Method and apparatus for automatic dissolution testing of products

A method and apparatus for optimally performing dissolution testing of pharmaceutical dosage forms, agricultural products, and components of industrial products wherein the method uses dissolution profiles from a known drug dosage form, or product, as reference data for a predictive process; and the apparatus is organized to carry out the method via both closed loop and open loop operating modes under the control of a central processor. An illustrative embodiment teaches the serial usage of the two operating modes in a single flow-through dissolution cell configuration to optimally predict the time course of in vivo bioavailability from in vitro dissolution measurements, while an alternate embodiment teaches the use of a plurality of dissolution cells and the simultaneous use of the closed and open loop operating modes to implement an Internal Standard capability. Additionally, an optimally adaptive capability is provided in the dissolution testing process via a random input modeling mode of operation.

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
The present invention relates generally to the field of automatic 
dissolution testing of products whose solubility and dissolution rate 
properties affect product performance, and more specifically to the 
optimal prediction of product dissolution characteristics using known 
product data as a reference for a feedback controlled apparatus. 
The methods disclosed and the electronically controlled apparatus described 
are presented in connected with in vitro dissolution testing of 
pharmaceutical drug dosage forms to predict in vivo bioavailability. 
However, both the methods and apparatus taught are equally applicable to 
dissolution testing of agricultural products formulated as controlled 
release herbicides, insecticides, fertilizers, and the like; and are 
further applicable to the dissolution testing of components of industrial 
products including solid materials whose solubility properties depend on a 
wide variety of factors. 
2. Description of the Prior Art 
Dissolution testing of components of industrial products whose solubility 
and dissolution rate properties affect product performance can be used as 
a screening and quality control tool. The solubility properties of solid 
materials can depend on polymorphic crystalline form, crystal habit, 
crystal shape, particle size and particle size distribution, and state of 
solvation. A simple and rapidly performed dissolution test can substitute 
for the determination of these physical properties by more time consuming 
and expensive methods such as x-ray crystallography, differential thermal 
analysis, microscopy, etc. The materials are instead determined as to 
whether they conform to a dissolution rate standard under specified 
conditions and in relation to a known reference sample of the same 
material characterized by the above physical properties and possessing the 
desired dissolution rate and solubility characteristics. 
The broad technique of determining dissolution rate properties is 
especially of interest in the testing of drug products where the 
therapeutic performance of drugs is closely related to the drug 
dissolution properties. Seemingly minor changes in drug product 
formulation, as well as the inadvertent variation in materials and 
manufacture that can occur between batches of the same product 
formulation, can influence the therapeutic performance of drugs. In vivo 
bioavailability testing of drug products in humans provides the most 
reliable means of ensuring bioequivalence. However, it is impractical to 
perform the extensive and expensive human testing that would be routinely 
required. Large numbers of human subjects would be placed at risk if such 
studies were conducted. Bioavailability testing in which humans are used 
as test subjects can be minimized by the development and implementation of 
in vitro dissolution standards that reflect in vivo drug-product 
performance. In vitro bioequivalence requirements have been established 
for some drugs such as digoxin. From among the various chemical and 
physical tests that can be performed on drug solids in vitro for 
correlating or predicting a drug product's in vivo bioavailability 
behavior, dissolution testing is the most sensitive and reliable. The 
correlative relationships most commonly reported between the vitro 
dissolution and in vivo bioavailability are of the single-point type: the 
percentage of the drug dissolved in a given time (or the time it takes to 
dissolve a given percentage of the drug in vitro) and some univariate 
characteristic of the drug product's in vivo response versus time profile 
(such as the peak blood level, the time required to reach the peak or 50% 
of the peak, or the area under the blood-level curves) are correlated. The 
selection of in vitro dissolution and in vivo bioavailability parameters 
for such single-point correlations is frequently arbitrary, and the 
results can be misleading. Obviously, it would be preferable to predict 
the entire average blood level, urinary recovery rate, 
pharmacological-response-time, or drug absorption rate vs. time profile 
that would be elicited by a drug product in a panel of human subjects 
rather than merely to correlate univariate characteristics of the 
dissolution profile with an in vivo bioavailability parameter. In all 
cases, however, the fidelity of the in vitro dissolution results in 
correlating and in predicting in vivo drug-product bioavailability depends 
upon the dissolution-test process variables, such as the 
dissolution-medium composition, the solubility volume of the medium (sink 
conditions that determine the extent to which the medium becomes saturated 
with the drug), and the agitation rates (stirring or flow rates). An 
improper choice of these process variables (e.g., an excessively high rate 
of agitation) can mask significant bioavailability differences among drug 
products. On the other hand, the dissolution test can be overly sensitive 
in detecting differences that are negligible in vivo. In the former case, 
using such improper dissolution-test parameters would result in the 
marketing of therapeutically ineffective drug products. In the latter 
case, the result would be the discarding of drug products that are 
entirely satisfactory in terms of in vivo performance. Serious economic 
losses could result from the use of an overly sensitive in vitro 
dissolution test for lot-to-lot reproducibility testing of drug products. 
