Modeling and control for highly variable and nonlinear systems

• US 8,229,872 B2
• Filed: 09/14/2007
• Issued: 07/24/2012
• Est. Priority Date: 09/16/2006
• Status: Active Grant

• Current Assignee: Terence Gilhuly
• Original Assignee: Terence Gilhuly
• Inventors: Gilhuly, Terence
• Primary Examiner(s): FERNANDEZ RIVAS, OMAR F
• Application Number:
  US12/311,104
• Publication Number:
  US 20090327204A1
• Time in Patent Office: 1,775 Days
• Field of Search: None
• US Class Current: 706/45
• CPC Class Codes: A61B 5/0002 Remote monitoring of patients using telemetry, e.g. transmission of vital signals via a communication network A61B5/07 takes precedence; transmission systems for measured values G08C; transmission H04B; transmission of digital information H04L; wireless communication networks H04W
• CPC Class Codes: A61B 5/01 Measuring temperature of body parts ; Diagnostic temperature sensing, e.g. for malignant or inflamed tissue clinical contact thermometers G01K13/20
• CPC Class Codes: A61B 5/02055 Simultaneously evaluating both cardiovascular condition and temperature
• CPC Class Codes: A61B 5/05 Detecting, measuring or recording for diagnosis by means of electric currents or magnetic fields; Measuring using microwaves or radio waves impedance plethysmography A61B5/0295; measuring movement of the entire body or parts thereof A61B5/11; detecting, measuring or recording bioelectric or biomagnetic signals of the body or parts thereof A61B5/24
• CPC Class Codes: A61B 5/1106 to assess neuromuscular blockade, e.g. to estimate depth of anaesthesia
• CPC Class Codes: A61B 5/4821 Determining level or depth of anaesthesia A61B5/1106 takes precedence
• CPC Class Codes: A61B 5/72 Signal processing specially adapted for physiological signals or for diagnostic purposes character recognition, recognising digital ink, document-oriented image-based pattern recognition G06V30/00; recognition or understanding of postal images G06V30/424
• CPC Class Codes: A61B 5/746 Alarms related to a physiological condition, e.g. details of setting alarm thresholds or avoiding false alarms alarms per se G08B
• CPC Class Codes: A61M 2005/14208 with a programmable infusion control system, characterised by the infusion program
• CPC Class Codes: G05B 17/02 electric
• CPC Class Codes: G16H 40/63 for local operation
• CPC Class Codes: G16H 50/50 for simulation or modelling of medical disorders
• CPC Class Codes: G16Z 99/00 Subject matter not provided for in other main groups of this subclass
• CPC Class Codes: Y02A 90/10 Information and communication technologies [ICT] supporting adaptation to climate change, e.g. for weather forecasting or climate simulation

Abstract

The present invention relates generally to methods of modeling and handling of nonlinearities for application of automatic control to systems with high inter-process variance and nonlinearities. The variance and nonlinearities make these systems difficult to control. Variance is accounted for by replacing the mathematical model of the system with a more representative model from a modelset that may or may not be chosen based on characteristics of the system under test, and then adapting using recursive estimation techniques. Nonlinearities defined by threshold to response and maximal responses are incorporated into linear models relating accumulated inputs to response. Example implementations in relation to automated drug delivery for neuromuscular blocking drugs through warning, advisory and closed-loop control systems are discussed.

Claims

1. A method of adapting a model of a process comprising at least one equation said equation including a set of at least one parameters, said model translating at least one input into at least one response, and said model beginning as at least one of an initial model taken from a modelset comprising one or more models of like processes similar in mathematical construct but with one or more differences in the at least one parameters or built as a mathematical function of models in the modelset comprising:

(a) collecting measurement data related to at least one measured responses;

(b) estimating model parameters to adapt the model of a process to the collected data; and

(c) evaluating said model of a process for comparative performance versus other process models in the modelset, and replacing the at least one parameters of the model of a process with the set of at least one parameters of another similar in mathematical construct process model from the modelset.

