Patent Publication Number: US-2020289037-A1

Title: Method and/or system for assessing a patient&#39;s glycemic response

Description:
This application claims the benefit of priority to U.S. Provisional Patent Appl. Nos. 61/588,340 titled “Model Based Insulin Therapy,” filed on Jan. 19, 2012 and 61/588,348 titled “Improved System to Regulate Glycemia,” filed on Jan. 19, 2012, assigned to the assignee of claimed subject matter, and incorporated herein by reference in their entirety. 
    
    
     BACKGROUND 
     1. Field 
     Subject matter disclosed herein relates to monitoring and/or controlling blood glucose levels in patients. 
     2. Information 
     The pancreas of a normal healthy person produces and releases insulin into the blood stream in response to elevated blood plasma glucose levels. Beta cells (β-cells), which reside in the pancreas, produce and secrete insulin into the blood stream as it is needed. If β-cells become incapacitated or die, a condition known as Type 1 diabetes mellitus (or in some cases, if β-cells produce insufficient quantities of insulin, a condition known as Type 2 diabetes), then insulin may be provided to a body from another source to maintain life or health. 
     Traditionally, because insulin cannot be taken orally, insulin has been injected with a syringe. More recently, the use of infusion pump therapy has been increasing in a number of medical situations, including for delivering insulin to diabetic individuals. For example, external infusion pumps may be worn on a belt, in a pocket, or the like, and they can deliver insulin into a body via an infusion tube with a percutaneous needle or a cannula placed in subcutaneous tissue. 
     As of 1995, less than 5% of Type 1 diabetic individuals in the United States were using infusion pump therapy. Presently, over 7% of the more than 900,000 Type 1 diabetic individuals in the U.S. are using infusion pump therapy. The percentage of Type 1 diabetic individuals that use an infusion pump is growing at a rate of over 2% each year. Moreover, the number of Type 2 diabetic individuals is growing at 3% or more per year, and growing numbers of insulin-using Type 2 diabetic individuals are also adopting infusion pumps. Additionally, physicians have recognized that continuous infusion can provide greater control of a diabetic individual&#39;s condition, so they too are increasingly prescribing it for patients. 
     A closed-loop infusion pump system may include an infusion pump that is automatically and/or semi-automatically controlled to infuse insulin into a patient. The infusion of insulin may be controlled to occur at times and in amounts that are based, for example, on blood glucose measurements obtained from an embedded glucose sensor in real-time. Closed-loop infusion pump systems may also employ the delivery of glucose and/or glucagon, in addition to the delivery of insulin, for controlling blood-glucose levels of a patient (e.g., in a hypoglycemic context). 
     SUMMARY 
     Briefly, example embodiments may relate to methods, systems, apparatuses, and/or articles, etc. for determining a meal profile of a patient indicative of an ingestion of a carbohydrate; determining an insulin profile of the patient indicative of insulin infused by the patient; obtaining one or more observations of a blood glucose concentration of said patient responsive to the meal profile and said insulin profile; and estimating one or more physiological parameters of the patient to model the blood glucose concentration based, at least in part, on the meal profile, the insulin profile and the one or more observations of said blood glucose concentration. At least one of the one or more physiological parameters may comprise a blood glucose concentration observed following a fasting period during an infusion of insulin to the patient at a constant basal rate. In a particular implementation, the meal profile may comprise a multi-component expression. For example, the meal profile may be defined by multiple humps. In another implementation, the insulin profile may comprise an expression of subcutaneous insulin and an expression of insulin infused. Here, for example, the insulin profile may be defined, at least in part, according to a pharmacokinetic model. 
     In one particular application, at least one of the estimated parameters may be applied in determining a meal bolus or a correction bolus. In another particular application, at least one of the estimated parameters may be applied in determining limits to an amount of insulin to be specified in an insulin pump command. In another particular application, at least one of the estimated parameters may be applied in tuning parameters of a controller to determine an amount of insulin to be infused to a patient on discrete command intervals. In yet another particular implementation, an insulin infusion basal rate for the patient may be computed based, at least in part, on at least one of the estimated physiological parameters. 
     In another implementation, an apparatus comprises: a special purpose computing apparatus to: determine a meal profile of a patient indicative of an ingestion of a carbohydrate; determine an insulin profile of the patient indicative of insulin infused by the patient; obtain one or more observations of a blood glucose concentration of the patient responsive to the meal profile and said insulin profile; and estimate one or more physiological parameters of the patient to model said blood glucose concentration based, at least in part, on the meal profile, the insulin profile and the one or more observations of the blood glucose concentration. In a particular implementation, at least one of the one or more physiological parameters comprises a blood glucose concentration observed following a fasting period during an infusion of insulin to the patient at a constant basal rate. 
     In one particular implementation, the meal profile comprises a multi-component expression. For example, the meal profile may be defined, at least in part, by multiple humps. In another particular implementation, the insulin profile may comprise an expression of subcutaneous insulin and an expression of insulin infused. In a particular example, the insulin profile may be defined, at least in part, according to a pharmacokinetic model. 
     In a particular application, the special purpose computing apparatus may apply at least one of the estimated parameters in determining a meal bolus or a correction bolus. In another particular application, the special purpose computing apparatus may further to apply at least one of the estimated parameters in determining limits to an amount of insulin to be specified in an insulin pump command. In yet another particular application, the special purpose computing apparatus may further apply at least one of the estimated parameters to tune parameters of a controller to determine an amount of insulin to be infused to a patient on discrete command intervals. In yet another particular application, implementation, the special purpose computing apparatus may compute an insulin infusion basal rate for the patient based, at least in part, on at least one of the one or more physiological parameters. 
     In a particular implementation, the apparatus may further comprise a continuous glucose monitoring device to provide the one or more observations of the blood glucose concentration based, at least in part, on signals generated by a glucose sensors. In another particular implementation, the apparatus may further comprise an insulin infusion pump to receive commands from the special purpose computing apparatus determined based, at least in part, on the estimated one or more physiological parameters. 
     In another implementation, an article may comprise a storage medium comprising machine-readable instructions stored thereon which are executable by a special purpose computing apparatus to: determine a meal profile of a patient indicative of an ingestion of a carbohydrate; determine an insulin profile of the patient indicative of insulin infused by the patient; obtain one or more observations of a blood glucose concentration of the patient responsive to the meal profile and said insulin profile; and estimate one or more physiological parameters of the patient to model said blood glucose concentration based, at least in part, on the meal profile, the insulin profile and the one or more observations of the blood glucose concentration. 
     In yet another implementation, an apparatus may comprise: means for determining a meal profile of a patient indicative of an ingestion of a carbohydrate; means for determining an insulin profile of the patient indicative of insulin infused by the patient; means for obtaining one or more observations of a blood glucose concentration of said patient responsive to the meal profile and the insulin profile; and means for estimating one or more physiological parameters of the patient to model the blood glucose concentration based, at least in part, on the meal profile, the insulin profile and the one or more observations of the blood glucose concentration. 
     Other alternative example embodiments are described herein and/or illustrated in the accompanying Drawings. Additionally, particular example embodiments may be directed to an article comprising a storage medium including machine-readable instructions stored thereon which, if executed by a special purpose computing device and/or processor, may be directed to enable the special purpose computing device/processor to execute at least a portion of described method(s) according to one or more particular implementations. In other particular example embodiments, a sensor may be adapted to generate one or more signals responsive to a measured blood glucose concentration in a body while a special purpose computing device/processor may be adapted to perform at least a portion of described method(s) according to one or more particular implementations based upon one or more signals generated by the sensor. 
    
