Substance monitoring and control in human or animal bodies

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First Claim
1. Apparatus for real time control of glucose in a human or an animal, the apparatus comprising:
 a sensor providing a time series of measurements of glucose level, said measurements being indicative of an inferred level of said glucose in a part of said human or animal, a processor which is adapted to perform the following steps;
calculate a first estimate of said inferred glucose level from said measured glucose level using a first glucoregulatory system model, calculate a second estimate of said inferred glucose level from said measured glucose level using a second glucoregulatory system model with said second system model being a variation of said first system model, and predict a combined estimate of the inferred glucose level based on a combination of the first and second estimates, wherein the processor is a state estimator and is adapted to define a state vector for each model, the state vector comprising a set of variables each having an associated uncertainty, the set of variables including a variable representing an unexplained change in glucose level with each model having a different standard deviation in the unexplained change in glucose level;
wherein the first and second glucoregulatory models each comprise a submodel of glucose kinetics in the blood of said human or animal, a submodel of interstitial glucose kinetics, a submodel of insulin absorption, a submodel of insulin action and a submodel of gut absorption; and
wherein the state vector includes the following states
x_{k}=(q_{1ƒ,k},q_{2ƒ,k}u_{S,k},F_{k},q_{3ƒ,k})^{T} where q_{1ƒ,k}, q_{2ƒ,k}, and q_{3ƒ,k}represent glucose amounts in the accessible, nonaccessible, and interstitial compartments excluding the contribution from meals, u_{s,k}is the unexplained glucose influx and F_{k}is glucose availability, and a dispenser that delivers a specified amount of medication to a user in response to a command from the processor based on the predicted combined estimate of the inferred glucose level.
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Abstract
Apparatus for monitoring a substance in human or animal in real time, the apparatus comprising a sensor providing a time series of measurements of substance level, said measurements being indicative of an inferred level of said substance in a part of said human or animal and a processor which applies an interacting multiple model strategy to a system model to provide a combined estimate of the inferred substance level from the substance level measurements. The substance may be glucose. The apparatus may also be adapted to control said substance using said interacting multiple model strategy to a system model to provide a combined estimate of a dose to be applied.
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34 Claims
 1. Apparatus for real time control of glucose in a human or an animal, the apparatus comprising:
 a sensor providing a time series of measurements of glucose level, said measurements being indicative of an inferred level of said glucose in a part of said human or animal, a processor which is adapted to perform the following steps;
calculate a first estimate of said inferred glucose level from said measured glucose level using a first glucoregulatory system model, calculate a second estimate of said inferred glucose level from said measured glucose level using a second glucoregulatory system model with said second system model being a variation of said first system model, and predict a combined estimate of the inferred glucose level based on a combination of the first and second estimates, wherein the processor is a state estimator and is adapted to define a state vector for each model, the state vector comprising a set of variables each having an associated uncertainty, the set of variables including a variable representing an unexplained change in glucose level with each model having a different standard deviation in the unexplained change in glucose level;
wherein the first and second glucoregulatory models each comprise a submodel of glucose kinetics in the blood of said human or animal, a submodel of interstitial glucose kinetics, a submodel of insulin absorption, a submodel of insulin action and a submodel of gut absorption; and
wherein the state vector includes the following states
x_{k}=(q_{1ƒ,k},q_{2ƒ,k}u_{S,k},F_{k},q_{3ƒ,k})^{T} where q_{1ƒ,k}, q_{2ƒ,k}, and q_{3ƒ,k}represent glucose amounts in the accessible, nonaccessible, and interstitial compartments excluding the contribution from meals, u_{s,k}is the unexplained glucose influx and F_{k}is glucose availability, and a dispenser that delivers a specified amount of medication to a user in response to a command from the processor based on the predicted combined estimate of the inferred glucose level.
 a sensor providing a time series of measurements of glucose level, said measurements being indicative of an inferred level of said glucose in a part of said human or animal, a processor which is adapted to perform the following steps;
 2. Apparatus according to claim 1, wherein the processor is adapted to calculate a combined estimate by weighting each estimate according to an associated mixing probability representing a respective probability of each said model correctly predicting said glucose level.
 3. Apparatus according to claim 2, wherein the processor is further adapted to update said mixing probability responsive to a difference between said predicted glucose level measurement of each respective said model and said glucose level measurement from said sensor.
 4. Apparatus according to claim 1, further comprising a user monitor to receive inputs from the user and/or to display the status of the apparatus.
 5. Apparatus according to claim 1, wherein the sensor measures the glucose intravenously, subcutaneously and/or intradermally.
 6. Apparatus according to claim 1, further comprising a realtime alarm which is activated when the combined estimate or the combined estimate of future glucose level is below a preset hypoglycaemia threshold or above a preset hyperglycaemia threshold.
 7. Apparatus for real time control of a substance in a human or an animal, the apparatus comprising:
 a sensor providing a time series of measurements of substance level, said measurements being indicative of an interred level of said substance in a part of said human or animal, a processor which applies an interacting multiple model strategy to a system model to predict a combined estimate of the inferred substance level from the substance level measurements, wherein the interacting multiple model strategy comprises first and second glucoregulatory models each of which comprise a submodel of glucose kinetics in the blood of said human or animal, a submodel of interstitial glucose kinetics, a submodel of insulin absorption, a submodel of insulin action and a submodel of gut absorption;
wherein said inferred substance level comprises a level of glucose in said blood and said substance level measurements comprise measurements of an interstitial glucose level;
wherein the processor is a state estimator and is adapted to define a state vector for each model, the state vector comprising a set of variables each having an associated uncertainty, the set of variables including a variable representing an unexplained change in glucose level with each model having a different standard deviation in the unexplained change in glucose level;
wherein the state vector includes the following states
x_{k}^{e}=(i_{1,k},i_{2,k},r_{D,k},r_{E,k},a_{1,k},a_{2,k},q_{1,k},q_{3,k},u_{S,k})^{T} where i_{1,k}and i_{2,k}is the amount of insulin in the two subcutaneous insulin depots at time k, r_{D,k}and r_{E,k}are the remote insulin actions affecting glucose disposal and endogenous glucose production, a_{1,k}and a_{2,k}are the amount of glucose in the two absorption compartments q_{1,k}, q_{2,k}, q_{3,k}represent glucose amounts in the accessible, nonaccessible, and interstitial compartments and u_{s,k}is the unexplained glucose influx; and
wherein said processor is configured to apply the interacting multiple model strategy to calculate a first estimate for said inferred glucose level from said measured substance level using said first glucoregulatory system model, calculate a second estimate for said inferred glucose level from said measured substance level using said second glucoregulatory system model and predict said combined estimate of the inferred glucose level based on a combination of said first and second estimates, and a dispenser that delivers a specified amount of medication to a user in response to a command from the processor based on the predicted combined estimate of the inferred glucose level.