Therefore, whether the dissolution test is being used as a quality control 
tool, as an in vivo bioequivalency requirement for multisource generic 
drug products, or as a substitute for human bioavailability testing during 
the development of new drug-product formulations, it is imperative that 
the dissolution test provide predictive results that are biologically 
relevant. 
Developing drug-product dissolution tests that predict the time course of 
drug-product bioavailability can be fraught with pitfalls, some of which 
may be avoided through knowledge and consideration of the physiochemical 
properties of the components of the drug product and the biological 
processes and conditions operative in the release of the drug from the 
gastrointestinal tract and its subsequent absorption. However, it is not 
only futile, but also unnecessary to attempt to reproduce the complex of 
biological factors operating in vivo in the effort to develop a 
satisfactory in vitro bioavailability test, although such attempts have 
been made. The devices that resulted from these efforts are of value now 
only as museum pieces. It would, however, be imprudent to ignore such 
knowledge when it can be used advantageously to circumvent a problem in 
the design of a dissolution test. 
There are two possible general approaches to developing in vivo relevant 
drug product dissolution tests. Both approaches seek to predict the entire 
time course of average blood levels that would be observed for a drug 
product in a panel of human test subjects. In this way, the dissolution 
test serves as a substitute for human testing. 
The first approach is a computational method that maximizes the amount of 
information that can be obtained from conventional methods of in vitro 
dissolution testing. Used most frequently are the USP rotating-basket 
apparatus, the FDA paddle method, the stationary-basket/rotating filter 
apparatus, Sartorious solubility and absorption simulators (Sartorius, 
Incorporated, Hayward, Calif.), and column-type flow-through assemblies. 
The last of these devices offers advantages with regard to the definition, 
flexibility of control, standardization, and reproducibility of process 
variables. This apparatus has been used by the inventor of the present 
invention to demonstrate the second approach to predicting in vivo 
blood-level curves that emerge from the apparatus in the form of 
dissolution rate versus time profiles. 
Since the computational approach with conventional apparatus depends upon 
the relatively arbitrary selection of process variables, its usefulness is 
limited. However, using feedback control to continuously vary the process 
variables, as described below, obviates this problem. For a more complete 
treatment of the mathematical (and theoretical) aspects of the 
dissolution, the interested reader is directed to three papers co-authored 
by the inventor. These are: V. F. Smolen et al., "Optimally Predictive In 
Vitro Drug Dissolution Testing for In Vivo Bioavailability," J. 
Pharmaceutical Sci., Vol. 65, No. 12, pp. 1718-1724, December 1976; V. F. 
Smolen et al., "Predicting the Time Course of In Vivo Bioavailability From 
In Vitro Dissolution Tests: Control Systems Engineering Approaches," 
Pharmaceutical Technology, pp. 89-102, June 1979; and V. F. Smolen et al., 
"Predictive Conversion of In-Vivo Drug Dissolution Data into In Vivo Drug 
Response Versus Time Profiles Exemplified for Warfarin," J. Pharmaceutical 
Sci., Vol. 66, No. 3, pp. 297-304, March 1977. 
The present invention is directed to an improved method and apparatus for 
carrying out the dissolution approach to optimally predicting in vivo drug 
bioavailability from pharmaceutical dosage forms, and other applications 
of dissolution testing. 
SUMMARY OF THE INVENTION 
It is therefore a primary object of the present invention to provide 
improved methods and apparatus for performing dissolution testing of 
pharmaceutical dosage forms, agricultural products, and components of 
industrial products whose solubility and dissolution rate properties 
affect product performance. 
Another object of the present invention is to provide improved methods and 
apparatus for predicting in vivo bioavailability of drug dosage forms from 
in vitro dissolution testing. 
Another object of the present invention is to provide methods and apparatus 
for dissolution testing of industrial products, including drug dosage 
forms, agricultural products, and the like, wherein a closed loop control 
process is first used to initialize the control loop process variables 
while operating on known reference data, and an open loop control process 
is then used to perform the predictive process using the process variables 
previously derived. 