    
     
       BRIEF DESCRIPTION OF THE FIGURES 
       Non-limiting and non-exhaustive features will be described with reference to the following figures, wherein like reference numerals refer to like parts throughout the various figures: 
         FIG. 1  is a block diagram of an example closed loop glucose control system in accordance with an embodiment. 
         FIG. 2  is a front view of example closed loop hardware located on a body in accordance with an embodiment. 
         FIG. 3( a )  is a perspective view of an example glucose sensor system for use in accordance with an embodiment. 
         FIG. 3( b )  is a side cross-sectional view of a glucose sensor system of  FIG. 3( a )  for an embodiment. 
         FIG. 3( c )  is a perspective view of an example sensor set of a glucose sensor system of  FIG. 3( a )  for an embodiment. 
         FIG. 3( d )  is a side cross-sectional view of a sensor set of  FIG. 3( c )  for an embodiment. 
         FIG. 4  is a cross sectional view of an example sensing end of a sensor set of  FIG. 3( d )  for an embodiment. 
         FIG. 5  is a top view of an example infusion device with a reservoir door in an open position, for use according to an embodiment. 
         FIG. 6  is a side view of an example infusion set with an insertion needle pulled out, for use according to an embodiment. 
         FIG. 7  is a schematic diagram of a system to characterize patient specific parameters for use in control of therapies according to an embodiment. 
         FIG. 8  is a plot illustrating a profile of insulin delivery to a patient according to an embodiment. 
     
    
    