 a sensor providing a time series of measurements of substance level, said measurements being indicative of an interred level of said substance in a part of said human or animal, a processor which applies an interacting multiple model strategy to a system model to predict a combined estimate of the inferred substance level from the substance level measurements, wherein the interacting multiple model strategy comprises first and second glucoregulatory models each of which comprise a submodel of glucose kinetics in the blood of said human or animal, a submodel of interstitial glucose kinetics, a submodel of insulin absorption, a submodel of insulin action and a submodel of gut absorption;
 8. Apparatus for real time control of glucose in a human or an animal, the apparatus comprising:
 a sensor providing a time series of measurements of glucose level, said measurements being indicative of an inferred level of said glucose in a part of said human or animal;
a processor which is adapted to construct at least two state vectors each comprising a set of variables for a respective one of at least two glucose level models, said state vectors representing states of said at least two models, said state vectors also including a variable representing an uncertainty in a change in glucose level with time, each of said variables having an associated probability distribution;
predict a value of a said glucose level using said probability distribution and said state vectors;
update values of said state vectors responsive to a difference between a predicted glucose level measurement for each said model and a glucose level measurement from said sensor;
update a mixing probability representing a respective probability of each said model correctly predicting said glucose level responsive to a difference between said predicted glucose level measurement of each respective said model and said glucose level measurement from said sensor; and
determine a combined predicted glucose level measurement for said human or animal by combining outputs from said glucose level models according to said updated mixing probability, wherein said at least two models each comprise a submodel of glucose kinetics in the blood of said human or animal, a submodel of interstitial glucose kinetics, a submodel of insulin absorption, a submodel of insulin action and a submodel of gut absorption; and
wherein the state vector includes the following states
x_{k}=(q_{1ƒ,k},q_{2ƒ,k},u_{S,k},F_{k},q_{3ƒ,k})^{T} where q_{1ƒ,k}, q_{2ƒ,k}, and q_{3ƒ,k}represent glucose amounts in the accessible, nonaccessible, and interstitial compartments excluding the contribution from meals, u_{s,k}is the unexplained glucose influx and F_{k}is glucose availability, and a dispenser that delivers a specified amount of medication to a user in response to a command from the processor based on the predicted combined estimate of the inferred glucose level.
 a sensor providing a time series of measurements of glucose level, said measurements being indicative of an inferred level of said glucose in a part of said human or animal;
 9. Apparatus according to claim 1 or claim 7, wherein the processor is adapted to calculate the specified amount of medication as the amount of medication required to bring the combined predicted glucose level measurement into line with a desired value.
 10. Apparatus for real time control of a substance in a human or an animal, the apparatus comprising a sensor providing a time series of measurements of substance level, said measurements being indicative of an inferred level of said substance in a part of said human or animal, a processor which is adapted to calculate an estimate of said inferred level, and a dispenser that delivers a specified amount of medication to a user in response to a command from the processor based on the calculated estimate of said inferred level, wherein the processor is adapted to calculate the specified amount of medication as the amount of medication required to bring the estimate of said inferred level in line with a desired value by calculating a first estimate of said specified amount of medication using a first system model, calculating a second estimate of said specified amount of medication using a second system model with said second system model being a variation of said first system model, and calculating a combined estimate of said specified amount of medication based on a combination of the first and second estimates, wherein said first system model and said second system model each comprise a submodel of glucose kinetics in the blood of said human or animal, a submodel of interstitial glucose kinetics, a submodel of insulin absorption, a submodel of insulin action and a submodel of gut absorption;
 wherein said inferred substance level comprises a level of said glucose in said blood and said substance level measurements comprises measurements of an interstitial glucose level;
wherein the processor is a state estimator and is adapted to define a state vector for each model, the state vector comprising a set of variables each having an associated uncertainty, the set of variables including a variable representing an unexplained change in glucose level with each model having a different standard deviation in the unexplained change in glucose level; and
wherein the state vector includes the following states
x_{k}=(q_{1ƒ,k},q_{2ƒ,k},u_{S,k},F_{k},q_{3ƒ,k})^{T} where q_{1ƒ,k}, q_{2ƒ,k}, and q_{3ƒ,k}represent glucose amounts in the accessible, nonaccessible, and interstitial compartments excluding the contribution from meals, u_{s,k}is the unexplained glucose influx and F_{k}is glucose availability.
 wherein said inferred substance level comprises a level of said glucose in said blood and said substance level measurements comprises measurements of an interstitial glucose level;
 11. Apparatus according to claim 10, wherein the dispenser delivers insulin, glucagon or a similar medication or combinations thereof.
 12. Apparatus according to claim 1 or claim 7, comprising a user interface for displaying a suggested insulin bolus to be applied, wherein the suggested insulin bolus is calculated by the processor as the amount of medication required to bring the combined estimate into line with a desired glucose value.
 13. Apparatus according to claim 10, wherein the desired glucose value varies with time to define a trajectory of values.
 14. Apparatus according to claim 12, wherein the processor applies an interacting multiple model strategy to the first and second glucoregulatory models to determine the amount of medication required.
 15. A computerimplemented method for real time control of glucose in a living human or an animal, the method comprising:
 inputting, to a processor, a time series of glucose level measurements from a sensor, said glucose level measurements being indicative of a inferred level of said glucose in a part of said human or animal, calculating, using said processor, a first estimate of said inferred glucose level from said measured substance level using a first glucoregulatory system model, calculating, using said processor, a second estimate of said inferred glucose level from said measured substance level using a second glucoregulatory system model with said second system model being a variation of said first system model, defining, using said processor, a state vector for each model, the state vector comprising a set of variables each having an associated uncertainty, the set of variables including a variable representing an unexplained change in substance level with each model having a different standard deviation in the unexplained change in substance level;
wherein the first and second glucoregulatory models each comprise a submodel of glucose kinetics in the blood of said human or animal, a submodel of interstitial glucose kinetics, a submodel of insulin absorption, a submodel of insulin action and a submodel of gut absorption;
wherein said inferred substance level comprises a level of said glucose in said blood and said substance level measurements comprises measurements of an interstitial glucose level;
wherein the state vector includes the following states
x_{k}=(q_{1ƒ,k},q_{2ƒ,k},u_{S,k},F_{k},q_{3ƒ,k})^{T} where q_{1ƒ,k}, q_{2ƒ,k}, and q_{3ƒ,k}represent glucose amounts in the accessible, nonaccessible and interstitial events excluding the contribution from meals, u_{s,k}is the unexplained glucose influx and F_{k}is glucose availability, predicting, using said processor, a combined estimate of the inferred glucose level based on a combination of the first and second estimates, and delivering a specified amount of medication to a user in response to a command from the processor based on the predicted combined estimate of the inferred glucose level.  View Dependent Claims (16, 17, 18, 19, 20)
 inputting, to a processor, a time series of glucose level measurements from a sensor, said glucose level measurements being indicative of a inferred level of said glucose in a part of said human or animal, calculating, using said processor, a first estimate of said inferred glucose level from said measured substance level using a first glucoregulatory system model, calculating, using said processor, a second estimate of said inferred glucose level from said measured substance level using a second glucoregulatory system model with said second system model being a variation of said first system model, defining, using said processor, a state vector for each model, the state vector comprising a set of variables each having an associated uncertainty, the set of variables including a variable representing an unexplained change in substance level with each model having a different standard deviation in the unexplained change in substance level;
