Mathematical modeling in chronic kidney disease

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Mathematical modeling in chronic kidney disease

• Peter Kotanko, MD
• Renal Research Institute, New York
• pkotanko_at_rriny.com
• Bangalore, March 2008

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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
19983381428-1437
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Uremic Solutes
Meyer T and Hostetter T. N Engl J Med
20073571316-1325
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Hemodialysis Circuit
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Hemodialysis Vascular Access by Native
Arteriovenous Fistula
Ifudu O. N Engl J Med 19983391054-1062
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Vascular Access (Shunt)
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Hemodialysis Combination of Diffusive
Convective Transport
Forni L and Hilton P. N Engl J Med
19973361303-1309
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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
20073571316-1325
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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, )

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Pathophysiology of chronic volume overload
Chronic volume overload
Increased blood pressure
End organ damage
Left ventricular hypertrophy
Vascular disease
Cerebro-vascular disease
Cardiovascular disease
Arrhythmia myocardial infarction sudden death
TIA stroke
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Removal of Fluid and Solutes by Ultrafiltration
with the Goal to Achieve Dry Weight (the Holy
Grail in dialysis)
Capillary Bed
Blood Compartment (venous)
Interstitial Fluid
Removal of Plasma Water During Dialysis by
Ultrafiltration
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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

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Concomitant Recording of Relative Blood Volume
Change and Calf ECV change
Blood volume monitor (BVM)
Dry weight monitor
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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 dont know
• capillary pressure
• interstitial protein conc.

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Goal

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

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Body composition in dialysis patients
implications for outcomes
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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

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BMI and survival in the general and the HD
population
Kalantar-Zadeh, 2006
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Same BMI Different Body Composition
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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
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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
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High Metabolic Rate Compartment and BMI are
inversely related
Sarkar, Kidney Int 2006
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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
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3-compartment modelof (hydrophilic) uremic toxin
kinetics (Cronin-Fine, IJAO 2007)
Visceral Organs
Extracellular Fluid
Muscle Mass
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Uremic Toxin Concentration Relates to Body Size
(Cronin-Fine, IJAO 2007)
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The Plasma Concentration of Pentosidine Relates
Inversely to BMI
80
70
R - 0.55 P lt 0.001
60
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Total pentosidine plasma concentration (pmol/mg
protein)
40
30
20
10
14
26
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(Slowik-Zylka, 2006)
BMI (kg/m2)
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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
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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,
831062)
FEMALES
MALES
N911
N1.093
HMRO mass of Body Weight
BMI kg/m2
BMI kg/m2
Kotanko Levin Int J Artif Organs, 2007
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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
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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 dont know tissue concentrations of
  uremic toxins, exchange rates

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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)

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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
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Systolic Blood Pressure Relates to Mortality
AJKD, 2006
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Very simple Markov model of SBP evolution
predicts survival
Kotanko, EDTA 2008
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Evolution of pre-HD SBP in surviving HD
patients(total N39.969 HD patients)
Follow-up time
Kotanko et al, ISN Nexus, 2007
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Evolution of pre-HD SBP in non-survivors
Follow-up time
Kotanko et al, ISN Nexus, 2007
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SBP Evolution by Gender Race
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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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• Thank you for your attention
• Gracias por su atención
• Danke für Ihre Aufmerksamkeit
• Go raibh maith agat
• Grazie per lAttenzione
• Aap saab ka shukriya
• Merci pour votre attention
• ???? ?????????

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