is present, net ultrafiltration is advised.
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Consequently, real-time net sodium balance (∑Na) monitoring is critical and computed by Eq. 13.
(Eq. 13) ∑Na(t) = [PNa(t) × (V – QUF × t)] – (NaPre × V)
∑Na(t) = PNa(t) × [V – (QUF × t)] – [PNa(0) × V]
In Case 1, ∑Na(1440) is +384 mmol if QUF “0,” but –62.4 mmol if QUF is 0.15 L/h.
∑Na(t) = [PNa(t) × V] – (NaPre × V); QUF = 0 ml/min
∑Na(1440) = (124 mM × 48.0 L) – (116 mM × 48.0 L) = +384 mmol
∑Na(t) = [PNa(t) × (V – QUF × t)] – (NaPre × V)
∑Na(1440) = [124 mM × (48.0 L – 0.15 L/h × 24 h)] – (116 mM × 48.0 L) = –62.4 mmol
The QUF that “zeroes” the sodium-load at time (t) is calculated as 3.1 L/24-h by Eq. 14.
(Eq. 14) QUF(t) = [(NaPost × V) – (NaPre × V)]/(NaPost∙t) = (∆Na × V)/(NaPost∙t)
QUF(t) = (V × ∆Na)/(NaPost∙t) = [(48 L × 8 mM)/124 mM∙1440 min]
= 3.1 L/1440 min ≈ 2.2 ml/min
Modeling Sodium Balance
For patients vulnerable to volume excess/overload, ∑Na 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 chronic kidney disease develops acute kidney injury and dyspnea. The admission weight is 2 kg more than his last-reported hospital discharge weight. Vital signs: Ht 170 cm, Wt 80 kg. T 36.5° C, HR 118 bpm, BP
98/56 mm Hg, RR 18 min–1, and Watson volume, 44.85 L. Laboratory data: NaPre 120 mM; BUN 50 mg/dl; serum creatinine 4.2 mg/dl, and Hct 0.33. Urine output is <0.05 ml/kg⋅h.
A 24-h target NaPost of 126 mM is planned. Pre-dilution CVVH is planned with parameters
of QP 200 ml/min, QRF 50 ml/min, QUF 2.5 ml/min, and NaAR 0.74. A 128 mM NaRF2 is formulated by adding 79 ml sterile water to an RF1 of 130 mM. To achieve net sodium balance of “0” after 24 h, net ultrafiltration of 2.14 L per 24-h is required, as below. Ultrafiltration beyond 24 h produces net total body sodium loss.
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QUF(t) = (V × ∆Na)/(NaPost∙t) = (44.85 L × 6 mM)/(126 mM∙24-h) = 2.14 L/24- h
Sodium Balance with Edema
If the entire 2-kg excess weight is assumed isotonic to plasma, total body sodium must be recalculated. The Watson volume of the 78-kg man is 44.18 L and increases to 46.18 L from 2 L of edema. Achieving “0” sodium balance requires just 0.06 L more net ultrafiltration. However, there is a 160 mmol sodium excess if edema is considered as isotonic plasma (Eq. 15). To shed the sodium surfeit, an additional 1.27 L more net ultrafiltration is required. Overall, net ultrafiltration of 3.47 L attains a PNa(1440) of 126 mM at 76.53 kg.