Another object of the present invention is to provide methods and apparatus 
for dissolution testing of a plurality of industrial products, including 
drug dosage forms, agricultural products, and the like, simultaneously, 
using an operating mode wherein closed loop and open loop control 
processes are accomplished concurrently using a known product formulation 
and its corresponding dissolution profile as reference data, to implement 
an Internal Standard operating mode. 
A still further object of the present invention is to provide an improved 
dissolution testing apparatus including a dissolution cell having 
proportional agitation means and to further provide an optimally adaptive 
capability into the dissolution testing process via a random input 
modeling mode of operation.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
Referring now to FIG. 1, there is shown an overall block diagram of the 
automatic flow-through dissolution testing system according to the present 
invention. For simplicity of exposition the various elements are not shown 
to scale, and the embodiment shown is a basic one. The descriptions 
throughout this specification are expressed in terms of the testing of a 
pharmaceutical drug dosage form, and the language is accordingly specific 
to this usage. Of course, the embodiments disclosed are illustrative and 
could readily be adapted for use with agricultural products, or with 
controlled release components of industrial products generally. The 
overall system 10 is shown as comprised of a basic dissolution cell 12 in 
which is positioned a specimen of the drug product 14 undergoing 
evaluation. The cell 12 has a filter membrane 12A and filter screen 12B, 
and is provided with a flow of various dissolution liquid via a cell input 
line 16 under the influence of a primary pump 18. Output from the 
dissolution cell 12 is carried by a cell output line 20 and is routed 
first via the upper portion of a recirculation line 22, and thereafter via 
a system output line 24. Within the recirculation line 22 is a 
recirculation pump 26 which propels the liquid therein into the lower 
portion of the recirculation line 22, and thereafter into a feeder line 
28, which serves as an input to the primary pump 18. The two arrows 30A 
and 30B show the direction of flow in the recirculation line 22 under the 
influence of the recirculating pump 26. 
A first reservoir 32 is used to contain a supply of a first dissolution 
medium 34, which is fed via a line 36 to the dissolution cell 12. The 
first dissolution medium 34, hereinafter alternately called the acid 
medium, if fed to the feeder line 28 under the influence of a pump 38. The 
flow direction of the acid medium 34 is shown by the flow arrows 40A and 
40B. A second reservoir 42 is used to contain a supply of a second 
dissolution medium 44, hereinafter alternately called the alkaline medium 
44. The alkaline medium 44 is fed via a line 46 and a check valve 48 to 
the feeder line 28, and subsequently through the primary pump 28 to the 
dissolution cell 12. The flow direction of the alkaline medium 44 is shown 
by the flow arrows 50A and 50B. As will be discussed in detail below, the 
flow path 40B of the acid medium 34 is due to the presence of the check 
valve 48, and the flow path 50B of the alkaline medium 44 is due to the 
dynamics of the action of the two pumps 38 and 18. 
The system output line 24 serves to conduct the flow of the processed media 
containing the desired concentration of the dissolved drug product out of 
the system, and further supports two key system measurements. A flow 
measurement device 52, serially positioned in the output line 24, provides 
a quantitative measurement of a liquid flow rate via a group of lines 54 
to a central processor 56. (Alternatively, this flow rate may be obtained 
electronically as the difference in control signals to the primary pump 18 
and the recycle pump 26.) A spectrophotometer 58, also serially positioned 
in the output line 24, provides a periodic (or continuous) measurement of 
the drug concentration in the output flow, and routes this measurement via 
a group of lines 60 to the central processor 56. Pumps 18, 26 and 38 are 
of the positive displacement peristaltic type and are capable of producing 
precisely controlled flow rates in the range of 0.2 to 140 ml per minute 
when properly controlled. The central processor 56 provides this control 
via signals on three groups of lines 62, 64 and 66 which modulate the 
excitation to the pumps as follows. Control signals on the line 62 are 
applied to a pump speed modulator 68, which in turn controls the 
excitation of the pump 26 via the lines 70; control signals on the lines 
64 are applied to a pump speed modulator 72, which in turn controls the 
excitation of the pump 18 via the lines 74; the control signals on the 
line 68 are applied to a pump speed modulator 76, which in turn controls 
the excitation to the pump 38 via the lines 78. In addition to the above 
three control signals, the central processor 56 further provides control 
signals to an agitation means comprised of a stirring paddle 80 located 
within the dissolution cell 12 and positioned below the filter screen 12B. 
