Method and apparatus for model-based control of an open-loop process

• US 5,010,473 A
• Filed: 08/31/1989
• Issued: 04/23/1991
• Est. Priority Date: 08/31/1989
• Status: Expired due to Term

• Current Assignee: Hospira Incorporated (Pfizer Inc.)
• Original Assignee: Duke University
• Inventors: Jacobs, James R.
• Primary Examiner(s): Smith, Jerry
• Assistant Examiner(s): GORDON, PAUL P
• Application Number:
  US07/401,996
• Time in Patent Office: 600 Days
• Field of Search: 364/148, 364/149, 364/150, 364/153, 604/151, 604/891, 604/51, 604/66, 604/31, 604/890.1, 604/65, 128/734
• US Class Current: 700/30
• CPC Class Codes: A61M 2005/14296 Pharmacokinetic models
• CPC Class Codes: A61M 5/172 electrical or electronic A61M5/16804, A61M5/16831 take precedence
• CPC Class Codes: G05B 13/04 involving the use of models or simulators

Abstract

A method and apparatus for controlling a model based open-loop process and more specifically, the concentration of a drug delivered intravenously to a patient as a function of the rate of infusion. A three-compartment pharmacokinetic model is preferably used to determine the plasma drug concentrations corresponding to two arbitrarily selected rates of infusion. Based upon the linear relationship between corresponding data pairs, each pair comprising a rate of infusion and a corresponding plasma drug concentration, an interpolated rate is determined by a microprocessor (100) as a function of a specified plasma drug concentration, in accordance with program steps stored in a read only memory (ROM) 104. The actual infusion rate of the drug during successive time intervals is repetitively used to compute the plasma drug concentration at the end of each time interval. In each successive iteration, state variables from the previous computation of the plasma drug concentration are used to determine the next interpolated infusion rate. Any interruptions in the output from an infusion device (112) and variations from the interpolated value of the infusion rate are compensated. Using this open-loop control method and apparatus, the specified plasma drug concentration is rapidly achieved.

Claims

1. A method for controlling a process to obtain a specified output, O_s, where the process is described by a linear model that defines an output of the process as a function of a specified control signal, wherein the control signal controls an actuator that affects the process, said method comprising the steps of:

(a) arbitrarily selecting a first value, X₁, and a second value, X₂, for the control signal, and initializing a plurality of state variables in the model;

(b) as a function of the first and second values of the control signal, which are respectively input to the model, determining corresponding first and second output values, O₁ and O₂, that would be obtained at the end of an interval of time, Δ

t, were the control signal to be applied for this interval;

(c) interpolating with respect to the first and second values of the control signal and corresponding first and second output values to determine a desired value, X_d, for the control signal that should produce the specified output, O_s, at the end of the time interval, Δ

t;

(d) for the time interval, Δ

t, operating the process using the desired value, X_d, determined in step (c) for the control signal;

(e) determining a value, X_a, of the control signal actually used by the actuator during the time interval, Δ

t;

(f) using the model, determining a computed value for the output, O_c, as a function of the value of the control signal determined in step (e); and

(g) reiteratively repeating steps (b) through (f), each successive iteration using values for the state variables in the model that depend on the computed value of the output determined in step (f) of the previous iteration, so that control of the process tracks changes in the specified output and the process quickly converges on the specified output.

2. The method of claim 1, wherein the step of interpolating comprises the steps of:

(a) determining the difference between the second and first control signals, X₂ -X₁ ;

(b) determining the difference between the second and first corresponding output values, O₂ -O₁ ;

(c) determining a slope of a line through a data pair (O₁, X₁) and a data pair (O₂, X₂), from the relationship;

space="preserve" listing-type="equation">slope=(O.sub.2 -O.sub.1)/(X.sub.2 -X.sub.1); and

(d) determining the desired control signal, X_d, as a function of the specified output, O_s, from the relationship;

space="preserve" listing-type="equation">X.sub.d =(O.sub.s -(O.sub.1 -slope*X.sub.1))/slope.