     DETAILED DESCRIPTION 
     In an example glucose control system environment, blood-glucose measurements may be employed in a closed loop infusion system for regulating a rate of fluid infusion into a body. In particular example embodiments, a control system may be adapted to regulate a rate of insulin, glucagon, and/or glucose infusion into a body of a patient based, at least in part, on a glucose concentration measurement taken from a body (e.g., from a glucose sensor and/or metered blood glucose measurement). In certain example implementations, such a system may be designed to model a pancreatic beta cell (β-cell). Here, such a system may enable a patient to control an infusion device for releasing insulin or glucagon into the patient&#39;s body for effective blood glucose management. Here, such a system may be adapted to control infusion of insulin and/or glucagon so as to control/maintain a patient&#39;s blood glucose within a target range, thus reducing the risk that a patient&#39;s blood glucose level transitions to dangerous extreme levels in the absence of patient action. 
     According to certain embodiments, examples of closed-loop systems as described herein may be implemented in a hospital environment to monitor and/or control levels of glucose in a patient. Alternatively, according to certain embodiments, examples of closed-loop systems as described herein may be implemented in non-hospital environments to monitor and/or control levels of glucose in a patient. Here, a patient or other non-medical professional may be responsible for interacting with a closed-loop system. 
     To maintain healthy glucose levels, a person with type 1 diabetes may manage their glycemia by monitoring blood glucose levels, controlling diet, exercise, and self-administering appropriate amounts of insulin at appropriate times. Deviations from such glycemic management, such as skipping an insulin bolus at meal time or underestimating the carbohydrate content of a meal may bring about prolonged hyperglycemia. Likewise, receiving too much insulin (e.g., by over-bolusing) for a given blood glucose level and/or meal may bring about severe hypoglycemia. Other external factors, such as exercise or stress, may also contribute to glycemic deviations. 
     In a particular embodiment of a closed-loop system, such a system may be adapted to control infusion of insulin and/or glucagon so as to control/maintain a patient&#39;s blood glucose within a target range, thus reducing the risk that a patient&#39;s blood glucose level transition to dangerous extreme levels. Again, such a mechanism may reduce the risk of hypoglycemia and hyperglycemia if a patient, non-medical professional or medical professional is not fully attentive to providing inputs to the system for effective glycemic management. 
     According to an embodiment, depending on a patient&#39;s particular physiology, a target or set-point glucose level may be established. For example, such a target or set-point glucose level may be defined based, at least in part, on guidelines established by the American Diabetes Association (ADA) and/or clinical judgment of a patient&#39;s physician. Here, for example, the ADA has recommended a pre-prandial blood glucose concentration of between 80-130 mg/dl, which is in the normal glycemic range. Alternatively, target or set-point glucose level may be fixed at 120 mg/dl. In yet another alternative, a target or set-point blood glucose concentration may vary over time depending on particular patient conditions. It should be understood, however, that these are merely examples of a target or set-point blood glucose concentration, and claimed subject matter is not limited in this respect. 
     According to an embodiment, a closed-loop system may be employed to maintain a patient&#39;s glucose level in a range about a predetermined set-point or target level as described in U.S. patent application Ser. No. 12/820,944, filed on Jun. 22, 2010, and assigned to the assignee of claimed subject matter. Here, insulin may be infused to the patient at a predetermined basal rate while the patient&#39;s glucose level is within the predetermined range. If the glucose level escapes that range, a different infusion rate may be applied based, at least in part, on the predetermined set-point or target level. For example, if the patient&#39;s glucose level exceeds the range, an infusion rate may be increased. In another example, if the patient&#39;s glucose level falls below a particular level, an insulin infusion rate may be reduced from the predetermined basal rate. Of course, these are merely examples of how the insulin infusion rate may be changed if a patient&#39;s glucose level escapes a particular range, and claimed subject matter is not limited in this respect. 
     By maintaining a predetermined basal insulin infusion rate while the glucose level is within a target range, extreme glycemic variations may be reduced or avoided altogether. This may provide a patient with improved glycemic control in circumstances in which they would otherwise be exposed to undesirable extremes of glycemia. Here, while such a patient may remain in control of insulin infusion decisions, particular embodiments may respond automatically in the absence of particular patient action (e.g., forgetting to bolus insulin to cover a meal) to prevent blood glucose from reaching extreme levels. 
     A controller may employ any one of several control techniques algorithms for computing determining commands for a pump in attempt to maintain a patient&#39;s observed blood glucose concentration within a target range. For example, a controller may employ a proportional-integral-derivative (PID) control algorithm in conjunction with controlling a patient&#39;s blood glucose level within a particular range as described in U.S. patent application Ser. No. 12/820,944, filed on Jun. 22, 2010, and assigned to the assignee of claimed subject matter. Here, such a PID algorithm may, at least in part, predict a level of blood glucose in a patient at some time in the future and, based on such a prediction, compute commands to be provided to an infusion pump. 
     Current PID algorithms typically have limited ability to be tailored to specific characteristics of a patient. While current PID algorithms may effectively respond to sensor measurement errors or some patient specific characteristics, current PID algorithms do not necessarily fully address patient specific characteristics, and much work remains to be done in this area. 
     Briefly, a profile of a patient&#39;s meal may be characterized, at least in part, by carbohydrate content. A profile of external insulin infused by the patient may also be characterized. One or more of the patient&#39;s physiological parameters may then be estimated based, at least in part, on the patient&#39;s meal profile, the patient&#39;s insulin profile and observations of the patient&#39;s blood glucose concentration. It should be understood, however, that this is merely an example embodiment and that claimed subject matter is not limited in this respect. 
     Obtaining a patient&#39;s physiological parameters as discussed above may assist in characterizing the patient&#39;s glycemic response to meals and insulin infusion (e.g., bolus, basal infusion or combinations thereof). These parameters may allow for more effective insulin therapies by, for example, better tuning parameters of a PID control algorithm for computing commands to an insulin infusion pump, setting meal and correction insulin boluses and setting insulin infusion limits to a pump. It should be understood, however, that these are merely examples of how estimates of a patient&#39;s physiological parameters may be applied for improving a therapy, and claimed subject matter is not limited in this respect. 
       FIG. 1  is a block diagram of an example closed-loop glucose control system in accordance with an embodiment. Particular embodiments may include a glucose sensor system  10 , a controller  12 , an insulin delivery system  14 , a glucagon delivery system  13 , and a glucose delivery system  15 , as shown in  FIG. 1 . In certain example embodiments, glucose sensor system  10  may generate a sensor signal  16  representative of blood glucose levels  18  in body  20 , and it may provide sensor signal  16  to controller  12 . Controller  12  may receive sensor signal  16  and generate commands  22  that are communicated to insulin delivery system  14 , glucagon delivery system  13 , and/or glucose delivery system  15 . Insulin delivery system  14  may receive commands  22  and infuse insulin  24  into body  20  in response to commands  22 . Likewise, glucagon delivery system  13  may receive commands  22  and infuse glucagon  23  into body  20  in response to commands  22 . Similarly, glucose delivery system  15  may receive commands  22  and provide glucose  25  into body  20  in response to commands  22 . 
     Glucose sensor system  10  may include a glucose sensor, sensor electrical components to provide power to a sensor and to generate sensor signal  16 , a sensor communication system to carry sensor signal  16  to controller  12 , and a sensor system housing for electrical components and a sensor communication system. A glucose sensor may measure blood glucose directly from a blood stream, indirectly via interstitial fluid using e.g. a subcutaneous sensor, some combination thereof, and so forth, just to name a few examples. As used herein, “blood glucose”, “measured blood glucose”, “blood glucose concentration”, “measured blood glucose concentration”, and the like may refer to a glucose level, a blood glucose level, a blood glucose concentration, and so forth that has been obtained via any type of glucose sensor. It should be understood, however that using a blood glucose sensor is only one particular technique for obtaining such observations or measurements, and that other techniques, such as measuring blood glucose inform observations of other body fluids (e.g., observations of the presence of glucose in interstitial fluid using a subcutaneous sensor), may be used without deviating from claimed subject matter. 
     Controller  12  may include electrical components and software to generate commands  22  for insulin delivery system  14 , glucagon delivery system  13 , and/or glucose delivery system  15  based on sensor signal  16 . Controller  12  may also include a controller communication system to receive sensor signal  16  and provide commands  22  to insulin delivery system  14 , glucagon delivery system  13 , and/or glucose delivery system  15 . In particular example implementations, controller  12  may include a user interface and/or operator interface (not shown) comprising a data input device and/or a data output device. Such a data output device may, for example, generate signals to initiate an alarm and/or include a display or printer for showing status of a controller  12  and/or a patient&#39;s vital indicators. Such a data input device may comprise dials, buttons, pointing devices, manual switches, alphanumeric keys, a touch-sensitive display, combinations thereof, and/or the like for receiving user and/or operator inputs. Such a data input device may be used for scheduling and/or initiating insulin bolus injections for meals, for example. It should be understood, however, that these are merely examples of input and output devices that may be a part of an operator and/or user interface and that claimed subject matter is not limited in these respects. 
     Insulin delivery system  14  may include an infusion device and/or an infusion tube to infuse insulin  24  into body  20 . Similarly, glucagon delivery system  13  may include an infusion device and/or an infusion tube to infuse glucagon  23  into body  20 . Likewise, glucose delivery system  15  may include an infusion device and/or an infusion tube to infuse glucose  25  into body  20 . In alternative embodiments, insulin  24 , glucagon  23 , and/or glucose  25  may be infused into body  20  using a shared infusion tube. In other alternative embodiments, insulin  24 , glucagon  23 , and/or glucose  25  may be infused using an intravenous system for providing fluids to a patient (e.g., in a hospital or other medical environment). It should be understood, however, that certain example embodiments may include an insulin delivery system  14  without a glucagon delivery system  13  and/or without a glucose delivery system  15 . 
     In particular embodiments, an infusion device (not explicitly identified in  FIG. 1 ) may include infusion electrical components to activate an infusion motor according to commands  22 , an infusion communication system to receive commands  22  from controller  12 , and an infusion device housing (not shown) to hold the infusion device. 
     In particular example embodiments, controller  12  may be housed in an infusion device housing, and an infusion communication system may comprise an electrical trace or a wire that carries commands  22  from controller  12  to an infusion device. In alternative embodiments, controller  12  may be housed in a sensor system housing, and a sensor communication system may comprise an electrical trace or a wire that carries sensor signal  16  from sensor electrical components to controller electrical components. In other alternative embodiments, controller  12  may have its own housing or may be included in a supplemental device. In yet other alternative embodiments, controller  12  may be co-located with an infusion device and a sensor system within a single housing. In further alternative embodiments, a sensor, a controller, and/or infusion communication systems may utilize a cable; a wire; a fiber optic line; RF, IR, or ultrasonic transmitters and receivers; combinations thereof; and/or the like instead of electrical traces, just to name a few examples. 
       FIGS. 2-6  illustrate example glucose control systems in accordance with certain embodiments. Such glucose control systems may be used, for example, in controlling a patient&#39;s glucose level about a target range as discussed above. It should be understood, however, that these are merely examples of particular systems that may be used for controlling a patient&#39;s glucose level about a target range and that claimed subject matter is not limited in this respect.  FIG. 2  is a front view of example closed loop hardware located on a body in accordance with certain embodiments.  FIGS. 3( a )-3( d )  and  4  show different views and portions of an example glucose sensor system for use in accordance with certain embodiments.  FIG. 5  is a top view of an example infusion device with a reservoir door in an open position in accordance with certain embodiments.  FIG. 6  is a side view of an example infusion set with an insertion needle pulled out in accordance with certain embodiments. 
     Particular example embodiments may include a sensor  26 , a sensor set  28 , a telemetered characteristic monitor  30 , a sensor cable  32 , an infusion device  34 , an infusion tube  36 , and an infusion set  38 , any or all of which may be worn on a body  20  of a user or patient, as shown in  FIG. 2 . As shown in  FIGS. 3( a ) and 3( b ) , telemetered characteristic monitor  30  may include a monitor housing  31  that supports a printed circuit board  33 , battery or batteries  35 , antenna (not shown), a sensor cable connector (not shown), and so forth. A sensing end  40  of sensor  26  may have exposed electrodes  42  that may be inserted through skin  46  into a subcutaneous tissue  44  of a user&#39;s body  20 , as shown in  FIGS. 3( d )  and  4 . Electrodes  42  may be in contact with interstitial fluid (ISF) that is usually present throughout subcutaneous tissue  44 . 
     Sensor  26  may be held in place by sensor set  28 , which may be adhesively secured to a user&#39;s skin  46 , as shown in  FIGS. 3( c ) and 3( d ) . Sensor set  28  may provide for a connector end  27  of sensor  26  to connect to a first end  29  of sensor cable  32 . A second end  37  of sensor cable  32  may connect to monitor housing  31 . Batteries  35  that may be included in monitor housing  31  provide power for sensor  26  and electrical components  39  on printed circuit board  33 . Electrical components  39  may sample sensor signal  16  (e.g., of  FIG. 1 ) and store digital sensor values (Dsig) in a memory. Digital sensor values Dsig may be periodically transmitted from a memory to controller  12 , which may be included in an infusion device. 
     With reference to  FIGS. 2 and 5  (and  FIG. 1 ), a controller  12  may process digital sensor values Dsig and generate commands  22  (e.g., of  FIG. 1 ) for infusion device  34 . Infusion device  34  may respond to commands  22  and actuate a plunger  48  that forces insulin  24  (e.g., of  FIG. 1 ) out of a reservoir  50  that is located inside an infusion device  34 . Glucose may be infused from a reservoir responsive to commands  22  using a similar and/or analogous device (not shown). In alternative implementations, glucose may be administered to a patient orally. 
     In particular example embodiments, a connector tip  54  of reservoir  50  may extend through infusion device housing  52 , and a first end  51  of infusion tube  36  may be attached to connector tip  54 . A second end  53  of infusion tube  36  may connect to infusion set  38  (e.g., of  FIGS. 2 and 6 ). With reference to  FIG. 6  (and  FIG. 1 ), insulin  24  (e.g., of  FIG. 1 ) may be forced through infusion tube  36  into infusion set  38  and into body  16  (e.g., of  FIG. 1 ). Infusion set  38  may be adhesively attached to a user&#39;s skin  46 . As part of infusion set  38 , a cannula  56  may extend through skin  46  and terminate in subcutaneous tissue  44  to complete fluid communication between a reservoir  50  (e.g., of  FIG. 5 ) and subcutaneous tissue  44  of a user&#39;s body  16 . 
     In example alternative embodiments, as pointed out above, a closed-loop system in particular implementations may be a part of a hospital-based glucose management system. Given that insulin therapy during intensive care has been shown to dramatically improve wound healing and reduce blood stream infections, renal failure, and polyneuropathy mortality, irrespective of whether subjects previously had diabetes (See, e.g., Van den Berghe G. et al. NEJM 345: 1359-67, 2001), particular example implementations may be used in a hospital setting to control a blood glucose level of a patient in intensive care. In such alternative embodiments, because an intravenous (IV) hookup may be implanted into a patient&#39;s arm while the patient is in an intensive care setting (e.g., ICU), a closed loop glucose control may be established that piggy-backs off an existing IV connection. Thus, in a hospital or other medical-facility based system, IV catheters that are directly connected to a patient&#39;s vascular system for purposes of quickly delivering IV fluids, may also be used to facilitate blood sampling and direct infusion of substances (e.g., insulin, glucose, glucagon, etc.) into an intra-vascular space. 
     Moreover, glucose sensors may be inserted through an IV line to provide, e.g., real-time glucose levels from the blood stream. Therefore, depending on a type of hospital or other medical-facility based system, such alternative embodiments may not necessarily utilize all of the described system components. Examples of components that may be omitted include, but are not limited to, sensor  26 , sensor set  28 , telemetered characteristic monitor  30 , sensor cable  32 , infusion tube  36 , infusion set  38 , and so forth. Instead, standard blood glucose meters and/or vascular glucose sensors, such as those described in co-pending U.S. Pat. No. 7,833,157; entitled “MULTILUMEN CATHETER”, may be used to provide blood glucose values to an infusion pump control, and an existing IV connection may be used to administer insulin to an patient. Other alternative embodiments may also include fewer, more, and/or different components than those that are described herein and/or illustrated in the accompanying Drawings. 
     Example system and/or environmental delays are described herein. Ideally, a sensor and associated component(s) would be capable of providing a real time, noise-free measurement of a parameter, such as a blood glucose measurement, that a control system is intended to control. However, in real-world implementations, there are typically physiological, chemical, electrical, algorithmic, and/or other sources of time delays that cause a sensor measurement to lag behind an actual present value. Also, as noted herein, such a delay may arise from, for instance, a particular level of noise filtering that is applied to a sensor signal. Such delays and/or time lags in obtaining sensor glucose measurements may ultimately affect closed-loop operation. Accordingly, and as discussed in greater detail below, feedback control mechanisms using various approaches by application of a predicted duration of a blood glucose level being outside of a target range to better address a patient&#39;s glycemic health. 
     As pointed out above, embodiments are directed to estimating physiological parameters of a patient to characterize the patient&#39;s glycemic response to ingestion of a meal and infusion of insulin.  FIG. 7  is a schematic diagram of a system  100  to model a patient&#39;s response to an infusion of insulin and ingestion of a meal containing carbohydrates according to an embodiment. Block  102  may model the patient&#39;s physiological response to delivery of a known quantity of external or endogenous insulin. Block  104  may model the patient&#39;s physiological response to ingestion of a meal comprising a known quantity of carbohydrates. Based, at least in part, on the exogenous insulin delivered at block  102 , carbohydrates ingested at block  104  and observations of the patient&#39;s blood glucose level, various patient-specific physiological parameters defined in blocks  102  and  104  may be estimated. 
     According to an embodiment, block  102  may model a patient&#39;s physiological response to exogenous insulin based, at least in part, on well-known insulin pharmacokinetics as described in Steil G M, Palerm C C, Kurtz N, et al. The effect of insulin feedback on closed loop glucose control. The Journal of clinical endocrinology and metabolism 2011; 96:1402-8. As pointed out above, an infusion pump may infuse insulin to a patient&#39;s subcutaneous tissue in response to a pump command from a controller. Block  102  may model the infusion of exogenous insulin as expressed in a Laplace domain to subcutaneous tissue according to expression (1) as follows: 
     