QUF(t) = (V × ∆Na)/(NaPost∙t) = (46.18 L × 6 mM)/(126 mM∙24-h) = 2.2 L/24-h
(Eq. 15) ∑Na(0) = PNa(0) × (Adjusted-V + Edema [kg])
= 120 mM × (44.18 + 2) L = 5542 mmol
∑Na(0) = PNa(0) × (Unadjusted-V) = 120 mM × 44.85 L = 5382 mmol
ΔTotal body sodium = 5542 – 5382 mmol = 160 mmol
Additional ultrafiltration volume = 160 mmol/126 mM = 1.27 L
Sodium Balance with Exogenous Fluids and Urine Output
During SBO, the imposition of exogenous cation (sodium- and potassium)-containing
fluids and respective flow rates on PNa and ∑Na must be tallied. Only cationic effects are analyzed as anions follow pari passu. An upward or downward deflection of the plasma Eff-[Na] occurs depending on fluid compositions and rates. Table 3 illustrates the 4-h effects on Eff-[Na] in a patient who receives 3 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] are exposed early on. In aggregate, with consideration of all inputs and outputs, the 4-h effects on Eff-[Na] and ECF volume are +0.8 mM and +0.05 L, respectively. Extrapolation of this analysis to a 24-h interval may
obligate re-adjustments of NaRF1 and/or QUF. Lastly, elaboration of hypotonic urine increases Eff-[Na] minimally, unless urine output is copious, i.e., >4 L/24-h.
Acute Sodium-Loading
Sodium-loading may be beneficial in normonatremic individuals with acute brain swelling. In hyponatremic, hypovolemic patients, sodium-loading may be carried out
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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 volume-overloaded or edematous patients.
STEP 6. TROUBLESHOOTING
Slow or No Plasma Sodium Concentration Elevation
If PNa 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 PNa is
mathematically inhibited by an NaAR that is lower than calculated. A QUF increase will not remedy the situation because DNa and NaAR are essentially unchanged. NaAR must
be augmented by increasing QP and/or QRF. In parallel, ∇Na(0) can be increased to rectify suboptimal PNa elevations. When PNa increases more rapidly than expected per se >1 mM per h for 4–6 h, the aforementioned maneuvers should be attenuated, stopped, or even reversed.
Inaccurate Sodium Concentration Adjustment Ratio
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 DNa of 25–40 ml/min can be pre-specified by
empirically establishing ∇Na, QP, QRF, and, optionally, QUF.
ADDITIONAL CONSIDERATIONS
Hyperglycemia from Dextrose-Containing Solutions
If RF solutions cannot be altered, delivery of a parallel, post-hemofilter 5% dextrose
infusion (D5W) 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 non-diabetic
man of Case 1 can tolerate a post-hemofilter D5W infusion of 300 ml/h, without hyperglycemia (Table 4). Absent carbohydrate metabolism, this infusion rate, in an
extracellular volume of 16 L, increases plasma glucose (PGlu) from 100 to 2150 mg/dl.
However, at a submaximal rate of glucose metabolism of 2.65 mg/kg∙min, PGlu remains
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stable at 100 mg/dl. Table 4 also delineates the influence of varying infusion rates of D5W
and RF1 (NaRF1, 130 mM) on the post-filter Eff-[Na]. Pre-filter D5W infusions have
minimal potential for generating severely elevated PGlu 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.
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
replacement fluid and/or dialysate [Na] to prevent increases of Eff-[Na] and PNa. If TSC is used during SBO, a priori sodium modeling is advised with appropriate laboratory monitoring at 4–8 h intervals, including ionized calcium levels that will decline with
untoward PNa elevations if hyper-citratemia occurs.
Sodium-Based Osmotherapy by other CRRT Modalities
Aside from pre-dilution CVVH, other CRRT modalities and protocols are available, and some employ pre- and post-hemofilter RF delivery (19). When QRF is partitioned pre- and
post-filter versus pre-filter alone, there is an incremental post-filter PNa elevation. Table 5 represents a quantitative analysis for pre- and post-hemofilter CVVH and reveals only a
0.5 mM increment with a 30/70 division of QRF between pre- and post-filter fractions. TSC has been exploited to increase PNa from normal-to-supranormal levels in cerebral edema patients (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 pre-dilution CVVH may be therapeutically exploited in hypotonic conditions with hyponatremia and oligo-anuria. We recommend a 6-step protocol based on calculation of NaAR to achieve a time-targeted PNa. 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.