2. The method of claim 1 where the modelset is comprised of models created by:

(a) administering a standard input given to a process receiving at least one inputs and producing at least one responses, said process having nonlinearities of at least one of a minimum input or minimum amount of accumulated input to produce a non-minimal response and a maximum response;

(b) recording the one or more responses produced by the standard input;

(c) assembling a dataset of matched response and time datapoints where response datapoints comprise non-minimal and non-maximal response measurements, and time datapoints comprise time of measurement;

(d) adjusting the dataset to correct for the nonlinearities on a second scale accounting for said nonlinearities where the process is modeled as linear on the second scale, by converting the response data according to a slope defined as the range of inputs or range of accumulated inputs that produces a range of measurable responses that are neither minimal nor maximal responses, divided by said range of measurable responses over said range of inputs or accumulated inputs; and

offset defined as an input or quantity of accumulated inputs required to establish a non-minimal measurable response; and

calculating the adjusted response on the second scale as the measured response multiplied by said response plus the offset;

(e) estimating at least one parameters for at least one mathematical function to describe the adjusted dataset; and

(f) calculating at least one continuous set of datapoints described by the at least one function whose at least one parameters are estimated in step (e).

3. The method of claim 1 where estimating the at least one parameters includes at least one of least squares estimation, recursive least squares estimation and recursive least squares estimation with forgetting.

4. The method of claim 3 where the at least one parameters are modified according to a recursive least square estimation algorithm with forgetting and the parameters for forgetting are modified.

5. The method of claim 1 where the modelset is associated with a database of one or more sets of characteristic data related to one or more processes whose process response models have been included in the modelset.

6. The method of claim 1 where the probability of deterioration of the process is estimated by comparison of the process response to response models within the modelset known to be deteriorated.

7. The method of claim 6 where the at least one inputs are drugs and the process represents a patient, and where presence of metabolic conditions or organ failures is predicted based on comparison of the adapted response model to response models of patients known not to have said metabolic conditions or organ failures.

8. The method of claim 6 where the process is a patient, the at least one inputs are drugs and the deterioration of the process relates to the presence of a specific disease, and the specific disease is detected by comparing the model to patient models of a subset where the patients are known to have the specific disease.

9. A system for indicating when at least one response of a process will reach at least one setpoint, the system comprising:

(a) a user interface for receiving process related data including process characteristics and inputs administered, and for displaying information including warnings;

(b) a communications interface through which the system obtains data from at least one sensor;

(c) a model of the process'"'"' at least one response comprising at least one equation said equation including a set of at least one parameters, said model translating at least one input into at least one response;

(d) a computing mechanism operatively connected to the communications interface to receive the sensor data and connected to the user interface to receive input from the user and to present data to the user, the computing mechanism configured to use the model of the process'"'"' at least one response to estimate current and future responses;

(e) memory operatively connected to the computing mechanism for storing and retrieving sensor data and data relevant to the computation, and for storing programs for operation by the computing mechanism; and

(f) a modelset comprising one or more models of like processes similar in mathematical construct but with one or more differences in the at least one parameters;

where said model begins as at least one of an initial model taken from the modelset or is built as a mathematical function of the models in the modelset, and is adapted by steps comprising;

(i) collecting measurement data related to at least one measured responses;

(ii) estimating the at least one parameters to adapt the model of a process to the collected data; and

(iii) evaluating said model of a process for comparative performance versus other process models in the modelset, and replacing the at least one parameters of the model of a process with the set of at least one parameters of another similar in mathematical construct process model from the modelset.

10. The system of claim 9 further comprising a database of characteristic data related to the processes whose process response models have been included in the modelset.

11. The system of claim 9 where the process is a patient, and the at least one responses includes a physiological response, a concentration of at least one drug or an effect due to at least one drug.

12. The system of claim 11 further comprising a database of characteristic data including demographic data, health and lifestyle related data associated with the processes whose process response models have been included in the modelset.

13. The system of claim 10 where the model of the process is evaluated for comparative performance with models in the modelset sharing characteristics in common with the process as indicated by data in the database of characteristic data.