These control signals are provided on a group of lines 82 to an interface 
device 84. An output from the interface device 84 is applied via lines 86 
to an agitation motor 88, which in turn activates the stirring paddle 80 
via the mechanical linkage shown as dashed lines 90. A group of control 
and data lines 92 interconnect the central processor 56 with a number of 
supporting units shown as a peripherals group 94. Included within this 
group 94 would be a data recorder 94A (analog and/or digital), an output 
printer 94B, and input keyboard 94C, and other well known and conventional 
devices. An overall measurement block 96 identifies those elements 
considered to be measurement apparatus, as compared to the remaining 
elements--56 and 94--which may be considered to be the signal processing 
and control portions of the system. 
In use, the system of FIG. 1 carries out the dissolution testing under the 
control of the central processor 56 as follows. By way of a brief 
overview, the system shown is operable in two modes, the first being a 
simulative (or closed loop mode) and the second being a predictive (or 
open loop mode). First, a known drug dosage form is used to "calibrate" 
the apparatus by operating it in the closed loop mode using known in vivo 
data (as played back from the recorder 94A) on the particular drug dosage 
form to optimize a number of parameters (hereinafter alternately referred 
to as the process variables) within the central processor 56. An iterative 
optimizing process may be used to systematically modify the process 
variables until the difference between the measured (in vitro) data and 
the known (in vivo) data are minimized, and independent of time. Secondly, 
predictive tests of unknown drug dosage forms are performed using open 
loop control of the apparatus employing the previously determined values 
of the process variables. To accomplish these steps, control 
(proportional, differential and integral) is exercised over one or more of 
the process variables determined by: (1) the composition; (2) the recycle 
flow of the dissolution medium; (3) the total flow rate of the dissolution 
medium; and (4) the rate of agitation within the dissolution cell. 
During the course of the closed loop phase of the operation, a change in 
the medium pH can be used to simulate the in vivo change from the stomach 
to the duodenum, and the recycling of the medium to dissolution cell 12 
allows variable sink conditions to be achieved to simulate the existing in 
vivo conditions due to differing barrier properties of drug absorbing 
biological membranes. Resistance to biological absorption is simulated by 
mixing the fresh medium with the solution leaving the cell. The recycling 
of solution through the dissolution cell in this manner decreases the 
driving force for dissolution. Upon establishing a desired constant flow 
rate at the outlet of the dissolution cell as determined by the flow 
measuring device 52, the time varying recycle flow rate and a changing 
flow from the gastric and intestinal juice reservoirs (i.e., first and 
second dissolution medium 34 and 44) are initiated. The spectrophotometer 
58 provides a measurement of the concentration of the drug in the liquid 
leaving the cell. An alternate configuration may include placing the 
spectrophotometer on the recycle flow line. This measured concentration 
value is compared within the central processor 56 with the known in vivo 
bioavailability rate, blood level, urinary recovery rate, or 
pharmacological response versus time profiles being simulated. Any error 
signal produced is converted within the central processor 56 so as to 
optimize the process variables driving the error signal to a minimum 
value. 
A detailed description of the operation of this system of FIG. 1 is 
facilitated with additional reference to the block diagrams of FIGS. 2 and 
3. Additionally, an illustrative hardware configuration is described in 
connection with the improved control system shown in FIG. 5. FIG. 2 shows 
a block diagram for the closed loop control of the dissolution testing 
system in the simulative mode; while FIG. 3 shows a block diagram for open 
loop control of the dissolution testing system in the predictive mode. 
Both the time variable form: R(t), and the transform variable form: R(s) 
of the system parameters will be used herein (interchangeably as required) 
as is well known in the control system art. The following process 
variables are applicable: 
Q(t)=volumetric flow rate (milliliters per minute) 
Q.sub.A =Q/A.sub.C =velocity through the cell (centimeters per minute) 
A.sub.C =cross-sectional area of the cell (square centimeters) 
R(t)=volumetric flow of recycle (milliliters per minute); i.e., it can be a 
constant or time-varying quantity 
M(t)=stirring rate within one dissolution chamber 
F.sub.1 (t)=fraction of the solvent which is drawn from the reservoir 
containing, for example, simulated gastric juice, water, or an organic 
solvent (34 of FIG. 1) 
F.sub.2 (t)=fraction of one solvent which is drawn from the reservoir 
containing, for example, simulated intestinal juice, 1.0 normal sodium 
hydroxide, or an organic solvent (44 of FIG. 1). 