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Box 1. Osmotherapy by Pre-dilution Continuous Venovenous Hemofiltration
1. Define ∆Na from time (0) to time (t) by defining NaPost, e.g., 8 mM after 24 h
∆Na(t) = NaPost – NaPre; NaPre = PNa(0); t = end-treatment time
2. Define NaAR from time (0) to t via URR, e.g., 30%–70% over 24 h
NaAR ≈ URR = [(BUN(0) – BUN(t)]/[BUN(0) – BUNDialysate]
3. Define ∇Na(0)
∇Na(0) = ∆Na(t)/NaAR = (NaPost – NaPre)/NaAR = NaRF2 – NaPre
4. Calculate NaRF2
NaRF2 = NaPre + ∇Na(0)
5. Adjust NaRF1 to NaRF2 by Methods 1–4 (Figure 3)
6. Calculate DNa from NaAR, Watson volume (V), and t
DNa = –(V/t) × [LN(1 – NaAR)]
7. Establish blood flow rate (QB) to define plasma flow rate (QP) via hematocrit (Hct)
QP = QB × (1 – Hct)
8. Calculate QRF from DNa and QP
QRF = (QP × DNa)/(QP – DNa)
9. Model pre-dilution CVVH at specified QP and QRF to determine QUF (see below)
Monitor PNa at 4- to 6-h intervals
10. Calculate sodium balance ∑Na from time (0) to t
∑Na(t) = [PNa(t) × (V – QUF × t)] – (NaPre × V)
NB: Adjust for additional inputs and outputs and edema (see text)
11. Calculate QUF for “0” sodium balance at time (t)
QUF(t) = [(NaPost × V) – (NaPre × V)]/(NaPost∙t) = (∆Na × V)/(NaPost∙t)
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Table 1a. | Sodium-based osmotherapy parameters
Row Parameter Definition Units Post-treatment [Na] minus pre- 1. ΔNa mmol/l, mM treatment [Na] 2. ∇Na(0) [Na]-gradient at time (t) = 0 mmol/l, mM 3. [Na] Sodium concentration mmol/l, mM 4. ∑Na Sodium balance mmol 5. DNa Dialysance of sodium ion ml/min Effective-[Na] of solutions 6. Eff-[Na] mmol/l, mM infused simultaneously Sodium concentration 7. NaAR Dimensionless adjustment ratio [Na] of a defined hypo- or 8. NaH mmol/l, mM hypertonic Solution H 9. NaPre Pre-treatment PNa, i.e., PNa(0) mmol/l, mM 10. NaPost Post-treatment PNa mmol/l, mM RF1-[Na], unadjusted- 11. NaRF1 mmol/l, mM replacement fluid RF2-[Na], sodium-adjusted- 12. NaRF2 mmol/l, mM replacement fluid 13. PNa(t) Plasma [Na] at time (t) mmol/l, mM 14. QH Solution H flow rate ml/min Respective blood and plasma 15. QB, QP ml/min fluid flow rates 16. QRF Replacement fluid flow rate ml/min 17. QUF Net ultrafiltration flow rate ml/min 18. QEff Eff-RF flow rate ml/min 19. RF1 Replacement Fluid 1 — 20. RF2 Replacement Fluid 2 — 21. t Time min 22. URR Urea Reduction Ratio Dimensionless Total body water, i.e., Watson 23. V ml, L volume Volume of added hypertonic 24. V4M ml, L saline (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.