14. The system of claim 13 where the process represents patients and the model of the process is evaluated for comparative performance with models in the modelset having similar demographic parameters that comprise at least one of age, sex, weight, height, lean body mass, body mass index, race, genetic data and history of smoking.

15. The system of claim 13 where the process represents patients and the model of the process is evaluated for comparative performance with models in the modelset having similar health characteristics that comprise at least one of heart failure, lung failure, liver failure, kidney failure, hypertension and diabetes.

16. The system of claim 15 where the process is evaluated for comparative performance with models in the modelset based on degree of disease or disorder progression.

17. The system of claim 11 where the drug is a neuromuscular blocking agent.

18. The system of claim 9 where the system further advises a user on how much of at least one input to administer to a process, such that at least one response of a process will reach at least one setpoint,

(a) where the user interface for receiving process related data including process characteristics and inputs administered, and for displaying information including warnings further displays advice;

and

(b) where the computing mechanism operatively connected to the communications interface to receive the sensor data and connected to the user interface to receive input from the user and to present data to the user, the computing mechanism configured to use the model of the process'"'"' at least one response to estimate current and future responses, further calculates quantities of the at least one input to be administered to arrive at a future desired response level.

19. The system of claim 18 further comprising a database of characteristic data related to the processes whose process response models have been included in the modelset.

20. The system of claim 18 where the process is a patient, the at least one input is a drug, and the at least one responses includes a physiological response, a concentration of drug or an effect due to at least one drug.

21. The system of claim 20 further comprising a database of characteristic data including demographic data, health and lifestyle related data associated with the processes whose process response models have been included in the modelset.

22. The system of claim 19 where the model of the process is evaluated for comparative performance with models in the modelset sharing characteristics in common with the process as indicated by data in the database of characteristic data.

23. The system of claim 22 where the process represents patients and the model of the process is evaluated for comparative performance with models in the modelset having similar demographic parameters that comprise at least one of age, sex, weight, height, lean body mass, body mass index, race, genetic data and history of smoking.

24. The system of claim 22 where the process represents patients and the model of the process is evaluated for comparative performance with models in the modelset having similar health characteristics that comprise at least one of heart failure, lung failure, liver failure, kidney failure, hypertension and diabetes.

25. The system of claim 24 where the process is evaluated for comparative performance with models in the modelset based on degree of disease or disorder progression.

26. The system of claim 18 further comprising adaptation of the model through estimating model parameters by at least one of least squares estimation, recursive least squares estimation and recursive least squares estimation with forgetting.

27. The system of claim 26 where the model is adapted according to a recursive least square estimation algorithm with forgetting and the parameters for forgetting are modified.

28. The system of claim 20 where the drug is a neuromuscular blocking agent.

29. The system of claim 9 where the system further administers in a closed loop fashion at least one input to a process, such that at least one response of a process will reach at least one setpoint,

(a) where the computing mechanism operatively connected to the communications interface to receive the sensor data and connected to the user interface to receive input from the user, the computing mechanism configured to use the model of the process'"'"' at least one response to estimate current and future responses, further calculates quantities of the at least one input to be administered to arrive at a future desired response level;

(b) and where the system further comprises output communication means to at least one drug input means to automate the at least one drug inputs.

30. The system of claim 29 further comprising a database of characteristic data related to the processes whose process response models have been included in the modelset.

31. The system of claim 29 where the process is a patient, the at least one input is a drug, and the at least one responses includes a physiological response, a concentration of drug or an effect due to at least one drug.

32. The system of claim 31 further comprising a database of characteristic data including demographic data, health and lifestyle related data associated with the processes whose process response models have been included in the modelset.

33. The system of claim 32 where the model of the process is evaluated for comparative performance with models in the modelset sharing characteristics in common with the process as indicated by data in the database of characteristic data.

34. The system of claim 33 where the process represents patients and the model of the process is evaluated for comparative performance with models in the modelset having similar demographic parameters that comprise at least one of age, sex, weight, height, lean body mass, body mass index, race, genetic data and history of smoking.

