Virtual Trials with b-spline Basis Functions and Stochastic Differential Equations

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• 作者：Liam M. Fisk^* ; ^{liam.fisk@pg.canterbury.ac.nz" class="auth_mail" title="E-mail the corresponding author} ; Paul D. Docherty^* ; Christopher G. Pretty^* ; Jennifer L. Dickson^* ; Geoffrey M. Shaw^** ; J. Geoffrey Chase^* ; ^{geoff.chase@canterbury.ac.nz" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Identification and validation ; chronic care and/or diabetes ; decision support and control
• 刊名：IFAC-PapersOnLine
• 出版年：2014
• 出版时间：2014
• 年：2014
• 卷：47
• 期：3
• 页码：10976-10981
• 全文大小：775 K

文摘

Virtual trials have proved useful in developing safe and efficacious glycaemic control protocols. However, these trials rely on lumping all changes in patient condition into the insulin sensitivity parameter. As electronic data collection provides higher temporal resolution than paper-based charts, irregular timings of both therapies and measurements clash with a regular, hourly insulin sensitivity profile. Additionally, unobservable endogenous changes are a factor for hour-to-hour variability. This research extends the virtual trial protocol to natively handle irregular data by regularising the insulin sensitivity profile, and utilising a simple stochastic differential equation. The insulin sensitivity profile was re-interpreted as a b-spline basis, allowing a higher order description with greater local support. The fitting error resulting from this regularisation was absorbed by a stochastic element in the glucose compartment, representing the hour-to-hour changes that cannot be attributed to changes in insulin sensitivity. The resulting virtual patients were demonstrated to be equivalent to the originals when a 0^th order basis was used. Inclusion of the stochastic element in this case simply ensured the model still fitted during periods of unmodelled high endogenous glucose production, while a 2^nd order basis uses this element to natively control the balance between changes in patient state and hour-to-hour unmodelled changes due to noise and endogenous processes. The resulting virtual trials are thus better able to preserve information in irregular data sets, and regulate the balance between controllable and uncontrollable glycaemic changes.