 21. A computerimplemented method for real time control of glucose in a living human or an animal, the method comprising inputting a time series of glucose level measurements from a glucose sensor;
 constructing, using said processor, at least two state vectors each comprising a set of variables for a respective one of at least two glucose level models, said state vectors representing states of said at least two models, said state vectors also including a variable representing an uncertainty in a change in glucose level with time, each of said variables having an associated probability distribution;
predicting, using said processor, a value of a said glucose level using said probability distribution and said state vectors;
updating, using said processor, values of said state vectors responsive to a difference between a predicted glucose level measurement for each said model and a glucose level measurement from said sensor;
updating, using said processor, a mixing probability representing a respective probability of each said model correctly predicting said glucose level responsive to a difference between said predicted glucose level measurement of each respective said model and said glucose level measurement from said sensor; and
determining, using said processor, a combined predicted glucose level measurement for said human or animal by combining outputs from said glucose level models according to said updated mixing probability, wherein said at least two models each comprise a submodel of glucose kinetics in the blood of said human or animal, a submodel of interstitial glucose kinetics, a submodel of insulin absorption, a submodel of insulin action and a submodel of gut absorption, and wherein the state vector includes the following states
x_{k}^{e}=(i_{1,k},i_{2,k},r_{D,k},r_{E,k},a_{1,k},a_{2,k},q_{1,k},q_{2,k},q_{3,k},u_{S,k})^{T} where i_{1,k}and i_{2,k}is the amount of insulin in the two subcutaneous insulin depots at time k, r_{D,k}and r_{E,k}are the remote insulin actions affecting glucose disposal and endogenous glucose production, a_{1,k}and a_{2,k}are the amount of glucose in the two absorption compartments, q_{1,k}, q_{2,k}, q_{3,k}represent glucose amounts in the accessible, nonaccessible, and interstitial compartments and u_{s,k}is the unexplained glucose influx, and delivering a specified amount of medication to a user in response to a command from the processor based on the predicted combined estimate of the inferred glucose level.  View Dependent Claims (22)
 constructing, using said processor, at least two state vectors each comprising a set of variables for a respective one of at least two glucose level models, said state vectors representing states of said at least two models, said state vectors also including a variable representing an uncertainty in a change in glucose level with time, each of said variables having an associated probability distribution;
 23. A method for real time control of a substance in a human or animal, the method comprising providing a time series of measurements of substance level to a processor, said measurements being indicative of an inferred level of said substance in a part of said human or animal, calculating, using said processor, an estimate of said inferred level, calculating, using said processor, a specified amount of medication to be the amount of medication required to bring the estimate of said inferred level in line with a desired value by calculating, using said processor, a first estimate of said specified amount of medication using a first system model, calculate, using said processor, a second estimate of said specified amount of medication using a second system model with said second system model being a variation of said first system model, calculating, using said processor, said specified amount of medication based on a combination of said estimates, and delivering said specified amount of medication to a user in response to a command from the processor based on the combination of said estimates, wherein the processor is a state estimator and is adapted to define a state vector for each model, the state vector comprising a set of variables each having an associated uncertainty, the set of variables including a variable representing an unexplained change in glucose level with each model having a different standard deviation in the unexplained change in glucose level;
 wherein the first and second models each comprise a submodel of glucose kinetics in the blood of said human or animal, a submodel of interstitial glucose kinetics, a submodel of insulin absorption, a submodel of insulin action and a submodel of gut absorption; and
wherein the state vector includes the following states
x_{k}=(q_{1ƒ,k},q_{2ƒ,k},u_{S,k},F_{k},q_{3ƒ,k})^{T} where q_{1,ƒ,k}, q_{2ƒ,k}, and q_{3ƒ,k}represent glucose amounts in the accessible, nonaccessible and interstitial compartments excluding the contribution from meals, u_{s,k}is the unexplained glucose influx and F_{k}is glucose availability.  View Dependent Claims (24, 25)
 wherein the first and second models each comprise a submodel of glucose kinetics in the blood of said human or animal, a submodel of interstitial glucose kinetics, a submodel of insulin absorption, a submodel of insulin action and a submodel of gut absorption; and
 26. A nontransitory carrier carrying computer program code to, when running on said processor, implement the method of claim 15.
 27. Apparatus according to claim 1, wherein the glucose kinetics submodel is described as ⅆq1(t)ⅆt=(SIDxD(t)+k21)q1(t)+k12q2F01+EGP(t)+FuA(t)+uS(t)ⅆq2(t)ⅆt=+k21q1(t)k12q2(t)gP(t)=q1(t)VG where q1(t) and q2(t) are the masses of glucose in the accessible and nonaccessible glucose compartments (mmol/kg), k21and k12are the fractional transfer rates (/min), F01is the noninsulin dependent glucose utilisation (mmol/kg/min), EGP(t) is the endogenous glucose production (mmol/kg/min), SI,Dis peripheral insulin sensitivity (/min per mU/l), F is glucose bioavailability (unitless), uS(t) is unexplained glucose influx (mmol/kg/min), gP(t) is plasma glucose concentration, VGis the glucose distribution volume in the accessible compartment (l/kg).
 28. Apparatus according to claim 1, wherein the interstitial glucose kinetics submodel is described as ⅆq3(t)ⅆt=k31(q3(t)q1(t))gIG(t)=q3(t)VG where q3(t) is the mass of glucose in the interstitial fluid (mmol/kg), k31is the fractional transfer rate (/min), and gIG(t) is interstitial glucose concentration.
 29. Apparatus according to claim 1, wherein the state vector comprises a subset of the parameters of each model.
 34. Apparatus according to claim 12, wherein the desired glucose value varies with time to define a trajectory of values.
1 Specification
This application is a National Stage application of PCT/GB2008/050932, filed Oct. 10, 2008, which claims the priority of Great Britain Patent Application No. 0719969.8, filed Oct. 12, 2007. The foregoing applications are incorporated by reference herein in their entirety.
This application relates to monitoring and controlling levels of substances, e.g. glucose, in human or animal bodies.
Insulin is secreted by the pancreas in a highly controlled fashion to maintain the plasma glucose concentration within a narrow physiological range. In type 1 diabetes, insulin is administered exogenously to mimic the basal and postprandial insulin needs. The standard therapy is based on multiple insulin injections using a combination of short and long acting insulin analogues supported by blood glucose selfmonitoring. Treatment by the continuous subcutaneous insulin infusion (CSII), i.e. using insulin pumps, is on the rise.
Continuous glucose monitoring promises to improve glucose control in subjects with diabetes (D. C. Klonoff. Continuous Glucose Monitoring: Roadmap for 21st century diabetes therapy. Diabetes Care 28 (5):12311239, 2005). New minimally invasive and noninvasive techniques are being developed; see examples such as U.S. Pat. No. 5,086,229 and U.S. Pat. No. 5,497,772.
Supporting the development of new minimally invasive and noninvasive measurement techniques, a range of mathematical methods has been proposed to aid data processing. Data processing is confounded by measurements of the glucose sensor being normally carried out in a fluid distinct from plasma, such as in the interstitial, dermal, or tear fluid. The kinetics properties of the transfer between plasma and the measurement fluid result in a delay between plasma and the measurement fluid (K. Rebrin, G. M. Steil, W. P. Van Antwerp, and J. J. Mastrototaro. Subcutaneous glucose predicts plasma glucose independent of insulin: implications for continuous monitoring. American Journal of PhysiologyEndocrinology and Metabolism 277 (3):E561E571, 1999). Thus, the ratio between the plasma glucose and the glucose in the measurement fluid changes with time and appropriate techniques are required to calculate an estimate of plasma glucose from sensor measurements apart from filtering out the measurement error.