       
         
           
             
               
                 
                   
                     
                       
                         
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     where Î D  is insulin intake expressed as a pulse between time t 1  and t 2  in deviation form (Î D =I D −I 0 ), and Î in  [U/hr] is the insulin intake at time t 1  [min] in deviation form (Î in =I in −I 0 ). 
     In a particular implementation, block  108  may behave according to a pharmacokinetic model expressing dynamics of plasma insulin (I p ) as a function of subcutaneous insulin. Here, according to Steil et al. cited above, plasma insulin (I p ) may be expressed in a Laplace domain according to expression (2) as follows: 
     
       
         
           
             
               
                 
                   
                     
                       
                         
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                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
     where Î P  expresses plasma insulin in deviation form (Î P =I P −I 0 ). Î P0  and dI P0  are the Î P  and derivative initial conditions, respectively, and may be estimated based, at least in part, on past delivered insulin. 
     In a particular implementation, expression (3) below may model effects of a patient&#39;s response to insulin infusion on blood glucose concentration as follows: 
     
       
         
           
             
               
                 
                   
                     
                       
                         G 
                         ^ 
                       
                        
                       
                         ( 
                         s 
                         ) 
                       
                     
                     = 
                     
                       
                         1 
                         
                           
                             ( 
                             
                               
                                 
                                   τ 
                                   1 
                                 
                                  
                                 s 
                               
                               + 
                               1 
                             
                             ) 
                           
                           · 
                           
                             ( 
                             
                               
                                 
                                   τ 
                                   2 
                                 
                                  
                                 s 
                               
                               + 
                               1 
                             
                             ) 
                           
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               K 
                               I 
                             
                             · 
                             
                               
                                 I 
                                 ^ 
                               
                               P 
                             
                           
                           - 
                           
                             
                               1 
                               
                                 
                                   ( 
                                   
                                     
                                       50 
                                        
                                       s 
                                     
                                     + 
                                     1 
                                   
                                   ) 
                                 
                                  
                                 
                                   ( 
                                   
                                     
                                       70 
                                        
                                       s 
                                     
                                     + 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                              
                             
                               ( 
                               
                                 
                                   
                                     
                                       G 
                                       ^ 
                                     
                                     0 
                                   
                                   · 
                                   α 
                                 
                                 + 
                                 
                                   
                                     ( 
                                     
                                       
                                         
                                           
                                             G 
                                             ^ 
                                           
                                           0 
                                         
                                         · 
                                         s 
                                       
                                       + 
                                       
                                         d 
                                          
                                         
                                           
                                             G 
                                             ^ 
                                           
                                           0 
                                         
                                       
                                     
                                     ) 
                                   
                                   · 
                                   β 
                                 
                                 + 
                                 
                                   
                                     ( 
                                     
                                       
                                         
                                           
                                             G 
                                             ^ 
                                           
                                           0 
                                         
                                         · 
                                         
                                           s 
                                           2 
                                         
                                       
                                       + 
                                       
                                         d 
                                          
                                         
                                           
                                             
                                               G 
                                               ^ 
                                             
                                             0 
                                           
                                           · 
                                           s 
                                         
                                       
                                     
                                     ) 
                                   
                                   · 
                                   χ 
                                 
                                 + 
                                 
                                   
                                     ( 
                                     
                                       
                                         
                                           
                                             G 
                                             ^ 
                                           
                                           0 
                                         
                                         · 
                                         
                                           s 
                                           3 
                                         
                                       
                                       + 
                                       
                                         d 
                                          
                                         
                                           
                                             
                                               G 
                                               ^ 
                                             
                                             0 
                                           
                                           · 
                                           
                                             s 
                                             2 
                                           
                                         
                                       
                                     
                                     ) 
                                   
                                   · 
                                   δ 
                                 
                               
                               ) 
                             
                           
                         
