Mathematical modeling in chronic kidney disease Peter Kotanko, MD Renal Research Institute, New York Bangalore, March 2008

Pastan S and Bailey J. N Engl J Med 1998;338: 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

Meyer T and Hostetter T. N Engl J Med 2007;357: Uremic Solutes

Hemodialysis Circuit

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

Vascular Access (Shunt)

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

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

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, …)

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

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

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

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

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.

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

Body composition in dialysis patients: implications for outcomes

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

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

Same BMI – Different Body Composition

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

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

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

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

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

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

The Plasma Concentration of Pentosidine Relates Inversely to BMI Total pentosidine plasma concentration (pmol/mg protein) BMI (kg/m2) R = P < (Slowik-Zylka, 2006)

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

Relation of Total Organ Mass to Body Weight in HD Patients MALES FEMALES Total organ mass was calculated using regression models by Gallagher et al (Am J Clin Nutr. 2006, 83:1062) Kotanko & Levin Int J Artif Organs, 2007 HMRO mass [% of Body Weight] BMI [kg/m 2 ] N=1.093 N=911

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

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

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)

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

AJKD, 2006 Systolic Blood Pressure Relates to Mortality

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

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

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

SBP Evolution by Gender & Race

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.

Thank you for your attention Gracias por su atención Danke für Ihre Aufmerksamkeit Go raibh maith agat Grazie per l´Attenzione Aap saab ka shukriya… Merci pour votre attention شكرا لإنتباهكم