The extended (linearised) Kalman filter has been proposed as a suitable computational vehicle for data processing of glucose sensor signal, see U.S. Pat. No. 6,575,905, U.S. Pat. No. 6,572,545, WO02/24065 and E. J. Knobbe and B. Buckingham. “The extended Kalman filter for continuous glucose monitoring” (Diabetes Technol. Ther. 7 (1):1527, 2005). Process noise is an integral component of the Kalman filter. The process noise represents the random disturbance which is not captured by the other model components and is distinct from the measurement error, which describes the random component of the measurement process. The characteristics of the process noise are usually obtained from retrospective analysis of experimental data. However, the characteristics and specifically the variance of the process noise may be subject to temporal variations due to physiological or lifestyle factors excluded from modelling. For example, following meal ingestion, the process noise will have considerably higher variance compared to that applicable to fasting conditions. The standard Kalman filter is unable to accommodate and correct for such temporal variations because it uses fixed values for the process noise.
There are other known methods for monitoring glucose levels, for example WO97/28787 uses an adaptive mathematic model and U.S. Pat. No. 5,497,772 uses an enzymatic sensor to sense glucose levels.
The advancements in the field of continuous glucose sensors have stimulated the development of closedloop systems based on combination of a continuous monitor, a control algorithm, and an insulin pump (R. Hovorka. Continuous glucose monitoring and closedloop systems. Diabet. Med. 23 (1):112, 2006). This is denoted as an artificial pancreas. The original concept was introduced in late 70's, see U.S. Pat. No. 4,055,175 and U.S. Pat. No. 4,464,170, for example.
A wide spectrum of control algorithms has been proposed to titrate insulin in a closedloop fashion, see a review by Parker et al (R. S. Parker, F. J. Doyle, III, and N. A. Peppas. The intravenous route to blood glucose control. IEEE Eng. Med. Biol. Mag. 20 (1):6573, 2001). Two main categories have been employed, classical feedback control embodied in the proportionalintegralderivative (PID) controller (G. M. Steil, K. Rebrin, C. Darwin, F. Hariri, and M. F. Saad. Feasibility of automating insulin delivery for the treatment of type 1 diabetes. Diabetes 55 (12):33443350, 2006), and model predictive control (MPC) (R. Hovorka, V. Canonico, L. J. Chassin, U. Haueter, M. MassiBenedetti, Federici M. Orsini, T. R. Pieber, H. C. Schaller, L. Schaupp, T. Vering, and M. E. Wilinska. Nonlinear model predictive control of glucose concentration in subjects with type 1 diabetes. Physiol Meas. 25 (4):905920, 2004).
The Kalman filter was also used as part of control algorithm for closedloop glucose control (R. S. Parker, F. J. Doyle, III, and N. A. Peppas. A modelbased algorithm for blood glucose control in type I diabetic patients. IEEE Trans. Biomed. Eng 46 (2):148157, 1999). A linearised Kalman filter was also proposed, see U.S. Pat. No. 6,572,545. The Kalman filter or the extended Kalman filter (described above) provide computationally efficient means to track and predict glucose excursions and are used in combination with a physiologicallybased glucoregulatory model represented by stochastic differential equations.
There are other known methods for controlling glucose levels, for example, US2003/0208113 describes a system for assisting a person to maintain blood glucose levels between predetermined limits and U.S. Pat. No. 4,055,175 describes glucose control using a model based on quadratic and biquadratic equations.
Statements of Invention
According to the invention there is provided a method of real time substance monitoring in a living human or animal, the method comprising:
 inputting a time series of substance level measurements from a sensor, said substance level measurements being indicative of a inferred level of said substance in a part of said human or animal,
 calculating a first estimate of said inferred substance level from said measured substance level using a first system model,
 calculating a second estimate of said inferred substance level from said measured substance level using a second system model with said second system model being a variation of said first system model and
 predicting a combined estimate of the inferred substance level based on a combination of the first and second estimates.
By using multiple models, the method may be considered to use an interacting multiple model strategy, i.e. a strategy in which two or more models may be defined with each model being a variation of the system model. Thus, in other words, according to another aspect of the invention, there is provided a method of real time substance monitoring in a living human or animal, the method comprising: inputting a time series of substance level measurements from a sensor, said substance level measurements being indicative of a inferred level of said substance, defining a system model which estimates said inferred substance level from said measured substance level, and applying an interacting multiple model strategy to the system model to provide a combined estimate of the inferred substance level.
The combined estimate may be a combined estimate of the current inferred substance level or a combined estimate of a future inferred substance level.
Each variation of the model may have a different process noise. As explained previously, the process noise represents the random disturbance which is not captured by the other model components. For each model, an estimate of the inferred substance level and the process noise is calculated in a computationally efficient manner. The estimates for each model are combined to provide a combined estimate of the inferred substance level. When combining the estimates, each estimate is preferably weighted according to an associated mixing probability, i.e. a probability of the estimate representing the true value. In other words, if one model is the most likely, this model is given the highest weighting so that the combined estimate is based primarily on this model. If no one model is the most likely, the weightings may be adjusted accordingly to give a more balanced representation of each model in the overall estimate. Said mixing probability may be updated responsive to a difference between said predicted glucose level measurement of each respective said model and said glucose level measurement from said sensor.
As an alternative to defining the models to have different process noise, the multiple models defined by the interacting multiple model strategy may differ in certain model constants. As described in the prior art, the extended Kalman filter may be used for a model which is nonlinear in a certain parameter. However, the extended Kalman filter approximates the solution and for highly nonlinear models this may be a problem. Using the interacting multiple model strategy permits the definition of a number of models, each differing in the fixed level of the parameter causing nonlinearity. These models run in parallel, with no approximations being necessary (albeit the models are confined to discrete levels of the nonlinear parameter) and the most appropriate parameter level may be chosen.
The interacting multiple model (IMM) strategy has been introduced to allow computationally efficient tracking of a maneuvering target (E. Mazor, A. Averbuch, Y. BarShalom, and J. Dayan. Interacting multiple model methods in target tracking: A survey. IEEE Transactions on Aerospace and Electronic Systems 34 (1):103123, 1998). A maneuvering target is characterised by temporal variability in acceleration, where the acceleration is, in effect, the process noise.
Besides use in radar and GPS tracking, see for example U.S. Pat. No. 5,325,098, U.S. Pat. No. 7,079,991, and U.S. Pat. No. 6,876,925, in the biomedical field the IMM approach has been used to monitor kinetic parameters (D. S. Bayard and R. W. Jelliffe. A Bayesian approach to tracking patients having changing pharmacokinetic parameters. J. Pharmacokinet. Pharmacodyn. 31 (1):75107, 2004) and the imaging field, see for example (P. Abolmaesumi and M. R. Sirouspour. An interacting multiple model probabilistic data association filter for cavity boundary extraction from ultrasound images. IEEE Trans. Med. Imaging 23 (6):772784, 2004).