The dissolution process extant within the system of FIG. 1 may commonly be 
described by a simple diffusion layer model: 
EQU dw/dt=DS/T(C.sub.s -C) 
where 
dw/dt=dissolution rate (milligrams per minute) 
D=diffusion coefficient for the solvent and solute under consideration 
(square centimeters per minute)--affected by dissolution media composition 
S=surface area for dissolution (square centimeters)--an intrinsic property 
of the material (dosage form) being tested 
C.sub.s =concentration of solute required to saturate the solvent 
(milligrams per milliliter)--affected by dissolution media composition 
C=actual solute concentration in solution (milligrams per 
milliliter)--affected by recycle flow and total volume flow 
T=effective thickness of the film or diffusion layer 
(centimeters)--affected by agitation rate and total volume flow rate. 
The relationship between variables in the diffusion layer equation and the 
process variables are seen as given for a fixed value of A.sub.C : 
T=a function of Q and agitation rate 
C=a function of the volume of the dissolution chamber, V, and the 
volumetric flow rate, Q, i.e., the residence time, V/Q, and the flow of 
recycle, R or R(t). To avoid changing the volume of the dissolution 
chamber by changing its length to change C, this could also be effected by 
changing the recycle flow 
C.sub.s =a function of the properties of the solvent. For example, using 
simulated gastric and intestinal juices mentioned previously, the process 
variables to be manipulated here are F.sub.1 and F.sub.2. The variables D 
and C.sub.s are obviously affected by the solvents used and the relative 
proportions of each composing the dissolution medium at any time. When the 
solvent mixture is specified, D and C.sub.s are also reflective of the 
properties of the solid being dissolved. 
S=in addition to being a function of Q, a function of the initial amount of 
drug, m.sub.o, and the physical properties of the solid. Once these 
variables are fixed, i.e., once a drug and a dosage form are decided upon, 
the time course of S as the experiment proceeds is reflective of the 
properties of the drug products. 
Referring first to FIG. 2, closed loop operation (simulative) in its basic 
form is shown as having an input signal A(s)--cumulative in vivo 
availability--applied to an input node where it is differenced with a fed 
back signal C(s)--concentration of the stream leaving the dissolution 
cell--to produce an error signal E(s). The error signal E(s) is applied to 
the input of a proportional-integral-derivative (PID) controller (actually 
to each of four controllers as detailed in connection with FIG. 5) having 
the gain characteristic (alternatively transfer function) G.sub.c (s). The 
output from the PID controller is a signal m(s) suitable to operate the 
respective actuator in the system. The four actuators of FIG. 1 include 
three proportional controlled pumps and one proportional controlled motor. 
These actuators are represented simply as having a particular transfer 
function G.sub.p/m (s), whose outputs are characterized by the four 
process variables R(s), M(s), Q(s), and F.sub.1 (s)--all as described 
below. The process variables are applied to the dissolution equipment 
having a transfer function G.sub.DE (s) whose output is the desired 
parameter C(s) or Q.sub.s (s).multidot.C(s)--as described below. Briefly, 
FIG. 2 depicts in conventional analog-like terms the simulative function 
of the dissolution testing system. The analog-like descriptive terminology 
is used for simplicity and, of course, digital embodiments may be used to 
implement the control loop contemplated. During this closed loop 
(simulative, or calibration run) operation, three key parameters within 
the PID controller are optimized as described below such that subsequent 
open loop operation as shown in FIG. 3 constitutes an optimally predictive 
operating mode. As shown in FIG. 3, the open loop control system block 
provides optimized values of M(t), R(t), F.sub.1 (t) and Q(t) to the 
actuators (servo driven pumps, and/or motors) which in turn impact on the 
dissolution cell to produce the desired output C(t) or Q.sub.s 
(t).multidot.C(t) as above described. 
The objective of the system of FIG. 1 is to obtain results that uniformly 
reflect the in vivo drug availability with optimal fidelity over time and 
varying drug release behavior of the dosage forms. For any given set of 
process variables, i.e., Q.sub.A, F.sub.1, (F.sub.2 =1-F.sub.1), the 
closed loop operation of the in vitro testing apparatus will produce a 
function Q.sub.s,i (t)C.sub.i (t) for each ith dosage so that the 
expression [A.sub.i (t)-[Q(t)-R.sub.i (t)]C(t)] or [A.sub.i (t)-C(t)] 
closely approximates zero. Functions R.sub.i (t), M.sub.i (t), Q.sub.i (t) 
and F.sub.1i (t) will be obtained for each dosage form of the drug tested 
that was chosen to possess different drug release dynamics. These 
functions can be read out by the central processor 56 onto magnetic tape, 
stored on magnetic disc, or in the central memory of the microprocessor 
during the closed loop operation of the apparatus. 