                         ) 
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                       
                   
                    
                   
                     α 
                     = 
                     
                       120 
                       + 
                       
                         τ 
                         1 
                       
                       + 
                       
                         τ 
                         2 
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                       
                   
                    
                   
                     β 
                     = 
                     
                       3500 
                       + 
                       
                         120 
                          
                         
                           τ 
                           1 
                         
                       
                       + 
                       
                         120 
                          
                         
                           τ 
                           2 
                         
                       
                       + 
                       
                         
                           τ 
                           1 
                         
                          
                         
                           τ 
                           2 
                         
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                       
                   
                    
                   
                     χ 
                     = 
                     
                       
                         3500 
                          
                         
                           τ 
                           1 
                         
                       
                       + 
                       
                         3500 
                          
                         
                           τ 
                           2 
                         
                       
                       + 
                       
                         120 
                          
                         
                           τ 
                           1 
                         
                          
                         
                           τ 
                           2 
                         
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                       
                   
                    
                   
                     δ 
                     = 
                     
                       3500 
                        
                       
                         τ 
                         1 
                       
                        
                       
                         τ 
                         2 
                       
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
     where Ĝ, K I , Ĝ 0 , dG 0 , τ 1 , and τ 2  are the blood glucose concentration in deviation form (Ĝ=G−G out,0 ), the insulin gain, the blood glucose initial conditions in deviation form (Ĝ 0 =G 0 −G out,0 ) blood glucose derivative initial conditions, and two time constants, respectively. 
     According to an embodiment, different components of a meal ingested by a patient may increase the patient&#39;s blood glucose concentration at different rates. For example, ingestion of a candy bar or highly glycemic fruit (e.g., pineapple or banana) may release a large amount of glucose into the patient&#39;s quickly while animal fat may release glucose into the patient&#39;s blood more gradually. As such, ingestion of a meal with a mixture of different types of food with different glycemic properties may produce corresponding multiple spikes in blood glucose concentration. In a particular implementation, block  104  may model the release of glucose into a patient&#39;s blood according to expression (4) as follows: 
     
       
         
           
             
               
                 
                   
                     
                       
                         G 
                         M 
                       
                        
                       
                         ( 
                         s 
                         ) 
                       
                     
                     = 
                     
                       
                         
                           
                             
                               K 
                               
                                 M 
                                 1 
                               
                             
                             · 
                             M 
                           
                           
                             
                               ( 
                               
                                 
                                   
                                     τ 
                                     
                                       M 
                                       1 
                                     
                                   
                                    
                                   s 
                                 
                                 + 
                                 1 
                               
                               ) 
                             
                             2 
                           
                         
                         · 
                         
                           exp 
                            
                           
                             ( 
                             
                               
                                 - 
                                 
                                   D 
                                   
                                     meal 
                                     1 
                                   
                                 
                               
                                
                               s 
                             
                             ) 
                           
                         
                       
                       + 
                       
                         
                           
                             
                               K 
                               
                                 M 
                                 2 
                               
                             
                             · 
                             M 
                           
                           
                             
                               ( 
                               
                                 
                                   
                                     τ 
                                     
                                       M 
                                       2 
                                     
                                   
                                    
                                   s 
                                 
                                 + 
                                 1 
                               
                               ) 
                             
                             2 
                           
                         
                         · 
                         
                           exp 
                            
                           
                             ( 
                             
                               
                                 - 
                                 
                                   D 
                                   
                                     meal 
                                     2 
                                   
                                 
                               
                                
                               s 
                             
                             ) 
                           
                         
                       
                     
                   
                   , 
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
     where G M  [mg/dL] is a blood glucose concentration increment from meal consumption, M is a profile of a meal including carbohydrate content consumed over a time period, D meal     1,2    [min] are time delays between the time of the meal intake and the time of the leading edge of a spike in blood glucose concentration, K M     1,2    are meal response gains, and τ M     1,2    are time constants. 
     Here, expression (4) recognizes two spikes in blood glucose concentration at two different times D meal     1,2    arising from a faster glycemic component and a slower glycemic component in a “double hump” profile. It should be understood, however, that a meal may be modeled as having three or more of such glycemic components releasing glucose at different times and rates, and that claimed subject matter is not limited in this respect. 
     According to an embodiment, block  104  may model meal profile M as a time dependent profile having of a beginning of a meal and an end of a meal. In a particular implementation, meal profile M may be represented in a Laplace domain in expression (5) as follows: 
     
       
         
           
             
               
                 
                   M 
                   = 
                   
                     
                       
                         M 
                         in 
                       
                       s 
                     
                      
                     
                       ( 
                       
                         
                           exp 
                            
                           
                             ( 
                             
                               
                                 - 
                                 
                                   t 
                                   1 
                                 
                               
                                
                               s 
                             
                             ) 
                           
                         
                         - 
                         
                           exp 
                            
                           
                             ( 
                             
                               
                                 - 
                                 
                                   t 
                                   2 
                                 
                               
                                
                               s 
                             
                             ) 
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
     where M in  is a meal intake [gr·CHO/hr] between a meal start time t 1  and a meal end time τ 2  [min]. (In one particular implementation, M in ,t 1  and t 2  may be based, at least in part, on a patient&#39;s estimated meal input in gr·CHO. This estimated meal input may be determined, for example, from manual inputs provided by the patient at a controller. Alternatively, values for M in ,t 1  and t 2  may be provided to a controller from a remote server downloaded from a network as part of a patient profile specifying patient specific parameters for glycemic control. If values for t 1  and t 2  are not indicated, for example, a default meal duration (e.g., 15 min.) may be selected. It should be understood, however that expression (5) is merely one technique that may be used for modeling a meal profile, and claimed subject matter is not limited in this respect. 
     As pointed out above according to an embodiment, physiological parameters of a patient may characterize the patient&#39;s glycemic response to ingestion of a meal and infusion of insulin. These parameters may include, for example, K I , τ 1 , and τ 2  in expression (3), and D meal     1,2   , K M     1,2    and τ M     1,2    in expression (4). It should be understood, however, that these are merely examples of physiological parameters which may be estimated to characterize a patient&#39;s glycemic response, and claimed subject matter is not limited in this respect. In one particular example, parameters of expressions (3) and (4) may be estimated by, for example relating expressions (3) and (4) to one another and incorporating observations of the patient&#39;s blood glucose concentration (e.g., using a continuous glucose monitoring device via a glucose sensor disposed in interstitial fluid as described above, periodic metered blood glucose samples, etc.). Here, expressions (3) and (4) may be related to one another according to expression (6) as follows: 
         G   out   =G   M ( t )+ Ĝ ( t )+ G   out,0 ,  (6)
 
     where: 
     G out,0  is an observed fasting blood glucose concentration [mg/dL] at a given basal insulin infusion rate of I 0 ; 
     G out  is the observed blood glucose concentration at time t; 
     G M  is a blood glucose concentration increment from meal consumption (e.g., from expression (4)); and 
     Ĝ is the blood glucose concentration in deviation form (e.g., from expression (3)). 
     Here, by relating expressions (3) and (4) together with multiple observations of blood glucose concentration, parameters K I , τ 1 , τ 2 , D meal     1,2   , K M     1,2    and τ M     1,2    may be estimated by applying any one of several “best fit” techniques. 
     In particular embodiments, Table 1 below summarizes examples of physiological parameters that may be estimated for a patient. 
     