The present applicant has recognised that the IMM is well suited to handle the temporal variations of the process noise of substance monitoring, for example when using a Kalman filter described above.
The substance being monitored is preferably glucose and the model is a glucoregulatory model. For glucose monitoring, the inferred glucose level may be the plasma glucose concentration which is not directly measurable and the measured glucose level may be the interstitial glucose level. The glucose level may be measured intravenously, subcutaneously and/or intradermally.
The glucoregulatory model may comprise five submodels, the submodel of insulin absorption, the submodel of insulin action, the submodel of gut absorption, the submodel of glucose kinetics, and the submodel of interstitial glucose kinetics. Alternatively, the glucoregulatory model may consist of a subset of the five models, e.g. the submodel of glucose kinetics and the submodel of interstitial glucose kinetics which interact to predict the inferred glucose level, e.g. plasma glucose concentration, from the measured glucose level, e.g. glucose level in the interstitial fluid.
For glucose monitoring, the process noise may represent the change in the unexplained glucose influx. The interacting multiple model strategy may comprise defining for each variation of the model, a state vector comprising a set of variables each having an associated uncertainty. The set of variables may comprise variables representing glucose amounts in the accessible, nonaccessible and/or interstitial compartments and a variable representing an unexplained change in glucose level.
Alternatively, the substance being monitored may be the depth of anaesthesia. More information on the control of anaesthesia and the appropriate models which may be used in the interacting multiple model strategy may be determined from EP 1278564 and related application EP 1725278 to Aspect Medical Systems Inc. Other references are D. A. Linkens and M. Mahfouf. “Generalized Predictive Control with Feedforward (Gpcf) for Multivariable Anesthesia.” International Journal Of Control56 (5):10391057, 1992, M. Mahfouf and D. A. Linkens. “Nonlinear generalized predictive control (NLGPC) applied to muscle relaxant anaesthesia.” International Journal Of Control71 (2):239257, 1998, M. M. Struys, E. P. Mortier, and Smet T. De. “Closed loops in anaesthesia.” Best. Pract. Res. Clin. Anaesthesiol. 20 (1):211220, 2006 or V Sartori, P Schumacher, T Bouillon, M Luginbuehl and M Morari “Online estimation of propofol pharmacodynamic parameters.” Annual International Conference of the IEEE Engineering in Medicine and Biology Society(2005), 1 747.
The method may comprise applying a Kalman filter. A Kalman filter has two distinct steps; a predict step which uses the state estimate from the previous timestep to produce an estimate of the state at the current timestep and an update step which comprises using measurements at the current timestep to refine the estimate from the predict step to arrive at a new, more accurate, state estimate for the current timestep. In other words, the method may comprise predicting the state estimate from the previous timestep to produce an estimate of the state at the current timestep and updating the estimate using measurements at the current timestep to refine the estimate from the predicting step to arrive at an updated state estimate for the current timestep. The covariance, i.e. a measure of the estimated accuracy of the state estimate, may be used when refining the estimate. The update step may also comprise updating the covariance.
The method may further comprise predicting an estimate for the mixing probability and updating the predicted estimate for the mixing probability based on measurements of the substance levels. The combined estimate preferably uses the updated mixing probability estimates.
The method may further comprise an interact step which links the various models. The interact step may comprise determining the mixing probability from the mode probability, i.e. the probability that the system model transitions from one variation model to another variation model.
According to another aspect of the invention there is a method of real time glucose monitoring in a living human or animal, the method comprising
 inputting a time series of glucose level measurements from a glucose sensor;
 constructing at least two state vectors each comprising a set of variables for a respective one of at least two glucose level models, said state vectors representing states of said at least two models, said state vectors also including a variable representing an uncertainty in a change in glucose level with time, each of said variables having an associated probability distribution;
 predicting a value of a said glucose level using said probability distribution and said state vectors;
 updating values of said state vectors responsive to a difference between a predicted glucose level measurement for each said model and a glucose level measurement from said sensor; and
 determining a combined predicted glucose level measurement for said human or animal by combining outputs from said glucose level models according to a mixing probability representing a respective probability of each said model correctly predicting said glucose level; and
 further comprising updating said mixing probability responsive to said predicted glucose level measurement of each respective said model and said glucose level measurement from said sensor.
The method may further comprise using the value of a first of state vectors to modify a second of said state vectors to thereby represent a transition between said models.
According to another aspect there is provided a method of controlling a substance in a human or animal in real time, the method comprising
 obtaining a combined estimate for the inferred substance level as previously described,
 inputting a desired reference value for the inferred substance level
 calculating, using said combined estimate, a dose to obtain said desired reference value and
 applying said dose to a patient.
According to another aspect there is provided a method for real time control of a substance in a human or animal, the apparatus comprising:
 calculating a combined estimate using real time monitoring as described above, and
 calculating a specified amount of medication as the amount of medication required to bring the combined estimate into line with a desired value and
 delivering said specified amount of medication to a user.
Additionally or alternatively, the calculation of the specified amount and/or does may be calculated using a method similar to that used for monitoring and the combined estimate may be calculated by any other method.
Thus, according to another aspect there is provided a method for real time control of a substance in a human or animal, the method comprising providing a time series of measurements of substance level, said measurements being indicative of an inferred level of said substance in a part of said human or animal, calculating an estimate of said inferred level, calculating a specified amount of medication to be the amount of medication required to bring the estimate of said inferred level in line with a desired value by calculating a first estimate of said specified amount of medication using a first system model, calculate a second estimate of said specified amount of medication using a second system model with said second system model being a variation of said first system model, calculating said specified amount of medication based on a combination of said estimates and delivering said specified amount of medication to a user. The method may further comprise calculating said estimate of said inferred level using real time monitoring as described above.
The substance being controlled may be glucose and the dose/medication applied may be insulin, glucagons or similar substances or a combined thereof. The substance being controlled may be the depth of anaesthesia glucose and the dose/medication applied may be anaesthesia.
According to another aspect of the invention, there is provided a method for controlling glucose in human or animal body, comprising calculating a combined estimate using real time monitoring as described above, and displaying a suggested insulin bolus to be applied on a user interface, wherein the suggested insulin bolus is calculated by the processor as the amount of medication required to bring the combined estimate into line with a desired glucose value. The method may comprise using the interacting multiple model strategy described above to calculate the insulin bolus to be applied.
According to another aspect there is provided apparatus for monitoring a substance in human or animal in real time, the apparatus comprising:
 a sensor providing a time series of measurements of substance level, said measurements being indicative of an inferred level of said substance in a part of said human or animal and
 a processor which is adapted to perform the following steps:
 calculate a first estimate of said inferred substance level from said measured substance level using a first system model,
 calculate a second estimate of said inferred substance level from said measured substance level using a second system model with said second system model being a variation of said first system model andpredicting a combined estimate of the inferred substance level based on a combination of the first and second estimates.
By using multiple models, the method may be considered to use an interacting multiple model strategy, i.e. a strategy in which two or more models may be defined with each model being a variation of the system model. Thus, in other words, according to another aspect of the invention there is provided apparatus for monitoring a substance in human or animal in real time, the apparatus comprising:
 a sensor providing a time series of measurements of said substance level, said measurements being indicative of an inferred level of said substance in a part of said human or animal and
 a processor which applies an interacting multiple model strategy to a system model to provide a combined estimate of the inferred substance level from the substance level measurements.
