Homeostatic model assessment
The HOMA authors used data from physiological studies to develop mathematical equations describing glucose regulation as a feedback loop.  They published computer software that solves the equations, so that insulin resistance and β-cell function can be estimated from fasting glucose and insulin levels. They also published an equation (see below) that gave approximately the same answers as an early version of the computer software. 
The computer model has since been improved to a HOMA2 model to better reflect human physiology and recalibrated to modern insulin assays. In this updated version it is possible to determine insulin sensitivity and β-cell function from paired fasting plasma glucose and radioimmunoassay insulin, specific insulin, or C-peptide concentrations. The authors recommend the computer software be used wherever possible.  
The HOMA model was originally designed as a special case of a more general structural (HOMA-CIGMA) model that includes the continuous infusion of glucose with model assessment (CIGMA) approach; both techniques use mathematical equations to describe the functioning of the major effector organs influencing glucose/insulin interactions.
The approximating equation for insulin resistance, in the early model, used a fasting plasma sample, and was derived by use of the insulin-glucose product, divided by a constant: (assuming normal-weight, normal subjects < 35 years, having 100% β-cell function an insulin resistance of 1)
|Glucose in Molar Units mmol/L||Glucose in mass units mg/dL|
The approximation formulae above relate to HOMA and are crude estimates of the model near normal levels of glucose and insulin in man. The actual calculated HOMA2 compartmental model is published  and is available as the interactive Homeostatic Model Assessment 2 (iHOMA2).
- Turner RC, Holman RR, Matthews D, Hockaday TD, Peto J (1979). "Insulin deficiency and insulin resistance interaction in diabetes: estimation of their relative contribution by feedback analysis from basal plasma insulin and glucose concentrations.". Metabolism. 28 (11): 1086–96. doi:10.1016/0026-0495(79)90146-X. PMID 386029.
- Matthews DR, Hosker JP, Rudenski AS, Naylor BA, Treacher DF, Turner RC (1985). "Homeostasis model assessment: insulin resistance and beta-cell function from fasting plasma glucose and insulin concentrations in man.". Diabetologia. 28 (7): 412–9. doi:10.1007/BF00280883. PMID 3899825.
- A. S. Rudenski; D. R. Matthews; J. C. Levy; R. C. Turner (September 1991). "Understanding insulin resistance: Both glucose resistance and insulin resistance are required to model human diabetes". Metabolism. 40 (9): 908–917. doi:10.1016/0026-0495(91)90065-5. ISSN 0026-0495. PMID 1895955.
- Wallace TM, Levy JC, Matthews DR (2004). "Use and abuse of HOMA modeling.". Diabetes Care. 27 (6): 1487–95. doi:10.2337/diacare.27.6.1487. PMID 15161807.
- Levy JC, Matthews DR, Hermans MP (1998). "Correct homeostasis model assessment (HOMA) evaluation uses the computer program.". Diabetes Care. 21 (12): 2191–2. doi:10.2337/diacare.21.12.2191. PMID 9839117.
- Turner et al. (1993) Measurement of insulin resistance and β-cell function: the HOMA and CIGMA approach. Current topics in diabetes research (eds) F. Belfiore, R. Bergman and G. Molinatti Front Diabetes. Basel, Karger 12: 66-75
- Hermans MP, Levy JC, Morris RJ, Turner RC (1999). "Comparison of tests of beta-cell function across a range of glucose tolerance from normal to diabetes.". Diabetes. 48 (9): 1779–86. doi:10.2337/diabetes.48.9.1779. PMID 10480608.
- Hermans MP, Levy JC, Morris RJ, Turner RC (1999). "Comparison of insulin sensitivity tests across a range of glucose tolerance from normal to diabetes.". Diabetologia. 42 (6): 678–87. doi:10.1007/s001250051215. PMID 10382587.
- Hill NR, Levy JC, Matthews DR (2013). "Expansion of the homeostasis model assessment of β-cell function and insulin resistance to enable clinical trial outcome modeling through the interactive adjustment of physiology and treatment effects: iHOMA2.". Diabetes Care. 36 (8): 2324–30. doi:10.2337/dc12-0607. PMC . PMID 23564921.