We know much about the glucose regulatory system, yet the application of this knowledge is limited because simultaneous measurements of insulin and glucose are difficult to obtain. We present a data assimilation framework for combining sparse measurements of the glucose regulatory system, available in the intensive care unit setting, with a nonlinear computational model to estimate unmeasured variables and unknown parameters. We also demonstrate a method for choosing the best variables for measurement. We anticipate that this framework will improve glucose maintenance therapies and shed light on the underlying biophysical process.