The substance being monitored is preferably glucose and the model is a glucoregulatory model. For glucose monitoring, the inferred glucose level may be the plasma glucose concentration which is not directly measurable and the measured glucose level may be the interstitial glucose level. The glucose level may be measured intravenously, subcutaneously and/or intradermally.
Alternatively, the substance being monitored may be the depth of anaesthesia.
The processor may be a state estimator and the interacting multiple model strategy may comprise defining for each variation of the model, a state vector comprising a set of variables each having an associated uncertainty. The set of variables may comprise variables representing glucose amounts in the accessible, nonaccessible and/or interstitial compartments and a variable representing an unexplained change in glucose level.
The glucoregulatory model may comprise five submodels, the submodel of insulin absorption, the submodel of insulin action, the submodel of gut absorption, the submodel of glucose kinetics, and the submodel of interstitial glucose kinetics. Alternatively, the glucoregulatory model may consist of a subset of the five models, e.g. the submodel of glucose kinetics and the submodel of interstitial glucose kinetics.
The apparatus may further comprise a user monitor with an input/output interface to receive inputs from the user, e.g. meals and exercise information and to display the status of the apparatus.
The apparatus may further comprise a realtime alarm which is activated when the combined estimate is below a preset hypoglycaemia threshold or above a preset hyperglycaemia threshold.
According to another aspect there is provided apparatus for monitoring glucose in human or animal in real time, the apparatus comprising:
 (an input or) a continuous glucose sensor providing an estimate of glucose level
 an optimal state estimator based on the interacting multiple model strategy and adopting a stochastic model to provide optimal estimate of glucose level from data obtained by the continuous glucose sensor
The interacting multiple model strategy may use a standard or extended Kalman filter.
The apparatus may comprise one or more additional glucose sensors providing independent estimates of glucose level. At least one sensor may measure glucose intravenously. At least one sensor may measure glucose subcutaneously. At least one sensor may measure glucose subcutaneously. At least one sensor may measure glucose intradermally.
The apparatus may further comprise a user monitor with an input/output interface to receive inputs from the user and to display the status of the apparatus.
The apparatus may further comprise a realtime alarm which is activated when the optimal glucose estimate is below a preset hypoglycaemia threshold or above a preset hyperglycaemia threshold.
The apparatus may use the interacting multiple model strategy to make a prediction of future glucose values and/or to indicate sensor failure when the estimate of the process noise exceeds a predefined value.
According to another aspect of the invention, there is provided apparatus for real time control of glucose in a human or animal, the apparatus comprising:
 a glucose sensor providing a time series of measurements of glucose level, said measurements being indicative of plasma glucose concentration,
 a processor which applies an interacting multiple model strategy to a glucoregulatory model to provide a combined estimate of the plasma glucose concentration from the measured glucose levels, and
 a dispenser for delivering a specified amount of medication to a user in response to a command from the processor,
 wherein the specified amount of medication is calculated by the processor as the amount of medication required to bring the combined estimate into line with a desired glucose value.
The dispenser may deliver insulin or insulin and glucagon, or insulin and another glucose controlling substance.
According to another aspect of the invention, there is provided apparatus for controlling glucose in human or animal body, comprising
 a glucose sensor providing a time series of measurements of glucose level, said measurements being indicative of plasma glucose concentration,
 a processor which applies an interacting multiple model strategy to a glucoregulatory model to provide a combined estimate of the plasma glucose concentration from the measured glucose levels, and
 a user interface for displaying a suggested insulin bolus to be applied
 wherein the suggested insulin bolus is calculated by the processor as the amount of medication required to bring the combined estimate into line with a desired glucose value.
The desired glucose value may vary with time to define a trajectory of desired or setpoint values. The trajectory may be input to the processor by a user, e.g. via a user interface which accepts input from a user.
The processor may comprise a model combiner to generate a combined estimate for the plasma glucose concentration using the interacting multiple model strategy and may comprise a dose estimator which applies the interacting multiple model strategy to determine the amount of medication required.
According to another aspect of the invention, there is provided an apparatus for controlling a substance in human or animal in real time, the apparatus comprising:
 an input to receive an estimate of the said substance
 an input to receive past control commands
 an input to receive the desired set point trajectory of the said substance
 an interacting multiple model strategy providing optimal estimate of the said substance
 an optimal dose estimator relating the control command to the time evolution of the said substance with the use of substantially the same interacting multiple model strategy
 a dispenser, which delivers the amount of medication specified by the control command.
The interacting multiple model strategy may use a standard or extended Kalman filter.
The substance being controlled is preferably glucose and the medication may be insulin or a combination of insulin and glucagons.
Alternatively, the substance being controlled may be the depth of anaesthesia and the medication may be anaesthesia.
The set point trajectory may be predefined, e.g. obtained from a health monitor which accepts input from a user.
According to another aspect of the invention, there is provided an artificial pancreas for controlling glucose levels in real time comprising:
 a continuous glucose monitor providing an estimate of glucose level
 an optimal state estimator based on the interacting multiple model strategy and adopting a stochastic physiological model of glucoregulation to provide optimal estimate of glucose level from data obtained by the continuous glucose monitor
 a glucose controller utilising a substantially same stochastic model of glucoregulation as the optimal glucose estimator and a substantially same interacting multiple model strategy to determine a control command
 a dispenser, which delivers the amount of medication specified by the control command
The artificial pancreas may be a portable device. The dispenser may infuse insulin or a combination of insulin and glucagon. The dispenser may infuse medication intravenously or subcutaneously.
The artificial pancreas may comprise one or more additional glucose monitors providing independent estimates of glucose level. At least one monitor may measure glucose intravenously. At least one monitor may measure glucose subcutaneously.
The artificial pancreas may further comprise a user monitor with an input/output interface to receive inputs from the user and to display status of the artificial pancreas.
The interacting multiple model strategy may use a standard or extended Kalman filter.
The artificial pancreas may receive information about any or all of user triggered insulin boluses, meals, exercise and insulin infusion. This information may be utilised by the physiological model of glucoregulation.
According to another aspect of the invention there is provided a method for estimating retrospectively basal insulin infusion, carbohydratetoinsulin ratio, and insulin sensitivity comprising the acts of:
 receiving timeseries of an estimate of glucose level
 receiving timeseries of administered insulin infusion and insulin boluses
 providing the timeseries to an interacting multiple model strategy, which adopts a stochastic physiological model of glucoregulation to provide optimal estimate basal insulin infusion, carbohydratetoinsulin ratio, and insulin sensitivity
According to another aspect of the invention there is provided a decision support system for suggesting in real time insulin bolus comprising:
 a continuous glucose monitor providing an estimate of glucose level
 an optimal state estimator based on the interacting multiple model strategy and adopting a stochastic physiological model of glucoregulation to provide optimal estimate of glucose level from data obtained by the continuous glucose monitor
 a glucose controller utilising a substantially same stochastic model of glucoregulation as the optimal glucose estimator and a substantially same interacting multiple model strategy to determine insulin bolus
 a user monitor with an input/output interface to receive inputs from the user and to display the suggested insulin bolus
 a dispenser, which delivers the amount of medication specified by the control command
The decision support system may further comprise a dispenser, which based on confirmation by the user delivers the insulin bolus. The insulin bolus may be a prandial insulin bolus or a correction insulin bolus.