       
         
           
               
             
               
                 TABLE 1 
               
             
            
               
                   
               
               
                 [mg/dL] 
               
            
           
           
               
               
               
               
            
               
                   
                 Parameter 
                   
                   
               
               
                   
                 symbol 
                 Description 
                 Estimation method 
               
               
                   
               
               
                   
                 K I   
                 Insulin gain [mg/dL per U/h] 
                 Modified 1800 ‘rule’ 
               
               
                   
                 τ 1   
                 Insulin time constant [min] 
                 Daily CGM data 
               
               
                   
                 τ 2   
                 Insulin time constant [min] 
                 Daily CGM data 
               
               
                   
                 K M1   
                 Meal gain [mg/dL per 
                 Daily CGM data 
               
               
                   
                   
                 gr CHO/h] 
                   
               
               
                   
                 K M2   
                 Meal gain [mg/dL per 
                 Daily CGM data 
               
               
                   
                   
                 gr CHO/h] 
                   
               
               
                   
                 τ M1   
                 Meal time constant [min] 
                 Daily CGM data 
               
               
                   
                 τ M2   
                 Meal time constant [min] 
                 Daily CGM data 
               
               
                   
                 D meal1   
                 Meal time delay [min] 
                 Daily CGM data 
               
               
                   
                 D meal2   
                 Meal time delay [min] 
                 Daily CGM data 
               
               
                   
                 I 0   
                 Insulin reference value [U] 
                 Fasting data 
               
               
                   
                 G out,0   
                 Glucose reference value 
                 Fasting data 
               
               
                   
               
            
           
         
       
     
     In one particular implementation, various parameters identified above may be estimated in a sequential fashion. For example, a value for K I  may first be estimated based, at least in part, on the so-called “1800 rule,” an assessment of a likely drop in a patient&#39;s blood glucose level from an amount of exogenous insulin provided. (see, e.g., Kaufman FR. Type 1 diabetes mellitus. Pediatrics in review/American Academy of Pediatrics 2003; 24:291-300) Here, a value for K I  may be estimated according to expression (7) as follows: 
     
       
         
           
             
               
                 
                   
                     
                       K 
                       I 
                     
                     = 
                     
                       
                         - 
                         3 
                       
                       · 
                       
                         DpU 
                         1800 
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       
                         DpU 
                         1800 
                       
                       = 
                       
                         1800 
                         TDI 
                       
                     
                     , 
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
     where: 
     DpU 1800  is the drop in mg/dL per unit of insulin may be predicted based, at least in part, on the “1800 rule”; and 
     TDI is a patient&#39;s total daily insulin. 
     Values for I 0  and G out,0  may be determined from observing a patient&#39;s blood glucose concentration over a few fasting periods (e.g., overnight). Here, a basal insulin infusion rate of I 0  applied during a fasting period and the patient&#39;s blood glucose may be observed as G out,0  at the end of that fasting period. With values estimated for K I  according to expression (7) in combination with values estimated for I 0  and G out,0 , values for remaining parameters τ 1,2 , K M1,2 , τ M1,2  and D meal1,2  may be computed by evaluating observations of blood glucose concentration in response to meals. In one implementation, values for remaining parameters τ 1,2  K M1,2 , τ M1,2 , and D meal1,2  may be determined to provide a “best fit” according to a minimization of a cost function in expression (8) as follows: 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           ∑ 
                           
                             k 
                             = 
                             1 
                           
                           
                             k 
                             = 
                             n 
                           
                         
                          
                         
                           
                             ( 
                             
                               
                                 CGM 
                                 k 
                               
                               - 
                               
                                 G 
                                 
                                   out 
                                   , 
                                   k 
                                 
                               
                             
                             ) 
                           
                           2 
                         
                       
                       n 
                     
                   
                   , 
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
     
     where CGM k  is a blood glucose concentration observed at time instant k, 
     and G out,k  is the model predicted blood glucose at sampling time k 
     In particular implementations, a blood glucose concentration observed at time instant k as CGM k  may be based on blood glucose concentration observed from a continuous glucose monitoring device. However, other techniques to observe a patient&#39;s blood glucose concentration, such as metered blood glucose sampling, may be used without deviating from claimed subject matter. 
     In particular implementations, in computing G out,k  for the cost function of expression (8), certain bounds may be placed on values forτ 1,2  K M1,2 , τ M1,2 , and D meal1,2 In one example implementation, the following boundaries may be established: 
     
       
         
           
             0 
             &lt; 
             
               τ 
               
                 1 
                 , 
                 2 
               
             
             ≤ 
             
               150 
                
               
                 [ 
                 min 
                 ] 
               
             
           
         
       
       
         
           
             0 
             &lt; 
             
               τ 
               
                 
                   M 
                    
                   
                       
                   
                    
                   1 
                 
                 , 
                 2 
               
             
             ≤ 
             
               90 
                
               
                 [ 
                 min 
                 ] 
               
             
           
         
       
       
         
           
             0 
             &lt; 
             
               K 
               
                 M 
                 
                   1 
                   , 
                   2 
                 
               
             
             ≤ 
             
               1 
                
               0 
                
               
                 0 
                  
                 
                   [ 
                   
                     
                       mg 
                       / 
                       dL 
                     
                     
                       gr 
                       · 
                       
                         CHO 
                         / 
                         hr 
                       
                     
                   
                   ] 
                 
               
             
           
         
       
       
         
           
             0 
             &lt; 
             
               D 
               
                 meal 
                  
                 
                     
                 
                  
                 1 
               
             
             &lt; 
             
               10 
                
               
                 [ 
                 min 
                 ] 
               
             
           
         
       
       
         
           
             0 
             &lt; 
             
               D 
               
                 meal 
                  
                 
                     
                 
                  
                 2 
               
             
             &lt; 
             
               60 
                
               
                 [ 
                 min 
                 ] 
               
             
           
         
       
     
     Also, limits may be placed on an absolute relative difference of observed blood glucose concentration CGM k  and initial condition G 0  as follows: 
     
       
         
           
             
                
               
                 
                   
                     CGM 
                     k 
                   
                   - 
                   
                     
                       G 
                       0 
                     
                      
                     
                       ( 
                       k 
                       ) 
                     
                   
                 
                 
                   CGM 
                   k 
                 
               
                
             
             ≤ 
             0.14 
           
         
       
     
     Also, limits may be placed on derivatives of initial conditions of blood glucose concentration. For example, derivatives of initial conditions of blood glucose concentrations may be bounded to be no greater than 5.0 mg/dl/min as follows: 
     
       
         
           
             | 
             
               
                 
                   dG 
                   0 
                 
                  
                 
                   ( 
                   k 
                   ) 
                 
               
               dt 
             
             | 
             
               ≤ 
               
                 
                   5 
                    
                   
                     [ 
                     
                       
                         mg 
                         / 
                         dL 
                       
                       min 
                     
                     ] 
                   
                 
                 . 
               
             
           
         
       
     
     As pointed out above, physiological parameters estimated for a patient may be used to determine an insulin basal rate to be provided to the patient by an insulin infusion pump. Here, with a target blood glucose concentration of 120.0 mg/dL and estimates of K I  and G out,0  with corresponding basal value I 0 , an insulin basal rate I Basal  may be determined according to relation (9) as follows: 
     
       
         
           
             
               I 
               Basal 
             
             = 
             
               
                 ( 
                 
                   
                     I 
                     0 
                   
                   + 
                   
                     
                       
                         1 
                          
                         2 
                          
                         0 
                       
                       - 
                       
                         G 
                         
                           out 
                           , 
                           0 
                         
                       
                     
                     
                       K 
                       I 
                     
                   
                 
                 ) 
               
               . 
             
