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A Regional Blood Flow Model for β2-Microglobulin Kinetics and for Simulating Intra-dialytic Exercise Effect

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An Erratum to this article was published on 16 March 2012

Abstract

A kinetic model based on first principles, for β2-microglobulin, is presented to obtain precise parameter estimates for individual patient. To reduce the model complexity, the number of model parameters was reduced using a priori identifiability analysis. The model validity was confirmed with the clinical data of ten renal patients on post-dilution hemodiafiltration. The model fit resulted in toxin distribution volume (V d) of 14.22 ± 0.75 L, plasma fraction in extracellular compartment (f P) of 0.39 ± 0.03, and inter-compartmental clearance of 44 ± 4.1 mL min−1. Parameter estimates suggest that V d and f P are much higher in hemodialysis patients than in normal subjects. The developed model predicts larger removed toxin mass than that predicted by the two-pool model. On the application front, the developed model was employed to explain the effect of intra-dialytic exercise on toxin removal. The presented simulations suggest that intra-dialytic exercise not only increases the blood flow to low flow region, but also decreases the inter-compartmental resistance. Combined, they lead to increased toxin removal during dialysis and reduced post-dialysis rebound. The developed model can assist in suggesting the improved dialysis dose based on β2-microglobulin, and also lead to quantitative inclusion of intra-dialytic exercise in the future.

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Abbreviations

α :

Fluid intake rate during inter-dialysis period (L min−1)

C art :

Arterial toxin concentration (measured concentration) (mg L−1)

C mn :

Toxin concentration in mth region, nth compartment (mg L−1) m \( \in \) [h,l], n \( \in \) [p,i]

CO:

Cardiac output (L min−1)

e :

Fluid volume fraction of extracellular space

f m :

Blood flow fraction to mth region

f P :

Fluid volume fraction of plasma compartment in extracellular space

\( G_{{\beta_{2} {\text{M}}}} \) :

β2-Microglobulin generation rate (mg min−1)

HCT:

Hematocrit

K D :

Dialyzer clearance (mL min−1)

K ip :

Inter-compartmental mass transfer coefficient (mL min−1)

k m :

Fluid volume fraction of mth region

K NR :

Non-renal clearance (mL min−1)

Q b/Q bp :

Blood/plasma flow to dialyzer (L min−1)

Q h/Q l :

Systemic blood flow to high/low flow region (L min−1)

Q hp/Q lp :

Systemic plasma flow to high/low flow region (L min−1)

Q s :

Systemic plasma flow (L min−1)

Q uf :

Constant ultrafiltration rate (L min−1)

V d :

Toxin distribution volume (L)

V mn :

Fluid volume in mth region, nth compartment (L)

Z :

Scaled sensitivity matrix

h/l:

High/Low flow region

p/i:

Plasma/Interstitium compartment

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Acknowledgments

We thank Dr. Richard A. Ward (University of Louisville, USA) for providing the de-identified patient data for testing the developed model. We also acknowledge Dr. Titus Lau and Dr. Kheng Boon Lim (National University Hospital, Singapore) for their valuable comments and suggestions.

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Authors and Affiliations

  1. Department of Chemical and Biomolecular Engineering, National University of Singapore, Singapore, Singapore

    Vaibhav Maheshwari, Lakshminarayanan Samavedham & Gade P. Rangaiah

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  1. Vaibhav Maheshwari
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  2. Lakshminarayanan Samavedham
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  3. Gade P. Rangaiah
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Corresponding author

Correspondence to Lakshminarayanan Samavedham.

Additional information

Associate Editor Gerald Saidel oversaw the review of this article.

An erratum to this article can be found at http://dx.doi.org/10.1007/s10439-012-0547-y.

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Maheshwari, V., Samavedham, L. & Rangaiah, G.P. A Regional Blood Flow Model for β2-Microglobulin Kinetics and for Simulating Intra-dialytic Exercise Effect. Ann Biomed Eng 39, 2879–2890 (2011). https://doi.org/10.1007/s10439-011-0383-5

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