3. The method of claim 1, wherein the process includes constraints on the values of the control signal that can be used by the actuator, and wherein the step of operating the process for the predetermined time interval includes the step of using a value for the control signal that approximates the desired value of the control signal as closely as the constraints allow.

4. The method of claim 3, wherein the constraints comprise limits on the maximum and minimum values of the control signal.

5. The method of claim 3, wherein the constraints comprise limits on the usable resolution for the values of the signal parameters.

6. The method of claim 3, wherein the actual control signal used may be substantially unequal to the desired control signal X_d for one or more time intervals due to an actuator fault, said step of determining the control signal actually used by the actuator including the step of computing a change in the output during a total accumulated time that the actuator fault continues, so that upon correction of the actuator fault, the step of determining the desired value of the control signal compensates for the total time in which the actuator was not responding to the desired control signal.

7. The method of claim 1, wherein the model is linear with respect to successive data pairs, each data pair comprising a control signal and a corresponding process output.

8. The method of claim 1, wherein the time interval is of a predetermined length unless an event is detected that alters the operation of the process or the specified output, causing the time interval to terminate prematurely.

9. A method for controlling the concentration of a drug administered intravenously at a controlled rate to a recipient to achieve a specified plasma drug concentration, wherein a linear pharmacokinetic model is used that predicts the plasma drug concentration as a function of the rate administered and as a function of a plurality of state variables and other parameters that define the current concentration of the drug in the recipient'"'"'s body, said method comprising the steps of:

(a) arbitrarily selecting a first and a second rate for administering the drug during an interval of time;

(b) using the model, determining a first and a second plasma drug concentration corresponding respectively to the first and second rates, if said rates were used during the interval of time;

(c) from the first and second rates and the first and second plasma drug concentrations, determining an interpolated drug delivery rate that should produce the specified plasma drug concentration of the drug in the recipient at the end of the interval of time;

(d) delivering the drug to the recipient nominally at the interpolated rate for the interval of time;

(e) determining an actual rate at which the drug is being delivered to the recipient;

(f) using the model, determining a computed plasma drug concentration that corresponds to the actual rate and setting the plurality of state variables as a function of the computed plasma drug concentration; and

(g) reiteratively repeating steps (b) through (f) for successive intervals of time, each iteration determining the interpolated rate using the model, wherein the plurality of state variables for that iteration depend on the computed plasma drug concentration from the previous iteration, thus compensating for any substantial variation between the interpolated rate of delivery and the actual rate, whereby the rate of delivery of the drug is controlled so that the specified plasma drug concentration is rapidly achieved.

10. The method of claim 9, wherein the drug is delivered to the recipient by an infusion device, said infustion device being operable to deliver the drug only at specific incremental rates, said step of delivering the drug at the interpolated rate comprising the step of delivering the drug at one of the specific incremental rates that is closest to the interpolated rate.

11. The method of claim 10, wherein the step of determining the actual rate includes the step of determining said one specific incremental rate used to deliver the drug.

12. The method of claim 10, wherein the step of determining the actual rate includes the step of determining if the drug was not delivered to the recipient by detecting a fault in the infusion device.

13. The method of claim 10, wherein the step of determining the actual rate includes the step of determining if the drug was not delivered to the recipient by detecting an occlusion in a line through which the drug is delivered to the recipient from the infusion device.

14. The method of claim 13, wherein the step of determining the interpolated rate compensates for non-delivery of the drug to the recipient for successive intervals of time, when delivery of the drug is again resumed, because the plurality of state variables changes as the computed plasma drug concentration changes during the time that the drug is not delivered to the recipient.

15. The method of claim 9, wherein the interval of time is of a predetermined duration, subject to a premature termination in response to the occurrence of a specified event affecting the actual drug delivery rate.