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Table 1b. | Sodium-based osmotherapy equations
Row Description Equation DNa = –(V/t) × LN(1 – NaAR) 1. Dialysance of sodium ion DNa = QP × [(QUF + QRF)/(QP + QRF)] Method 1 calculation of VRF2 = VRF1 × (NaRF1/NaRF2) 2. added water volume VW = VRF1 × [(NaRF1 – NaRF2)/NaRF2] Method 2 calculation of 3. VX = VRF1 × [(NaRF1 – NaRF2)/NaRF1)] water exchange volume Method 3 volume calculation 4. of added 4 M hypertonic V4M = VRF1 × [(NaRF2 – NaRF1)/(Na4m – NaRF2)] saline volume (23.4%) Method 4 calculation of 5. QH = QEff × [(NaRF1 – Eff-[Na])/(NaRF1 – NaH) Solution H fluid flow rate Method 4 Replacement Fluid QRF1 = QEff × [(Eff-[Na] – NaH)/(NaRF1 – NaH) 6. 1 (RF1) flow rate 7. Plasma flow rate calculation QP = QB × (1 – Hct) PNa(t) = PNa(0) + ∇Na(0) × (1 – e–DNa∙t/V); PNa(0) = NaPre Sodium concentration at 8. PNa(t) = PNa(0) + (NaRF2 − NaPre) × [(1 – e–DNa∙t/V)] treatment time (t) PNa(t) = NaPre + [(NaRF2 − NaPre) × NaAR] 9. Replacement Fluid flow rate QRF = (QP × DNa)/(QP – DNa) ∑Na(t) = [PNa(t) × (V – QUF × t)] – (NaPre × V) 10. Sodium balance at time (t) ∑Na(t) = [PNa(t) × (V – QUF × t)] – (PNa(0) × V)
NaAR = 1 – e–DNa∙t/V Sodium concentration 11. NaAR = ΔNa/∇Na(0) = (NaPost – NaPre)/(NaRF2 − adjustment ratio NaPre) Sodium concentration change ∆Na = ∇Na(0) × NaAR 12. at end-treatment time (t) ∆Na = NaPost – NaPre Sodium concentration 13. ∇Na(0) = NaRF2 – NaPre gradient, initial NaRF2 = NaPre + (∆Na/NaAR) 14. Sodium concentration of RF2 NaRF2 = NaPre + [ΔNa(t)/(1 – e–DNa∙t/V)]
Time at which specified PNa 15. tX = –(V/DNa) × LN{[NaRF2 – PNa(tX)]/(NaRF2 – NaPre)} occurs (tX) Ultrafiltration rate to achieve QUF(t) = [(NaPost × V) – (NaPre × V)]/(NaPost∙t) 16. net “0” sodium balance at QUF(t) = (∆Na × V)/(NaPost∙t) time (t) URR = 1 – e–KUrea∙t/V 17. Urea reduction ratio URR = [BUN(0) – BUN(t)]/[BUN(0) – BUNDialysate] VMan = 2.447 – 0.09156 × (Age, years) 18. Watson volume + 0.1074 × (Ht, cm) + 0.3362 × (Wt, kg) VWoman = –2.097 + 0.1069 × (Ht, cm) + 0.2466 × (Wt, kg)
See Table 1b for definitions of variables.
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Table 2. | Time-dependencies of plasma sodium concentration adjustment ratio and plasma sodium concentration during sodium-based osmotherapy
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)
Pre-dilution continuous venovenous hemofiltration 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 39.1 L Watson volume treated with the same parameters. Abbreviations: [Na], sodium concentration; NaAR,
sodium concentration adjustment ratio; PNa, plasma [Na]; PNa(0), PNa at time (t) = 0; PNa(t), PNa
at time (t); and ∆Na(t), PNa(t) minus PNa(0).
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Table 3. | Effects of intravenous solutions and urine output on the plasma effective- sodium concentration
4-h Solution RF 0.45% Solution A Solution B UO Results 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-[Na] (mM) 130.0 129.3 130.3 127.3 134.2 130.8
The replacement fluid is infused simultaneously with 3 separate solutions as shown, with ongoing urine output. Isolated effects of each solution or urine output on Eff-[Na] are displayed in the row labeled, “Eff-[Na].” Aggregate effects of solutions and urine output are presented in the column labeled, “4-h Results.“ Abbreviations: [Na], plasma sodium concentration; Eff-[Na], a blended solution of [Na] of RF1 and one of the solutions listed; RF, replacement fluid with [Na] = 130 mM. To simplify calculations, the RF-[K] is assumed equal to plasma [K] and therefore, not described.
