Kidney-related operations research: A review

Abstract

Operations research and optimization in healthcare and disease modeling have received significant attention in the last three decades. This article surveys several perspectives of operations research techniques in kidney disease, such as graph theory, queueing theory, Markov chain, and phase-type distribution (PTD). The kidney-related problems include kidney exchange problem, the modeling of kidney disease progression, kidney transplantation, and the complex relationship between chronic kidney disease (gradual loss of kidney function over time) and acute kidney injury (sudden episode of kidney failure in a few hours or a few days). Each section is summarized by some discussion regarding the limitation of proposed methods in the literature. Finally, the article is concluded by offering some research direction to fill in the gaps in the literature.

Keywords:

• Acute kidney injury
• chronic kidney disease
• graph theory
• kidney disease
• kidney transformation
• Markov decision process
• operations research
• phase-type distribution
• queueing theory

Acknowledgment

The authors would like to thank Prof. Panos M. Pardalos, Prof. Azra Bihorac, Prof. Parta Hatamizadeh, and Prof. Amir Kazory for providing a visiting research opportunity for studying kidney disease at the PRISMA Group at the Division of Nephrology, Hypertension, & Renal Transplantation, Department of Medicine, University of Florida. Also, we would like to thank Prof. John A. Kellum of the Department of Critical Care Medicine, University of Pittsburgh, for his constructive discussion about an earlier version of the article, the paradigm of AKI to CKD, and its future research direction.

Notes

1 GFR is a test used to check how well the kidneys are working. Specifically, it estimates how much blood passes through the glomeruli each minute.

2 AER is a test to describe how much kidney leaks albumin into the urine per 24 hours.

3 ACR is an annual test after a diagnosis of diabetes or HBP, comparing the amount of albumin in the sample against its concentration of creatinine.

4 MATLAB code is available at https://sites.google.com/site/joshmikemath/code

5 Graft survival rate is an estimate of the probability of the transplant kidney functioning at a finite time after transplantation.