The invention further provides processor control code to implement the abovedescribed methods, in particular on a data carrier such as a disk, CD or DVDROM, programmed memory such as readonly memory (Firmware), or on a data carrier such as an optical or electrical signal carrier. Code (and/or data) to implement embodiments of the invention may comprise source, object or executable code in a conventional programming language (interpreted or compiled) such as C, or assembly code, code for setting up or controlling an ASIC (Application Specific Integrated Circuit) or FPGA (Field Programmable Gate Array), or code for a hardware description language such as Verilog (Trade Mark) or VHDL (Very high speed integrated circuit Hardware Description Language). As the skilled person will appreciate such code and/or data may be distributed between a plurality of coupled components in communication with one another.
The glucoregulatory may comprise five submodels, the submodel of insulin absorption, the submodel of insulin action, the submodel of gut absorption, the submodel of glucose kinetics, and the submodel of interstitial glucose kinetics. Alternatively, the glucoregulatory model may consist of a subset of the models described, e.g. the submodel of glucose kinetics and the submodel of interstitial glucose kinetics.
The insulin absorption submodel is described by a two compartment (two depot) model
The insulin action submodel is described as
The gut absorption submodel is described by a two compartment model
The glucose kinetics submodel is described as
The EGP is obtained as
The change in unexplained glucose influx u_{s}(t) (the process noise) is described by a stochastic differential equationdu_{s}(t)=dw(t) (13)where w(t) is 1dimensional driving Wiener process.
The basal insulin concentration BIC is calculated from the basal insulin requirement (BIR; U/h) as
The interstitial glucose kinetics submodel is described as
As shown in
More details of the strategy are shown in
The extended state vector x_{k}which uses all the submodels defined above includes nine statesx_{k}^{e}=(i_{1,k},i_{2,k},r_{D,k},r_{E,k},a_{1,k},a_{2,k},q_{1,k},q_{2,k},q_{3,k},u_{S,k})^{T} (17)where i_{1,k}and i_{2,k}is the amount of insulin in the two subcutaneous insulin depots at time k, γ_{D,k}and γ_{E,k}are the remote insulin actions affecting glucose disposal and endogenous glucose production, a_{1,k}and a_{2,k}are the amount of glucose in the two absorption compartments, q_{1,k}, q_{2,k}, q_{3,k}represent glucose amounts in the accessible, nonaccessible, and interstitial compartments and u_{s,k}is the unexplained glucose influx (process noise).
The function ƒ is used to calculate the predicted state x_{k}from the previous estimate x_{k−1}x_{k}=ƒ(x_{k−1},u_{k},w_{k}) (18)
 where w_{k}is a 1dimensional driving Wiener process (see 13)z_{k}=h(x_{k},v_{k}) (19)z_{k}is the measurement at time k of the true state x_{k}h is the observation model which maps the true state space into the observed space andv_{k}is the observation noise which is assumed to be zero mean Gaussian white noise with covariance R_{k}(see also eqn 60 below)
The state transition for i_{1,k}(i.e. the transition from time k−1 to time k) is defined by the following expressions
The state transition for i_{2,k}is defined by the following expressions
The state transition for r_{D,k}is defined by the following expressions
The state transition for r_{E,k}is defined by the following expressions
The state transition for a_{1,k}is defined by the following expressions
The state transition for a_{2,k}is defined by the following expressions
The state transitions for q_{1,k}, q_{2,k}, andq_{3,k}are defined by the following expressionsq_{1,k}=ƒ_{70}+ƒ_{77}q_{1,k−1}+ƒ_{78}q_{2,k−1}+ƒ_{79}u_{S,k−1} (42)q_{2,k}=ƒ_{80}+ƒ_{87}q_{1,k−1}+ƒ_{88}q_{2,k−1}+ƒ_{89}u_{S,k−1} (43)q_{3,k}=ƒ_{12,0}+ƒ_{12,7}q_{1,k−1}+ƒ_{12,8}q_{2,k−1}+ƒ_{12,12}q_{3,k−1}+ƒ_{12,9}u_{S,k−1} (44)where coefficients ƒ_{70}, ƒ_{77}, ƒ_{78}, ƒ_{79}, ƒ_{80}, ƒ_{87}, ƒ_{88}, ƒ_{89}, ƒ_{12,0}, ƒ_{12,7}, ƒ_{12,8}, ƒ_{12,9}, and ƒ_{12,12}can be obtained algebraically as described in Appendix or by numerical approximations.
The state transitions for u_{S,K}is an identity, i.e.u_{S,k}=u_{S,k−1} (45)
Considering a subset state vector x_{k}, which includes states with associated uncertaintyx_{k}=(q_{1ƒ,k},g_{2ƒ,k},u_{S,k},F_{k},q_{3ƒ,k})^{T} (46)where q_{1ƒ,k}, q_{2ƒ,k}, andq_{3ƒ,k}represent glucose amounts in the accessible, nonaccessible, and interstitial compartments excluding the contribution from meals (more correctly the last meal), u_{s,k}is (as before) the unexplained glucose influx (process noise) and F_{k}is the state transition model which is applied to the previous state x_{k−1}(see eqn 55).
The total amount of glucose in the compartments is calculated asq_{1,k}=q_{1ƒ,k}+q_{1m,k} (47)q_{2,k}=q_{2ƒ,k}+q_{2m,k} (48)q_{3,k}=q_{3ƒ,k}+q_{3m,k} (49)where q_{1m,k}, q_{2m,k}, andq_{3m,k}represent glucose amounts in the accessible, nonaccessible, and interstitial compartments due to the (last) meal.
The glucose masses due to the meal are calculated asq_{1m,k}=F_{k}ƒ_{7,10} (50)q_{2m,k}=F_{k}ƒ_{8,10} (51)q_{3m,k}=F_{k}ƒ_{12,10} (52)
The state transition is obtained asx_{k}=F_{k}^{0}+F_{k}x_{k−1}+G_{k}w_{k} (53)where
F_{k}^{0}is the additive transition model which is independent of the previous state x_{k−1}and the process noise
F_{k}is the state transition model which is applied to the previous state x_{k−1}
G_{k}is the additive transition model which is applied to the process noise w_{k}
If a glucose measurement is not made in time instance t_{k}, the unexplained glucose influx is regressed towards zero with a halftime m_{1/2}
We find that the covariance Q_{k}of the unexplained glucose influx isQ_{k}=cov(G_{k}w_{k})=σ_{w,k}^{2}G_{k}G_{k}^{T} (59)
At each time interval, a measurement z_{k}of interstitial glucose concentration is made. This measurement is noisy measurement of the plasma glucose. The measurement noise is normally distributed with mean 0 and standard deviation σ_{Z,k}z_{k}=Hx_{k}+v_{k} (60)where
H is the observation model which maps the true state space into the observed spaceH=[000ƒ_{12,10}/V_{G}1/V_{G}] (61)and
v_{k}is the observation noise which is assumed to be zero mean Gaussian white noise with covariance R_{k}R_{k}=E[v_{k}v_{k}^{T}]=[σ_{Z,k}^{2}] (62)
The initial starting position is assumed identical to the first glucose measurement {tilde over (g)}_{IG,0}and an apriori bioavailability {tilde over (F)}
The uncertainty in glucose concentration and bioavailability is expressed in the initial value of the covariance matrix P_{00}
A multiple model strategy is used to improve model tracking. Overall, N models are defined, which differ in the standard deviation of the unexplained glucose influx w_{k}σ_{w1,k}=σ_{w1}/√{square root over (Δt_{k})}σ_{w2,k}=σ_{w2}/√{square root over (Δt_{k})}. . .σ_{wN,k}=σ_{wN}/√{square root over (Δt_{k})} (65)where σ_{w(i−1)}wiwithout loss of generality.