At this stage, the apparatus merely simulates the A(t) functions determined 
from in vivo experimentation. Analog R.sub.i (t) function signals recorded 
on magnetic tape for each dosage form can be conveniently processed on the 
central processor 56 and their values can be averaged, over dosage forms, 
at each time to obtain an average, R(t) function representing the mean 
behavior of all dosage forms included in the closed loop operations. A 
second set of open loop runs must then be performed for each dosage form 
with the R(t), M(t), F.sub.1 (t), and Q(t) functions programmed to control 
the process variables. The number of closed loop runs performed on 
different dosage forms of the same drug and the resulting number of 
C.sub.i (t) functions and the corresponding number of R.sub.i (t), M.sub.i 
(t), Q.sub.i (t) and F.sub.1i (t) process variables included in the R(t), 
M(t), Q(t) and F.sub.1 (t) functions will depend on the properties of any 
specific drug and the drug release characteristics of the dosage forms 
being tested. If the dynamics of the in vivo and in vitro system 
approximate linear behavior, then only one reference dosage form is 
required. When appropriate, an objective function F.sub.o can be formed 
from the M(t), F.sub.1 (t), Q(t), R(t), C.sub.i (t) and A(t) functions. A 
minimal value of the objective function is achieved by systematically 
selecting different solvents, geometries of the agitator, or if one or 
more process variables are kept constant, different fixed values of the 
process variables not allowed to continuously vary with time. A minimum 
value of the objective function corresponds to optimal open loop operation 
of the apparatus under such conditions. As mentioned, various means can be 
implemented to control the recycle flow dynamics. 
The system of FIG. 1 should be operated in the simplest manner that 
provides acceptable in vitro results with regard to in vivo drug 
availability behavior. To determine the magnitude of sensitivity of the 
fidelity of the test to different operating conditions, the test can be 
initially performed in successive phases of increasing complexity and 
equipment requirements. 
Phase I can be performed without any automatic control, using fixed, time 
invariant, values of the process variables, M, F.sub.1, Q, and R. An 
optimal composition and pH of the dissolution medium may be found and 
thereafter maintained constant. 
Phase II can be performed similarly to Phase I but with the inclusion of 
automatic control of M(t) as a process variable. 
Phase III can employ automatic computer control of a time-varying 
dissolution media composition F.sub.1 (t) in addition to M(t). 
Phase IV can add R(t) as an automatically controlled process variable. 
Phase V can utilize M(t), F.sub.1 (t), R(t) and Q(t) as automatically 
controlled process variables. 
The order in which automatic control of the process variables is introduced 
depends on the properties of the drug, e.g., such as its solubility and 
intrinsic dissolution rate in different solvents. 
These submodes of operation can be repeated for different dosage forms of 
the same drug to obtain the optimal conditions over all reference dosage 
forms. The simplest mode of operation possessing an acceptable fidelity 
would then be chosen for future studies with the drug. 
For a somewhat more comprehensive description of the mathematical factors 
involved in the above, the interested reader is referred to the 
aforementioned 1976 article authored by the inventor. A more theoretical 
treatment of the relationship summarized above is also contained in an 
additional paper--V.F.Smolen, "Theoretical and Computational Basis for 
Drug Bioavailability Determinations Using Pharmacological Data II Drug 
Input .revreaction. Response Relationships,"J. Pharmacokinetics and 
Biopharmaceutics, Vol. 4, No. 4, pp. 355-375, 1976. 