           
         
       
     
     While an infusion pump may deliver insulin to a patient at a constant basal rate I Basal  under some conditions, the infusion pump may also deliver one or more boluses with or shortly following a meal. In a particular example illustrated in  FIG. 8 , a profile of insulin delivery indicates a basal rate I Basal  along with three boluses including a single impulse bolus provided at mealtime followed by two smaller square boluses. In a particular implementation, a patient&#39;s physiological parameters as estimated above may be used to determine the size of insulin boluses to be delivered to the patient during and following meals. 
     According to an embodiment, components of a post meal bolus may be computed based, at least in part, on a value for above I Basal  computed according to expression (9). In one implementation, a post meal bolus may have a profile as a brief change in an insulin basal infusion rate. Expression (10) as follows provides a profile for a post meal bolus including an impulse bolus at a time k at mealtime, followed by a first elevated basal rate from k+1 minute to k+120 minutes, a second elevated base rate from k+121 minutes to k+240 minutes and a third elevated basal rate from k+241 minutes to k+360 minutes: 
     
       
         
           
             
                 
             
              
             
               
                 bolus 
                  
                 
                   ( 
                   k 
                   ) 
                 
               
               = 
               
                 
                   Meal 
                   CR 
                 
                 + 
                 correctionbolus 
               
             
           
         
       
       
         
           
             
                 
             
              
             
               
                 insulin 
                  
                 
                   ( 
                   
                     
                       k 
                       + 
                       1 
                     
                     : 
                     
                       k 
                       + 
                       
                         12 
                          
                         0 
                       
                     
                   
                   ) 
                 
               
               = 
               
                 
                   
                     PPbasal 
                     1 
                   
                   · 
                   Meal 
                 
                 + 
                 
                   I 
                   Basal 
                 
               
             
           
         
       
       
         
           
             
                 
             
              
             
               
                 insulin 
                  
                 
                   ( 
                   
                     
                       k 
                       + 
                       121 
                     
                     : 
                     
                       k 
                       + 
                       
                         24 
                          
                         0 
                       
                     
                   
                   ) 
                 
               
               = 
               
                 
                   
                     PPbasal 
                     2 
                   
                   · 
                   Meal 
                 
                 + 
                 
                   I 
                   Basal 
                 
               
             
           
         
       
       
         
           
             
                 
             
              
             
               
                 insulin 
                  
                 
                   ( 
                   
                     
                       k 
                       + 
                       241 
                     
                     : 
                     
                       k 
                       + 
                       
                         36 
                          
                         0 
                       
                     
                   
                   ) 
                 
               
               = 
               
                 
                   
                     PPbasal 
                     3 
                   
                   · 
                   Meal 
                 
                 + 
                 
                   I 
                   Basal 
                 
               
             
           
         
       
       
         
           
             correctionbolus 
             = 
             
               { 
               
                 
                   
                     0 
                   
                   
                     
                       
                         
                           
                             
                               CGM 
                               k 
                             
                             - 
                             
                               BG 
                               target 
                             
                           
                           CF 
                         
                         - 
                         IOB 
                       
                       &lt; 
                       0 
                     
                   
                 
                 
                   
                     
                       
                         
                           
                             CGM 
                             k 
                           
                           - 
                           
                             BG 
                             
                               t 
                                
                               a 
                                
                               r 
                                
                               g 
                                
                               e 
                                
                               t 
                             
                           
                         
                         CF 
                       
                       - 
                       IOB 
                     
                   
                   
                     otherwise 
                   
                 
               
             
           
         
       
     
     Where bolus(k) is an insulin impulse [U] given at the discrete moment k, Meal is the meal size in grams of carbohydrates (gr·CHO), CF is a patient&#39;s insulin sensitivity 
     
       
         
           
             
               [ 
               
                 
                   mg 
                   / 
                   dL 
                 
                 U 
               
               ] 
             
             , 
           
         
       
     
     CR is a carbohydrate ratio of the meal 
     
       
         
           
             
               [ 
               
                 
                   gr 
                   · 
                   CHO 
                 
                 U 
               
               ] 
             
             , 
           
         
       
     
     PPbasal 1,2,3  are three values that multiplied by the Meal (gr·CHO) and added to the I Basal  produce a six hour postprandial bolus. IOB [U] is the estimated insulin on board based on the history of delivered insulin. In addition, the post meal bolus of expression (10) may be determined subject to the following constraints : 
     
       
         
           
             
               
                 
                   
                     subject 
                      
                     
                         
                     
                      
                     to 
                      
                     
                       : 
                     
                   
                    
                   
                     
 
                   
                    
                   
                     I 
                     : 
                     
                       C 
                       ∈ 
                       
                         [ 
                         
                           0 
                           , 
                           
                             5 
                              
                             0 
                           
                         
                         ] 
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     CF 
                     ∈ 
                     
                       [ 
                       
                         1 
                         , 
                         inf 
                       
                       ] 
                     
                   
                    
                   
                     
 
                   
                    
                   
                     subject 
                      
                     
                         
                     
                      
                     to 
                      
                     
                       : 
                     
                   
                    
                   
                     
 
                   
                    
                   
                     0 
                     ≤ 
                     
                       PPbasal 
                       
                         1 
                         , 
                         2 
                         , 
                         3 
                       
                     
                     ≤ 
                     
                       
                         basal 
                         max 
                       
                       Meal 
                     
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
           
         
       
     
     where a maximum insulin infusion basal rate, basal max , may be set by default to 4 [U/h]. 
     A profile for a post meal bolus may be determined so as to balance risks of hyperglycemia and hypoglycemia to the patient. Here,  G   pre&lt;0  may denote a magnitude of blood glucose predicted to be in a hypoglycemic region while  G   pre≥0  may denote a magnitude of blood glucose predicted to be in a hyperglycemic region.  G   pre&lt;0  or  G   pre≥0  for values of PPbasal, CF or I:C—In a particular implementation, PPbasal, CF or I:C may be set/optimized so as to minimize expression (12) below.  G   pre&lt;0  may quantify an amount or percentage of time that G out  is predicted to be in some predefined hypoglycemia range while  G   pre≥0  may quantify an amount of time that G out  is predicted to be out of the predefined hypoglycemic range. In another implementation, values for G out  may be predicted for given values of PPbasal, CF or I:C where part of the predicted values of G out  may be in a hypoglycemic range, represented by  G   pre&lt;0 , while remaining values of G out  are represented by  G   pre≥0 . As pointed out above in a particular implementation, a value for CF, CR, PPbasal may be selected so as to minimize the following cost function of expression (12): 
     
       
         
           
             
               
                 
                   
                     min 
                     
                       CF 
                       , 
                       CR 
                       , 
                       PPbasal 
                     
                   
                    
                   
                     
                       
                         
                           
                             
                               G 
                               _ 
                             
                             
                               pre 
                               &lt; 
                               0 
                             
                             2 
                           
                           × 
                           10 
                         
                         + 
                         
                           
                             G 
                             _ 
                           
                           
                             pre 
                             ≥ 
                             0 
                           
                           2 
                         
                       
                     
                     . 
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
           
         
       
     
     An insulin infusion pump may receive commands on discrete intervals determined based, at least in part, on a PID control system. In one particular implementation, a command u(k) to an infusion pump to deliver an amount of insulin may be determined according to expression (10) as follows: 
     
       
         
           
             
               
                 
                   
                       
                   
                    
                   
                     
                       
                         u 
                          
                         
                           ( 
                           k 
                           ) 
                         
                       
                       = 
                       
                         
                           
                             K 
                             c 
                           
                            
                           
                             ( 
                             
                               
                                 e 
                                  
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                               + 
                               
                                 
                                   T 
                                   
                                     T 
                                     I 
                                   
                                 
                                  
                                 
                                   
                                     ? 
                                   
                                   · 
                                   
                                     GSD 
                                      
                                     
                                       ( 
                                       k 
                                       ) 
                                     
                                   
                                 
                               
                             
                             ) 
                           
                         
                         + 
                         
                           u 
                           _ 
                         
                       
                     
                     , 
                     
                       
 
                     
                      
                     
                       
                         ? 
                       
                        
                       
                         indicates text missing or illegible when filed 
                       
                     
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
           
         
       
     
     where:
 
K C , τ I  and τ D  are the controller gain, integrator time constant, and differential time constant, respectively;
 
e(k) is an error between a blood glucose reference measurement and a predetermined set-point or target blood glucose concentration at time instant k;
 
ū is the control initial conditions;
 
GSD(k) an estimated rate of change in blood glucose concentration at time instant k; and
 
T is the sampling time.
 
