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
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
• 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.
Dr. Dan Cooley, Advisor
Dr. Jean Opsomer, Committee Member
Dr. Louis Scharf, Electrical & Computer Engineering, Outside Committee Member