Referring to FIG. 4, there is shown an overall block diagram of an 
alternate embodiment of the present invention directed to producing the 
desired predictive dissolution profile action in an Internal Standard 
operating mode. The embodiment shown is particularly advantageous in the 
testing of a number of drug dosage forms simultaneously--by comparison to 
a reference drug dosage form--and may be used for simultaneously testing 
large batches of a single drug dosage form, or of simultaneously 
evaluating a number of different drug dosage forms. The apparatus is 
basically a parallel arrangement of a plurality of single flow-through 
dissolution systems as shown in FIG. 1, using a single central 
processor/peripheral for control. The Internal Standard system 100 is 
shown as comprised of the elements of the embodiment of FIG. 1, in the 
form of a central processor 56 interconnected with a peripherals group 94 
via a group of lines 92. A trunk of input/output lines 102 from the 
central processor 56 are routed to a reference dissolution testing 
subsystem 10R, via a group of input/output lines 102R; and to a first 
unknown dissolution testing subsystem 10A via a group of output lines 
102A; and further to an " Nth" unknown dissolution testing subsystem 10N 
via a group of output lines 102N. The number of independent dissolution 
subsystems may be fairly large--a dozen, or more--being limited by purely 
perfunctory considerations such as cost and convenience in usage. With 
continued reference to FIG. 4 and occasional reference to FIG. 1, the 
subsystems 10R, 10A, 10N (of FIG. 4) may be identical to the measurement 
block 96 (of FIG. 1). The subsystem 10R, in combination with the central 
processor 56, the peripherals groups 94 and the interconnecting lines 92, 
102 and 102R constitute a dissolution testing system identical to that of 
FIG. 1, operating in the closed loop mode of operation as previously 
described. The subsystems 10A-10N function in the open loop mode as 
previously described. The primary operating difference is that the N 
subsystems containing an unknown drug dosage form and operating open loop 
are controlled simultaneously by the identical control signals being 
generated by the control processor 56 responsive to the output 
measurements made on the reference dissolution cell, as compared to the 
reference drug in vivo dissolution profile. Thus, the in vivo dissolution 
profile being outputted by the recorder 94A as a time series of known 
data, in combination with a time series of control signal values produced 
by the central processor 56 serves as an Internal Standard in the sense 
that the predictive profiles are produced in the open loop mode by signals 
which are simultaneously being produced by closed loop mode of operation 
using a reference drug and data as the basis. A cursory review of the 
operation of the basic embodiment of FIG. 1, as compared with that of FIG. 
4, will reconfirm that only comparatively minor differences in operation 
of the subsystems are involved. For example, the subsystems 10A-10N have 
no need to perform the measurement of flow rate and drug concentration in 
their output lines. Only the subsystem 10R requires that information. In 
the interest of the uniformity of apparatus, and as a means of providing 
additional versatility to the Internal Standard system 100, any or all of 
the subsystems 10A-10N may include the components required to measure 
these output parameters and provide related signals to the central 
processor 56. In this latter case, the central processor 56 is merely 
instructed to ignore the specific output data produced by those particular 
subsystems which are to be operated open loop. 
Summarizing, the Internal Standard embodiment of FIG. 4 includes the signal 
processing elements (the central processor 56 and peripherals group 94) of 
FIG. 1 as described in more concrete terms in connection with the 
embodiment of FIG. 55, along with a plurality of the measuring blocks 96 
of FIG. 1. Of the number of measuring blocks, one (subsystem 10R) serves 
as a reference subsystem and operates in a closed loop mode as described 
in connection with FIG. 2 with the signal processing elements, while the 
remainder (subsystems 10A to 10N) are controlled by the signal processing 
elements in the open loop mode as described in connection with FIG. 3. 
Thus, the plurality of subsystems 10A-10N each produce a predictive 
dissolution profile of a separate drug dosage form while all are 
referenced to a single reference drug dosage form. 
Referring now to FIG. 5, there is shown a block diagram of an improved 
control system for use with the dissolution testing system 10. The 
improved control system 200 inserts an optimally adaptive capability into 
the dissolution testing process via a random input modeling (RIM) mode of 
operation. Briefly, this mode impacts on operation in the closed loop mode 
wherein the average in vivo human drug response profile input, A(t), for a 
reference drug product is reproduced as the concentration vs. time 
profile, C(t), output from the apparatus through feedback control of one 
or more of the process variables controlling the conditions of the 
dissolution testing. Random input modeling is performed to tune a PID 
controller for each process variable and accomplish on-line, optimally 
adaptive control. These process variables may include the composition 
(e.g., pH) of the dissolution medium; agitation via stirring paddles; 
agitation via primary flow rate; and/or sink conditions in the form of 
recycle flow of medium back into the dissolution cell. 
The improved control system 200 may be considered as as expanded version of 
the closed loop control system shown in more generalized form in FIG. 2. 
