Mathematical modeling in chronic kidney disease

1. Mathematical modeling in chronic kidney disease Peter Kotanko, MD Renal Research Institute, New York pkotanko@rriny.com Bangalore, March 2008

4. Life Expectancy at 45 to 54 and 55 to 64 Years of Age in the U.S. Resident Population and among Persons with Selected Chronic Diseases Pastan S and Bailey J. N Engl J Med 1998;338:1428-1437

5. Uremic Solutes Meyer T and Hostetter T. N Engl J Med 2007;357:1316-1325

6. Hemodialysis Circuit

7. Hemodialysis Vascular Access by Native Arteriovenous Fistula Ifudu O. N Engl J Med 1998;339:1054-1062

8. Vascular Access (Shunt)

9. Hemodialysis: Combination of Diffusive & Convective Transport Forni L and Hilton P. N Engl J Med 1997;336:1303-1309

10. Blood Urea Nitrogen Levels in Two Theoretical Patients Undergoing Conventional Thrice-Weekly Hemodialysis for 3 Hours on Monday, Wednesday, and Friday Meyer T and Hostetter T. N Engl J Med 2007;357:1316-1325

11. Overhydration in dialysis patients • During each dialysis session the amount of fluid taken on in the inter-dialytic period has to be removed (as much as 6 L/4 hrs) • Chronic overhydration results in cardiovascular disease (high blood pressure, left ventricular hypertrophy, …)

12. Pathophysiology of chronic volume overload Chronic volume overload Increased blood pressure End organ damage Left ventricular hypertrophy Vascular disease Arrhythmia; myocardial infarction; sudden death Cardiovascular disease Cerebro-vascular disease TIA; stroke

13. Removal of Fluid and Solutes by Ultrafiltration with the Goal to Achieve “Dry Weight” (the “Holy Grail” in dialysis) Capillary Bed Interstitial Fluid Blood Compartment (venous) Removal of Plasma Water During Dialysis by Ultrafiltration

14. But there is are problems … • There is no uniform definition of “dry weight” • There is no universally accepted method to determine “dry weight” • Determination of “dry weight” by bioimpedance (BIA) of the calf is a potential means • Multifrequency BIA determines the extracellular volume in a given segment

15. Concomitant Recording of Relative Blood Volume Change and Calf ECV change Blood volume monitor (BVM) Dry weight monitor

16. Questions: Can the dynamics of interstitial fluid be modeled in order to determine “dry weight” without the need of frequent BIA measurements? What we know: ultrafiltration rate (HD machine) relative change in blood volume (BVM) change in calf ECV (Dry Weight Monitor) serum albumin level What we don’t know: capillary pressure interstitial protein conc.

17. Goal • Bringing the patient to dry weight, • avoiding the deleterious consequences of overhydration, • reducing the need for uncomfortable measurements

18. Body composition in dialysis patients: implications for outcomes

19. Background • There is convincing evidence that in contrast to findings in the general population high body mass index (BMI; weight [kg] / (height [m])2) in dialysis patients is associated with improved survival • But: BMI does not differentiate between various components of body composition

20. BMI and survival in the general and the HD population Kalantar-Zadeh, 2006

21. Same BMI – Different Body Composition

22. RRI Hypothesis • Uremic toxin generation occurs predominantly in the visceral organs (“high metabolic rate compartment”; HMRC). The mass of key uremiogenic viscera (gut, liver) is relative to body weight or BMI larger in small people • Uremic toxins (both lipophilic and hydrophilic) are taken up by adipose and muscle tissues and metabolized and/or stored • The amount of in-tissue metabolism of uremic toxins depends on the fat and muscle mass • Most important: Since dialysis dose is prescribed per urea distribution volume (=total body water), small patients may be at an increased risk of under-dialysis Levin, Gotch, JASN 2001 Sarkar, KI 2006 Kotanko, Blood Purif 2007

23. Predictions made by the RRI model • Concentration of uremic toxins relate inversely to body size • Production rate of uremic toxins per unit of body mass is higher in small subjects • Large patients may have better surrogate outcomes • Small patients experience better outcomes with higher dialysis doses Sarkar, Semin Dial 2007

24. High Metabolic Rate Compartment and BMI are inversely related Sarkar, Kidney Int 2006

25. Body size, gut, muscle, fat, and uremic toxins Large patient Fat Muscle Small patient Muscle Fat Uremic Toxin Generation Uremic Toxin Generation Visceral Organs Sarkar, KI 2006 Kotanko, Blood Purif 2007

26. 3-compartment modelof (hydrophilic) uremic toxin kinetics(Cronin-Fine, IJAO 2007) Visceral Organs Extracellular Fluid Muscle Mass

27. Uremic Toxin Concentration Relates to Body Size (Cronin-Fine, IJAO 2007)

28. The Plasma Concentration of Pentosidine Relates Inversely to BMI 80 70 R = - 0.55 P < 0.001 60 50 Total pentosidine plasma concentration (pmol/mg protein) 40 30 20 10 14 18 22 26 34 38 42 30 (Slowik-Zylka, 2006) BMI (kg/m2)

29. Body size, gut, muscle, fat, and uremic toxins Large patient Fat Muscle Small patient Muscle Fat Uremic Toxin Generation Uremic Toxin Generation Visceral Organs Sarkar, KI 2006 Kotanko, Blood Purif 2007

30. Relation of Total Organ Mass to Body Weight in 2.004 HD Patients Total organ mass was calculated using regression models by Gallagher et al (Am J Clin Nutr. 2006, 83:1062) FEMALES MALES N=911 N=1.093 HMRO mass [% of Body Weight] BMI [kg/m2] BMI [kg/m2] Kotanko & Levin Int J Artif Organs, 2007

31. Survival Stratified by Tertiles of Race- and Sex-Specific Visceral Organ Mass (% of Weight) N = 2004 P = 0.0001 (log-rank test) Mean Survival (days) Low Tertile: 1031 Middle Tertile: 935 High Tertile: 876 Kotanko, IJAO 2007

32. Question: is it possible to model the dynamics of uremic toxins with a model including estimates of fat and visceral mass? • What we know: estimates of body composition (fat, muscle, total body water, visceral mass, blood levels of toxins) • What we don’t know: tissue concentrations of uremic toxins, exchange rates

33. Goal down the road …. • Future dialysis prescription may account for aspects of body composition beyond urea distribution volume and thus improve the care independent of body composition (females/males; small/large)

34. Hypothesis: Low SBP is the Terminal Pathway of Various Pathological Processes High Systolic Blood Pressure Antihypertensive Therapy Cardiovascular Disease Malnutrition Inflammation Infection Low Systolic Blood Pressure

35. Systolic Blood Pressure Relates to Mortality AJKD, 2006

36. Very simple Markov model of SBP evolution predicts survival Kotanko, EDTA 2008

37. Evolution of pre-HD SBP in surviving HD patients(total N=39.969 HD patients) Follow-up time Kotanko et al, ISN Nexus, 2007

38. Evolution of pre-HD SBP in non-survivors Follow-up time Kotanko et al, ISN Nexus, 2007

39. SBP Evolution by Gender & Race

40. Question: what is the best way to model correlated longitudinal SBP data taking covariates into account ?Ultimate goal: development of an automated alarm system to trigger early diagnostic & therapeutic intervention in deteriorating patients.

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