"Everything should be made as simple as possible, but not simpler." - Albert Einstein

Seminar Announcement

Continuous Blood-glucose Monitoring in Insulin-dependent Diabetes Mellitus: An Application of the Extended Kalman Filter

Atul Sharma, M.S. Candidate, Department of Statistics, Colorado State University

Friday, September 18, 2009

10:30 a.m., Room 008, Statistics Building

ABSTRACT

State-space models are powerful tools for the description, analysis, prediction and control of complex dynamical systems, their defining feature being the identification of an unobserved or hidden state vector whose time evolution is described by a formal system or process model. A complementary model describes the measurement or observation process. In insulin-dependent diabetes (type I IDDM), both hypoglycemia (low blood sugar) and hyperglycemia (high blood sugar) constitute serious risks. Successful therapy must balance competing dangers, which has historically evolved with advances in the technologies available for routine blood glucose monitoring. To this end, several manufacturers have introduced continuous glucose monitoring systems (CGMS) to infer blood glucose concentrations from a continuous-time, interstitial fluid (ISF) sensor embedded in the skin of the abdomen. The lack of a reliable relationship between skin and blood glucose concentrations (e.g. 50-150% in either direction) remains a significant barrier to applying this technology in a useful way. Novel elements of this treatment include:

• Process and observation Models: Previous reports have applied the Kalman filter paradigm to the blood glucose estimation problem. Palerm et al (2005) modeled interstitial fluid glucose concentrations as a random walk to identify hypogylycemia as a simple binary outcome, without attempting to identify hyperglycemia. Knobbe and Buckingham (2005) introduced a simplified diffusion-limited transport process based on animals studies implicating diffusion lag as the principle cause of the observed disequilibration between fluid compartments. Here, we adopt a physically and biologically plausible model of intercompartmental glucose transport to account for the role of diffusion kinetics in both blood and interstitial fluid (ISF) compartments, with a time-varying glucose source term to reflect the net balance of glucose absorption (gut), insulin-induced uptake (muscle), and synthesis (liver).

• Kalman Smoother: To improve prediction accuracy by revisiting and updating earlier estimates as new observations become available, we implement an efficient backward smoothing algorithm, which retains the O(n) complexity of the ‘classical’ EKF. This algorithm is the basis of a hybrid, real-time combination of forward and backward recursions, combining a limited number of backward smoothing steps with each observation. Algorithmic efficiency is an important consideration, since the intended application is a portable, real-time monitor running on an embedded microprocessor.

• Divided Difference Filter (DDF): We formally compare performance with that of a novel, non-linear, derivative-free filter based on the Stirling polynomial interpolation formula, which is applicable to a wider class of models and is easier to derive and implement. More importantly, the DDF is said to deliver comparable accuracy with less computational complexity (N¨orgaard et al, 2000).

• Comparison with reference method: Bland-Altman plots are used to assess bias and 95% limits of agreement, a well established clinical method for comparing laboratory assays with a reference method, leaving the clinician with the final word as to how much agreement is clinically necessary.

Advisory Committee:
Dr. Dan Cooley, Advisor
Dr. Jean Opsomer, Committee Member

Dr. Louis Scharf, Electrical & Computer Engineering, Outside Committee Member