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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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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DOI: https://doi.org/10.1007/s10439-011-0383-5