Construction of a Mathematical Model for Conventional Haemodialysis and Continuous Renal Replacement Therapy in Subjects with Hyponatraemia or Hypernatraemia and/or hyperkalaemia

Author(s)

Abstract
Background:
Dialysis in patients with dysnatraemia and hyperkalaemia is generally difficult because needing to minimize [Na] correction while ensure rapid [K] correction, and thus a need for mathematical model.
Methods:
A model was derived with 80 regular ESRD dialysis sessions and 10 acute dialysis (AD) sessions. Clinical audit was performed assessing error of this model with new set of 33 AD of HD and CRRT with [Na] <=130 or >=150mmol/L pre-dialysis.
Results:
Na prediction could be derived with dialysate flow rate (Qd) clearance calculation and solute transport, assuming that all plasma flow is changed to the dialysate Na concentration, i.e., Qd with limit by plasma flow rate. However, a refined calculation was for intracellular solute such as K and urea, for Qd being multiplied by the factor of: Blood water flow rate / (blood water flow rate + dialysate flow rate), i.e., BWFR/ (BWFR+Qd).
And, because of varying “volume of distribution”, the total body water (TBW) needs to be adjusted with fuzzy factor, namely fNa, fK, and furea, which were determined as 0.846, 1.931, and 1.128 respectively (of Watson TBW). Extracellular electrolyte has lower fuzzy factor than predominant intracellular electrolyte.
The errors in absolute number for serum Na, K, urea and osmolarity estimation prediction were 1.8 ±1.3, 0.32 ±0.34, 2.3 ±1.9 and 3.8 ±3.2 mmol/L, respectively. Good reliability and correlation were shown between predicted and measured parameters.
Conclusion:
Model substantiates fuzzy factor correction for TBW, and also dialysis clearance calculation with Qd limit by plasma flow rate for extracellular electrolyte, and in contrast, the need of Qd dilution by factor of (BWFR/(BWFR+Qd)) for intracellular electrolyte. Low errors in absolute number between predicted and actual electrolyte were shown.

Keywords
Haemodialysis, Continuous Renal Replacement Therapy, Hyponatraemia, Hypernatraemia, Hyperkalaemia, Acute Kidney Injury, End Stage Kidney Disease

Cite this paper
Keng-Hee Koh, Construction of a Mathematical Model for Conventional Haemodialysis and Continuous Renal Replacement Therapy in Subjects with Hyponatraemia or Hypernatraemia and/or hyperkalaemia , American Journal of Nephrology and Urology. Volume 1, Issue 1, January 2023 | PP. 1-26. 10.54647/ajnu1101002

References

[ 1 ]	Yessayan L, Yee J, Frinak S, Szamosfalvi B. Continuous Renal Replacement Therapy for the Management of Acid-Base and Electrolyte Imbalances in Acute Kidney Injury. Adv Chronic Kidney Dis. 2016;23(3):203-210.
[ 2 ]	Sterns RH. Disorders of plasma sodium--causes, consequences, and correction. N Engl J Med. 2015;372(1):55-65.
[ 3 ]	Koh KH. Impact of pre-dilution and flushing on continuous renal replacement therapy. Singapore Med J. 2006;47(9):785-795.
[ 4 ]	Adrogué HJ, Madias NE. Hyponatremia. N Engl J Med. 2000;342(21):1581-1589.
[ 5 ]	Lim VS, Flanigan MJ, Fangman J. Effect of hematocrit on solute removal during high efficiency hemodialysis. Kidney Int. 1990;37(6):1557-1562.
[ 6 ]	Little MA, Conlon PJ, Walshe JJ. Access recirculation in temporary hemodialysis catheters as measured by the saline dilution technique. Am J Kidney Dis. 2000;36(6):1135-1139.
[ 7 ]	Watson PE, Watson ID, Batt RD. Total body water volumes for adult males and females estimated from simple anthropometric measurements. Am J Clin Nutr. 1980;33(1):27-39.
[ 8 ]	Lim TO, Ding LM, Zaki M, et al. Distribution of body weight, height and body mass index in a national sample of Malaysian adults. Med J Malaysia. 2000;55(1):108-128.
[ 9 ]	Huang WY, Weng WC, Peng TI, Ro LS, Yang CW, Chen KH. Central pontine and extrapontinemyelinolysis after rapid correction of hyponatremia by hemodialysis in a uremic patient. Ren Fail. 2007;29(5):635-638.
[ 10 ]	Wendland EM, Kaplan AA. A proposed approach to the dialysis prescription in severely hyponatremic patients with end-stage renal disease. Semin Dial. 2012;25(1):82-85.
[ 11 ]	Yessayan L, Yee J, Frinak S, Szamosfalvi B. Treatment of severe hyponatremia in patients with kidney failure: Role of continuous venovenous hemofiltration with low-sodium replacement fluid. Am J Kidney Dis. 2014; 64: 305– 310.
[ 12 ]	Spasovski G, Vanholder R, Allolio B, et al. Clinical practice guideline on diagnosis and treatment of hyponatraemia [published correction appears in Nephrol Dial Transplant. 2014 Jun;40(6):924]. Nephrol Dial Transplant. 2014; 29 Suppl 2:i1-i39.
[ 13 ]	Verbalis JG, Goldsmith SR, Greenberg A, et al. Diagnosis, evaluation, and treatment of hyponatremia: expert panel recommendations. Am J Med. 2013;126(10 Suppl 1):S1-S42.
[ 14 ]	Sterns RH. Treatment of Severe Hyponatremia. Clin J Am SocNephrol. 2018;13(4):641-649.
[ 15 ]	Sterns RH, Hix JK, Silver S. Treating profound hyponatremia: a strategy for controlled correction. Am J Kidney Dis. 2010;56(4):774-779.
[ 16 ]	Sterns RH. Disorders of plasma sodium--causes, consequences, and correction. N Engl J Med. 2015;372(1):55-65.
[ 17 ]	Daugirdas JT, Al-Kudsi RR, Ing TS, Norusis MJ. A double-blind evaluation of sodium gradient hemodialysis. Am J Nephrol. 1985;5(3):163-168.
[ 18 ]	Pirklbauer M. Hemodialysis treatment in patients with severe electrolyte disorders: Management of hyperkalemia and hyponatremia. Hemodial Int. 2020;24(3):282-289.