35. The system of claim 33 where the process represents patients and the model of the process is evaluated for comparative performance with models in the modelset having similar health characteristics that comprise at least one of heart failure, lung failure, liver failure, kidney failure, hypertension and diabetes.

36. The system of claim 35 where the process is evaluated for comparative performance with models in the modelset based on degree of disease or disorder progression.

37. The system of claim 29 further comprising adaptation of the model through estimating model parameters by at least one of least squares estimation, recursive least squares estimation and recursive least squares estimation with forgetting.

38. The system of claim 37 where the model is adapted according to a recursive least square estimation algorithm with forgetting and the parameters for forgetting are modified.

39. The system of claim 31 where the drug is a neuromuscular blocking agent.

40. A method of describing a measured response from a process receiving at least one inputs and producing at least one responses, said process having nonlinearities of at least one of a minimum input or minimum amount of accumulated input to produce a non-minimal response measurement and a maximum response measurement, on a second scale accounting for said nonlinearities where the process is modeled as a process linear on the second scale, by converting the response according to a slope and offset comprising:

(a) defining said slope as the range of inputs or range of accumulated inputs that produces a range of measurable responses that are neither minimal nor maximal responses, divided by said range of measurable responses over said range of inputs or accumulated inputs;

(b) defining an offset parameter as an input or quantity of accumulated inputs required to establish a non-minimal measurable response; and

(c) calculating the second response as the measured response multiplied by said response, plus the offset.

41. The method of claim 40 where the offset is modified from its normal value for the process to replicate at least one abnormal process.

42. The method of claim 40 where the process is a patient, the at least one inputs are drugs, the at least one responses is a physiological response and the second scale describes an estimate of receptor occupancy.

43. The method of claim 42 further comprising converting the estimate of receptor occupancy to an estimate of drug present.

44. The method of claim 42 where the process relates to neuromuscular blockade and the inputs are neuromuscular blockade drugs;

the at least one response is a neuromuscular response; and

the offset is the percentage of receptors blocked before effect is detectable.

45. The method of claim 44 where the neuromuscular response is evoked by train-of-four (TOF) stimulation, the offset is at least about 50% of receptors blocked and the maximum effect is found when no response is elicited from said TOF stimulation.

46. The model of claim 45 where the offset is reduced to simulate a muscular disorder or disease.

47. A method of calculating a linear response model for a process receiving at least one inputs and producing at least one responses, said process having nonlinearities, where said nonlinearities include at least one of a minimum input or minimum amount of accumulated input to produce a non-minimal response and a maximum response, comprising:

(a) administering at least one standard input to the process;

(b) recording one or more responses produced by the standard input;

(c) assembling a dataset of matched response and time datapoints where response datapoints comprise non-minimal and non-maximal response measurements, and time datapoints comprise time of measurement;

(d) adjusting the dataset to correct for the nonlinearities on a second scale accounting for said nonlinearities, where the process is modeled as a process linear on the second scale by converting the response data according to a slope defined as the range of inputs or range of accumulated inputs that produces a range of measurable responses that are neither minimal nor maximal responses, divided by said range of measurable responses over said range of inputs or accumulated inputs; and

an offset defined as an input or quantity of accumulated inputs required to establish a non-minimal measurable response; and

calculating the adjusted response on the second scale as the measured response multiplied by said response plus the offset;

(e) estimating at least one parameters for at least one mathematical function to describe the adjusted dataset; and

(f) calculating at least one continuous set of datapoints described by the at least one function whose parameters are derived in step (e).

48. The method of claim 47 further comprising converting the continuous set of datapoints with a state space representation.

49. The method of claim 47 where a Laguerre representation of the model is used and filter gains are calculated from the continuous set of datapoints.

50. The method of claim 47 where the parameters for the at least one mathematical function are derived through nonlinear estimation.

51. The method of claim 47 where the process is a patient and the at least one input is a drug and said input includes at least one of the manufacturer'"'"'s recommended dose, an effective dose in 95% of the patients (ED95) and double the ED95 dose.