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Table 4. | Effects of a 5% dextrose infusion on the plasma effective-sodium concentration during pre- and post-dilution continuous venovenous hemofiltration
D5W infusion 30 80 160 240 300 (ml/h) CHO load 0.28 0.74 1.48 2.22 2.78 (mg/kg∙min) PGLU, without carbohydrate 125 500 1100 1700 2150 metabolism for 24-h (mg/dl) Maintenance metabolic rate 0.15 0.62 1.36 2.10 2.65 (mg/kg∙min) Eff-[Na] (mM) 126.5 120.6 111.1 101.6 94.5 [PNa(0), 116 mM] Effects of a 5% dextrose infusion on the plasma effective-sodium concentration in a hypothetical, non-diabetic, 42-year-old, 178 cm, 90-kg man with Watson volume 48 L and
PNa(0) 116 mM (see text, Case 1) after 24 h of pre- and post-dilution continuous venovenous
hemofiltration with parameters: NaRF1, 130 mM; QP, 225 ml/min; combined D5W and RF1 flow rate, 1.1 L/h (18.3 ml/min); 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 PGlu (row 3). If CHO metabolism is present
and below the lipogenic threshold of 4 mg/kg·min, a stable PGlu of 100 mg/dl is maintained
(row 4). The rate-effect of a parallel, post-blood pump, pre-filter D5W infusion on Eff-[Na] is shown (row 5) and demonstrates that hyponatremia may be aggravated by excessively rapid
D5W infusions. Abbreviations: [Na], plasma sodium concentration; CVVH, continuous
venovenous hemofiltration; CHO, carbohydrate; D5W, 5% dextrose solution; RF, replacement
fluid; Eff-[Na], Effective-[Na] of combined infusions of D5W and RF; NaRF1, RF1-[Na]; PGLU,
plasma glucose concentration, QD5W, D5W flow rate; QP, plasma flow rate; and RF1, unadjusted-Replacement Fluid 1.
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Table 5. | Effect of pre- and post-dilution replacement fluid infusion on post-treatment plasma sodium concentration
Variable Units Pre-only Pre-/Post- Pre-/Post-
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-/Post-dilution 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 NaPre 120 mM undergoes 24 h of
continuous venovenous hemofiltration with the following parameters: NaRF1 130 mM, QP 200
ml/min, and QRF 3 L/h. Three simulations are shown: pre-dilution only and pre- and post-
dilution with QRF pre- and post-infusion ratios of 50/50 and 30/70. DNa, NaAR, and PNa(1440)
increase with an increasing proportion of post-dilution QRF. The maximal PNa(1440) difference among the 3 pre-/post-hemofilter combinations is 0.5 mM. Abbreviations: [Na], sodium
concentration; DNa, dialysance of sodium; NaAR, sodium concentration adjustment ratio;
NaRF1, replacement fluid [Na]; PNa, plasma [Na]; PNa(1440), PNa at t = 1440 min; QP, plasma
flow rate; and QRF, replacement fluid flow rate.
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Figure 1. | Model of sodium-based osmotherapy using pre-dilution continuous venovenous hemofiltration. The extracorporeal circuit is comprised of a hemofilter and replacement fluid. The hemofilter plasma inflow rate (QP) is advected by a sodium-adjusted-replacement fluid
(NaRF2). The sodium concentration gradient, ∇Na(t), equals the [Na]-difference between NaRF2
and PNa(t). NaAR is defined by sodium ion dialysance (DNa), time (t), and total body water volume
(V). Hemofilter effluent equals the sum of QRF2 and net ultrafiltration rate (QUF). Abbreviations:
[Na], sodium concentration; ∇Na(t), [Na]-gradient at time (t), or PNa(t)-to-NaRF2 difference; DNa,
dialysance of sodium ion; NaAR, sodium concentration adjustment ratio; NaRF2, RF2-[Na]; QP,
plasma flow rate; QRF2, RF2 flow rate; QUF, net ultrafiltration flow rate; RF2, sodium-adjusted- replacement fluid 2; V, volume (Watson volume); and t, time.
