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

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.

Apparatus for controlling a process to obtain a specified output, O.sub.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, X.sub.1, and a second value, X.sub.2, for the control signal that could be applied to control the actuator for a time interval, .DELTA.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, O.sub.1 and O.sub.2 ;
• 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.sub.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.sub.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.sub.c, for the output of the process as a function of the actual value, X.sub.a, of the control signal, and to repetitively and reiteratively determine the desired value, X.sub.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.

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 .DELTA.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.