The Markov transition probability from mode (or model) i to j is defined as p_{ji}, i.e. the probability that the system will switch from model i to model j is p_{ji}.
At step S102, there is an optional interact step to obtain for model 0, a mode state vector x, a covariance P and a mixing probability μ at time k−1. For i and j, the mixing probability μ_{ji,kk}at time k (the weights with which the estimates from the previous cycle k−1 are given to each filter at the beginning of the current cycle k) is defined as
The model interaction for mode j proceeds as
At step S104, there is a predict step to obtain for each model j, an estimate for the mode state vector x, covariance P and mixing probability μ at time k based on the observations, up to and including time k−1. In other words, the predict step uses the state estimate from the previous timestep to produce an estimate of the state at the current timestep.
The predict step for mode j consists ofˆ_{j,kk−1}=F_{k}^{0}+F_{k}ˆ_{0,j,k−1k−1} (70)P_{j,kk−1}=F_{k}P_{0,j,k−1k−1}F_{k}^{T}+Q_{j,k} (71)
At step S106, there is an update step which uses measurement information at the current timestep k to refine for each model j, the estimates for the mode state vector x, covariance P and mixing probability μ for the current timestep obtained from step S104. The resulting estimates should be more accurate estimates for the current timestep.
In case of a glucose measurement {tilde over (g)}_{IG,k}, for each mode j the update consists of evaluating the measurement residual {tilde over (y)}_{j,k}
The optimal Kalman gain is obtained as
The updated state estimate is obtained as
The updated estimate covariance for the optimal Kalman gain is obtained as
Alternatively, if K_{j,k}is not the optimal Kalman gain, the updated estimate covariance is obtained asP_{j,kk}=(I−K_{j,k}H)P_{j,kk−1}(I−K_{j,k}H)^{T}+K_{j,k}R_{k}K_{j,k}^{T} (78)
The likelihood function Λ_{j,k}of mode j is obtained as
Finally at step S108, there is a combine step whereby the estimated states and covariances for each model are combined to prove overall state and covariance estimates. The overall estimated state vector is obtained from a summation of all estimated state vectors multiplied by their weighting or mixing probability. Similarly, the estimated covariance is derived from a summation of all estimated covariances taking into account the relevant mixing probabilities.
Referring to
The extended input vector u^{+}is defined asu^{+}=(v_{t}u)^{T} (85)where v_{i}denotes insulin bolus given at time i andu is insulin infusion with the first element of u, u_{1}, defining the insulin infusion rate to be delivered.
Thus the control law in matrix notation isJ=J_{1}+J_{2}=∥A(u^{+}−u_{r}^{+})+y_{r}−w∥+∥Λ(u−u^{−1})∥ (86)where w is the set point (i.e. desired glucose level), u_{r}is the operating point, y_{r}is the output associated with the operating point, and A represents the model given by Eqs. (1)(11) linearised around the operating point
The two components of the control law J_{1}and J_{2}and their partial derivatives with respect to u^{+}can be written as
The derivative of J with respect to u^{+}is then obtained as
The solution is found asu^{+}=−C^{−1}c (99)
The measured glucose levels are input to a processor34which calculates a refined estimate of glucose level using the interacting multiple model strategy. The processor34uses the refined estimated to calculate a dose to be applied to the patient. The processor34is connected to an insulin pump36and delivers a control command to the insulin pump36in apply the calculated insulin infusion rate to the patient.
The apparatus also comprises an optional user monitor38which is connected to the processor34. The user monitor38has an input interface to receive inputs from the user such as meal intake, exercise, etc. This information is input to the processor34to use when calculating the refined glucose estimate and dose. The user monitor38also receives system status information from the processor and has an output interface to display such information to the patient.
No doubt many effective alternatives will occur to the skilled person. It will be understood that the invention is not limited to the described embodiments and encompasses modifications apparent to those skilled in the art lying within the spirit and scope of the claims appended hereto.
This appendix describes the closedform approximation of coefficients ƒ_{70}, ƒ_{77}, ƒ_{78}, ƒ_{79}, ƒ_{80}, ƒ_{87}, ƒ_{88}, ƒ_{89}, ƒ_{12,0}, ƒ_{12,7}, ƒ_{12,8}, ƒ_{12,9}, and ƒ_{12,12}.
The first element of u, u_{1}, defines the insulin infusion rate to be delivered. The amount of glucose appearing during the time interval [t_{k−1}, t_{k}) can be approximated by a linear function u_{G}(t) (mmol/kg/min) as
The fractional first order turnover rate k_{01}from the accessible glucose compartment is obtained as a piecewise constant approximation during the time interval Δt_{k}
Denote r_{k}the rate of change in u_{k}
Define the auxiliary variables v_{1}to v_{18}
The partial derivatives g_{1}=∂q_{1,k}/∂u_{G,k}, g_{2}=∂q_{2,k}/∂u_{G,k}, and g_{5}=∂q_{3,k}/∂u_{G,k}can be obtained as
These partial derivatives can be used to calculate other coefficientsƒ_{70}=ƒ_{79}u_{G,k−1}+g_{1}r_{k} (117)ƒ_{80}=ƒ_{89}u_{G,k−1}+g_{2}r_{k} (118)ƒ_{12,0}=ƒ_{12,9}u_{G,k−1}+g_{5}r_{k} (119)ƒ_{12,12}=v_{12} (120)
The coefficients k_{7,10,k}, k_{8,10,k}, and k_{12,10,k}at time t_{k}are calculated recursively using corresponding coefficients k_{7,10,k−1}, k_{8,10,k−1}, and k_{12,10,k−1}obtained in the previous time instance t_{k−1}ƒ_{7,10}=ƒ_{7,10,k−1}ƒ_{77}+ƒ_{8,10,k−1}ƒ_{78}+ƒ_{79}u_{A,k−1}+g_{1}(u_{A,k}−u_{A,k−1}) (121)ƒ_{8,10}=ƒ_{8,10,k−1}ƒ_{88}+ƒ_{7,10,k−1}ƒ_{87}+ƒ_{89}u_{A,k−1}+g_{2}(u_{A,k}−u_{A,k−1}) (122)ƒ_{12,10}=ƒ_{12,10,k−1}ƒ_{12,12}+ƒ_{7,10,k−1}ƒ_{12,7}+ƒ_{8,10,k−1}ƒ_{12,8}+ƒ_{12,9}u_{A,k−1}+g_{5}(u_{A,k}−u_{A,k−1}) (123)