16. Apparatus for controlling a process to obtain a specified output, O_s, where the process is described by a model that defines an output of the process as a function of a specified control signal and wherein the process is affected by an actuator in response to the control signal, said apparatus comprising:

(a) processor means for;

(i) arbitrarily selecting a first value, X₁, and a second value, X₂, for the control signal that could be applied to control the actuator for a time interval, Δ

t;

(ii) initializing a plurality of state variables used in the model;

(iii) as a function of the first and second values of the control signal, which are input to the model, respectively determining first and second output values, O₁ and O₂ ; and

(iv) interpolating with respect to the first and second values of the control signal and corresponding first and second output values to determine a desired value, X_d, for the control signal that should produce the specified output at the end of the time interval;

(b) means for determining successive time intervals and producing time signals indicative of each of said time intervals;

(c) said processor means being connected to receive said time signals and being further operative to operate the process using a closest available control signal to the desired value X_d ; and

(d) means for determining an actual value of the control signal implemented during operation of the actuator during the interval of time;

said processor means being further operative to determine a computed value, O_c, for the output of the process as a function of the actual value, X_a, of the control signal, and to repetitively and reiteratively determine the desired value, X_d, for successive intervals of time, using values for the plurality of state variables in the model that depend on the computed value of the output determined in a preceding iteration, so that the process rapidly converges on the specified output.

17. The apparatus of claim 16, wherein the processor means comprise a microprocessor and a nonvolatile electronic memory in which is stored a program directing the operation of the microprocessor.

18. The apparatus of claim 16, wherein the means for determining an actual value of the control signal comprise means for determining that the actuator was interrupted during one or more of the time intervals, preventing the specified value of the output from being realized.

19. The apparatus of claim 16, wherein the process or means interpolate by:

(a) determining the difference between the second and first control signals, X₂ -X₁ ;

(b) determining the difference between the second and first corresponding output values, O₂ -O₁ ;

(c) determining the slope of a line through a data pair (O₁, X₁) and a data pair (O₂, X₂), from the relationship;

space="preserve" listing-type="equation">slope=(O.sub.2 -O.sub.1)/(X.sub.2 -X.sub.1); and

(d) determining the desired control signal, X_d, as a function of the specified output, O_s, from the relationship;

space="preserve" listing-type="equation">X.sub.d =(O.sub.s -(O.sub.1 -slope*X.sub.1))/slope.

20. Apparatus for controlling the intravenous administration of a drug to a recipient at a controlled rate to achieve a specified plasma drug concentration, wherein a linear model is used that determines the plasma drug concentration as a function of the rate at which it is administered and as a function of a plurality of state variables and other parameters that define the current concentration of the drug in the recipient'"'"'s body, said apparatus comprising:

(a) processor means, for;

(i) selecting a first and a second arbitrary rate for administering the drug during a time interval Δ

t;

(ii) using the model, determining a first and a second plasma drug concentration that corresponds to the first and second arbitrary rates for administering the drug; and

(iii) based on the first and second arbitrary rates and corresponding first and second plasma drug concentrations, determining an interpolated drug delivery rate that should produce the specified plasma drug concentration of the drug in the recipient at the end of the time interval;

(b) infusion means, connected to the processor means, for delivering the drug to the recipient nominally at the interpolated rate;

(c) timer means for determining successive intervals of time, said timer means producing time signals that indicate the duration of each time interval; and

(d) means for determining an actual rate at which the drug is administered to the recipient by the infusion means;

said processor means being further operative to apply the model to determine a computed plasma drug concentration that corresponds to the actual rate during a current time interval, where the plurality of state variables used in the model vary as a function of the computed plasma drug concentration from prior time intervals, and being still further operative to determine an interpolated drug delivery rate and a computed plasma drug concentration using the model, for successive intervals of time, and thereby controlling the infusion means to operate substantially at the interpolated drug delivery rate so that the computed blood plasma concentration rapidly approaches the specified plasma drug concentration.

21. The apparatus of claim 20, wherein the means for determining the actual rate at which the drug is administered comprise an occlusion detector to detect if an occlusion of a delivery line connecting the infusion means to the recipient has prevented the drug from being delivered to the recipient.

22. The apparatus of claim 20, wherein the means for determining the actual rate at which the drug is administered comprise a fault detector that can detect a failure in the infusion means, which prevents the drug from being delivered to the recipient.