     According to an embodiment, values for controller gain K C , integrator time constant τ I  and differential time constant To may be determined based, at least in part, on one or more physiological parameters estimated for a patient as described above. In one example implementation, values for controller gain K C , integrator time constant τ I  and differential time constant τ D  may be determined based, at least in part, on the fourth-order expression (3). Here, exclusive of initial conditions, expression (3) may be characterized by a process p having the form 
     
       
         
           
             
                 
             
              
             
               
                 
                   ? 
                 
                 
                   ? 
                 
               
                
               
                 
                   ? 
                 
                 . 
                 
                   
 
                 
                  
                 
                   ? 
                 
               
                
               
                 indicates text missing or illegible when filed 
               
             
           
         
       
     
     The fourth-order expression of process p may be approximated as a second-order expression 
     
       
         
           
             
               p 
               ~ 
             
             = 
             
               
                 
                   K 
                   I 
                 
                 
                   
                     ( 
                     
                       
                         
                           τ 
                           
                             1 
                              
                             1 
                           
                         
                          
                         s 
                       
                       + 
                       1 
                     
                     ) 
                   
                    
                   
                     ( 
                     
                       
                         
                           τ 
                           22 
                         
                          
                         s 
                       
                       + 
                       1 
                     
                     ) 
                   
                 
               
               . 
             
           
         
       
     
     Here, K I , τ 11 , and τ 22  may be equated to obtain estimates for K C , integrator time constant τ I  and differential time constant τ D  may according to expressions (11), (12) and (13) as follows: 
     
       
         
           
             
               
                 
                   
                     K 
                     c 
                   
                   = 
                   
                     
                       
                         τ 
                         11 
                       
                       + 
                       τ22 
                     
                     
                       λ 
                       · 
                       
                         K 
                         I 
                       
                     
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
             
               
                 
                   
                     τ 
                     I 
                   
                   = 
                   
                     
                       τ 
                       
                         1 
                          
                         1 
                       
                     
                     + 
                     
                       τ 
                       
                         2 
                          
                         2 
                       
                     
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
             
               
                 
                   
                     τ 
                     D 
                   
                   = 
                   
                     
                       
                         τ 
                         
                           1 
                            
                           1 
                         
                       
                       · 
                       
                         τ 
                         
                           2 
                            
                           2 
                         
                       
                     
                     
                       
                         τ 
                         
                           1 
                            
                           1 
                         
                       
                       + 
                       
                         τ 
                         
                           2 
                            
                           2 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
           
         
       
     
     where: 
     λ is a tuning parameter that may be set by offline optimization; and 
     τ 11  and τ 22  are insulin time constants for the second order expression for {tilde over (p)}. 
     According to an embodiment, a controller for an insulin infusion pump may set a limit on a maximum amount of insulin to be delivered in an infusion pump command cycle for commands u(k). Here, such a limit Umax may be determined according to relation (15) as follows: 
     
       
         
           
             
               
                 
                   
                     U 
                      
                     
                         
                     
                      
                     max 
                   
                   = 
                   
                     
                       I 
                       0 
                     
                     + 
                     
                       
                         
                           BG 
                           LBL 
                         
                         - 
                         
                           G 
                           
                             out 
                             , 
                             0 
                           
                         
                       
                       
                         K 
                         I 
                       
                     
                   
                 
               
               
                 
                   ( 
                   15 
                   ) 
                 
               
             
           
         
       
     
     where I 0  is the estimated basal rate defined for a patient, an observed G out,0  a fasting blood glucose concentration determined as discussed above, BG LBL  mg/dL is a lower buffer limit blood glucose concentration as Umax is approached, and K I  is an insulin gain determined as discussed above. In a particular implementation, Umax may comprise a maximum insulin rate that, if delivered to a patient overnight (or any other fasting period) for a relative long period, the patient&#39;s blood glucose would approach eventually to the value of BG LBL  (mg/dL). For example, if a patient&#39;s estimated I 0  is 1.0 U/h, G out,0  is 120 mg/dL, the K I  (insulin gain) is −100 mg/dL per U/h, and we may set BG LBL  to 70 mg/dL. Then, Umax would be equal to 
     
       
         
           
             
               1 
               + 
               
                 
                   
                     7 
                      
                     0 
                   
                   - 
                   
                     1 
                      
                     2 
                      
                     0 
                   
                 
                 
                   
                     - 
                     1 
                   
                    
                   0 
                    
                   0 
                 
               
             
             = 
             
               1.5 
                
               
                   
               
                
               
                 U 
                 / 
                 
                   h 
                   . 
                 
               
             
           
         
       
     
     Therefore, delivery of 1.5 U/h even under sensor glucose fault without endangering the patient may still be safe because the patient&#39;s blood glucose would, theoretically, not fall below 70 mg/dL (or other value defined as BG LBL ). 
     Unless specifically stated otherwise, as is apparent from the preceding discussion, it is to be appreciated that throughout this specification discussions utilizing terms such as “processing”, “computing”, “calculating”, “determining”, “estimating”, “selecting”, “identifying”, “obtaining”, “representing”, “receiving”, “transmitting”, “storing”, “analyzing”, “associating”, “measuring”, “detecting”, “controlling”, “delaying”, “initiating”, “setting”, “delivering”, “waiting”, “starting”, “providing”, and so forth may refer to actions, processes, etc. that may be partially or fully performed by a specific apparatus, such as a special purpose computer, special purpose computing apparatus, a similar special purpose electronic computing device, and so forth, just to name a few examples. In the context of this specification, therefore, a special purpose computer or a similar special purpose electronic computing device or apparatus may be capable of manipulating or transforming signals, which are typically represented as physical electronic and/or magnetic quantities within memories, registers, or other information storage devices; transmission devices; display devices of a special purpose computer; or similar special purpose electronic computing device; and so forth, just to name a few examples. In particular example embodiments, such a special purpose computer or similar may comprise one or more processors programmed with instructions to perform one or more specific functions. Accordingly, a special purpose computer may refer to a system or a device that includes an ability to process or store data in the form of signals. Further, unless specifically stated otherwise, a process or method as described herein, with reference to flow diagrams or otherwise, may also be executed or controlled, in whole or in part, by a special purpose computer. 
     It should be noted that although aspects of the above systems, methods, devices, processes, etc. have been described in particular orders and in particular arrangements, such specific orders and arrangements are merely examples and claimed subject matter is not limited to the orders and arrangements as described. It should also be noted that systems, devices, methods, processes, etc. described herein may be capable of being performed by one or more computing platforms. In addition, instructions that are adapted to realize methods, processes, etc. that are described herein may be capable of being stored on a storage medium as one or more machine readable instructions. If executed, machine readable instructions may enable a computing platform to perform one or more actions. “Storage medium” as referred to herein may relate to media capable of storing information or instructions which may be operated on, or executed by, one or more machines (e.g., that include at least one processor). For example, a storage medium may comprise one or more storage articles and/or devices for storing machine-readable instructions or information. Such storage articles and/or devices may comprise any one of several non-transitory media types including, for example, magnetic, optical, semiconductor, a combination thereof, etc. storage media. By way of further example, one or more computing platforms may be adapted to perform one or more processes, methods, etc. in accordance with claimed subject matter, such as methods, processes, etc. that are described herein. However, these are merely examples relating to a storage medium and a computing platform and claimed subject matter is not limited in these respects. 
     Although what are presently considered to be example features have been illustrated and described, it will be understood by those skilled in the art that various other modifications may be made, and equivalents may be substituted, without departing from claimed subject matter. Additionally, many modifications may be made to adapt a particular situation to the teachings of claimed subject matter without departing from central concepts that are described herein. Therefore, it is intended that claimed subject matter not be limited to particular examples disclosed, but that such claimed subject matter may also include all aspects falling within the scope of appended claims, and equivalents thereof.