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Figure 2. | Time- and sodium gradient-dependent changes in plasma sodium concentration. Data are modeled from a hypothetical 42-year-old, 178 cm, 90-kg man) with Watson volume 48.0
L (see text, Case 1). PNa is 116 mM before pre-dilution continuous venovenous hemofiltration is carried out at 4 different [Na]-gradients. NaAR equals 0.4 after 1440 min of sodium-based osmotherapy. At end-treatment, PNa increases in direct proportion to ∇Na(0). Abbreviations: [Na], sodium concentration; ∇Na(0), [Na]-gradient between plasma and replacement fluid at time (0); NaAR, sodium concentration adjustment ratio; and PNa, plasma [Na].
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Figure 3. | Sodium concentration adjustment methods of replacement fluids. Method 1: Sterile water is added to Replacement Fluid 1 of volume VRF1 and sodium concentration NaRF1 to
produce Replacement Fluid 2 of volume VRF2 and sodium concentration NaRF2. Method 2: A
volume from Replacement Fluid 1 VX is exchanged with sterile water to produce Replacement
Fluid 2 of volume VRF2 and sodium concentration NaRF2. Method 3: A volume of 4 M NaCl solution is added to Replacement Fluid 1 to produce Replacement Fluid 2 of volume VRF2 and sodium
concentration NaRF2. Method 4: A hyper-, iso-, or hypotonic Solution H is infused post-blood pump, pre-hemofilter, and in parallel with Replacement Fluid 1 to produce a blended Effective- [Na] solution and flow rate. Abbreviations: H, a solution of defined sodium concentration (hypo-
, iso-, or hypertonic); [Na], sodium concentration; Eff-Na, Effective-[Na] of blended solution; NaH,
Solution H-[Na]; QEff, additive flow rate of QRF1 and QH; QH, Solution H flow rate; RF1,
Replacement Fluid 1; RF2, Replacement Fluid 2; NaRF1, RF1-[Na], NaRF2, RF2-[Na]; QRF1, RF1 flow rate; QRF2, RF2 flow rate; V4M, 4 M saline volume; VRF1, RF1 volume; VRF2, RF2 volume; VW, water
volume added to RF1; and VX, RF1 exchange volume.
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Figure 4. | Plasma sodium concentration dependency on Watson volume. 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 (F) with Watson volume 39.1 L (•). The baseline plasma and replacement fluid sodium concentrations of both patients are, respectively, 116 mM and 136 mM. Continuous venovenous hemofiltration treatment parameters: QP, 225 ml/min; QRF, 18.3
ml/min; QUF, 0 ml/min; and treatment-time, 4320 min. The PNa of the woman is greater at all
timepoints due to her smaller Watson volume. Abbreviations: QP, plasma flow rate; QRF,
replacement fluid rate; QUF, net ultrafiltration fluid rate; and PNa, plasma sodium concentration.
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Figure 5. | Time course of plasma sodium concentration and total body sodium balance during pre-dilution continuous venovenous hemofiltration. Treatment parameters of a hypothetical, non-edematous, 170 cm, 80 kg, 30-year-old man with Watson volume 44.85 L, are as follows (see text, Case 2): NaRF2, 128 mM; QP, 200 ml/min; QRF2, 50 ml/min; QUF, 2.5 ml/min; and treatment-
time, t = 1440 min. At end-treatment, NaAR is 0.74 and PNa increases from 120 mM to 126 mM (top plot). Negative sodium balance begins at t = 240 min. Cumulative sodium loss is 185 mmol at end-treatment (bottom plot). Abbreviations: [Na], sodium concentration; DNa, dialysance of
sodium ion; NaAR, sodium concentration adjustment ratio; NaRF2, RF2-[Na]; PNa, plasma [Na]; QP, plasma flow rate; QRF2, RF2 flow rate; QUF, net ultrafiltration rate; RF, replacement fluid; RF2, sodium adjusted-replacement fluid 2; and V, Watson volume.
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