In FIG. 5, the improved control system 200 is shown as a four channel 
device wherein each channel corresponds to a particular process variable 
to be optimized. Thus, four proportional-integral-derivative (PID) 
controllers 202, 204, 206 and 208 have as their common inputs an error 
signal E(t) derived as the difference between the input signal A(t) and 
the output signal C(t). Each PID controller also has an individual set of 
adjust lines taken from the group of parameter adjust lines 210. While the 
improved control system 200 is clearly shown as being a digital 
embodiment, the specific apparatus used to implement the controlling has 
been deemphasized--except for a few places where digital-to-analog (D/A) 
and analog-to-digital (A/D) converters are needed--in order to better 
clarify the RIM technique which is the heart of the improvement being 
described. The particular parameters adjusted via the lines 210 are 
described below. Individual outputs from the four PID controllers are 
routed to a corresponding number of summing junctions 212, 214, 216 and 
218, respectively; each summing junction also having a pseudo-random 
binary signal (PRBS) applied to it from a PRBS generator 220, via a four 
section low pass filter 220A. Individual outputs from the four summing 
junctions are routed to a corresponding number of D/A converters 222, 224, 
226 and 228; and are further routed via a group of lines 230 to other 
control elements within the parameter adjust section. A set of individual 
analog control signals from the four D/A's are then applied to a 
corresponding number of actuators 232, 234, 236 and 238--which correspond 
to the various pumps/motors described in connection with FIG. 1. The 
correspondence is as follows: the pH actuator 232 may correspond to the 
pump 38 and its associated modulator; the agitation actuator 234 may 
correspond to the stirring paddle 80 and its associated motor; the primary 
flow actuator 236 may correspond to the primary pump 18 and its associated 
modulator; and the recycle actuator 238 may correspond to the recycle pump 
26 and its associated modulator. The four actuators function, as 
previously described, to control the process variables establishing the 
conditions of the dissolution testing resulting in an output concentration 
of the drug form detected by a spectrophotometer 242 (corresponding to the 
element 58 of FIG. 1). The concentration vs time profile C(t)--the desired 
output quantity--is digitized in an A/D converter 244 and is applied first 
via a path 246 to an input node 248 where it is differenced with the A(t) 
signals; and further via a path 250 to the inputs of four process variable 
tuners 252, 254, 256 and 258. The tuners are substantially identical and 
hence the structure and function of one only will be described. The tuners 
may be implemented as a discrete collection of digital circuits operating 
under the control of a central processor (element 56 of FIG. 1); and may 
also be implemented via separate, but cooperating microprocessors; and may 
further be embedded in the central processor 56 itself. Tuner 258, the one 
associated with optimizing the recycle flow rate R(t), is shown as 
comprised of a cross-correlator 260 to which is applied a pair of input 
signals on the lines 230A and 250A. The path 250A provides the C(t) 
signal, while the path 230A provides a combined signal containing the 
control signal plus the random signal--from the output of summing junction 
218. The output from the cross-correlator is integrated in integrator 262, 
whose output is in turn applied to recycle curve element 264 which 
produces a process reaction curve directed to optimizing the recycle flow 
rate parameter. A control parameter determining element 266 receives the 
output from the recycle curve element 264 and periodically produces 
updated values for three key parameters, which are applied via an 
interfacing element 268, for use in the PID controller 208. These three 
key parameters are the overall controller gain K.sub.C ; the integral time 
T.sub.I ; and the derivative time T.sub.D. The interested reader is 
referred to a 1953 published article wherein the parameter-tuning 
technique of the present invention is described. See, Cohen, G. H. and 
Coon, G. A., "Theoretical Considerations of Retarded Control," Trans. 
ASME, Vol. 74, 1953, pp. 827. The technique has become very well known in 
the control system arts and is referred to hereinafter as the "Cohen-Coon 
method". 
In order to improve the fidelity of the bioavailability prediction when the 
improved control system 200 is operating in the open loop mode, it is 
useful to first determine the proper control parameter (K.sub.C, T.sub.I 
and T.sub.D) settings for each of the PID controllers 202, 204, 206 and 
208. This is best done by random input modeling during an experimental run 
performed with a reference drug form in the closed loop mode of operation. 
The recycle rate control channel is illustrative of the method used. 
Superimposed on each channel control signal is a pseudo-random binary 
signal with an amplitude at least one standard deviation greater than the 
noise level in the channel and a bandwidth corresponding to ten times the 
bandwidth of the channel. Active electronic filtering of the output from 
the PRBS generator 220 by a low pass filter 220A may or may not be 
necessary due the possibility of auto-filtering by the mechanical damping 
characteristics of the actuators used. The signal output of the 
spectrophotometer 242 will contain the results of the control signal plus 
the PRBS. This signal C(t) is cross-correlated with the combined input 
signal (control signal plus PRBS) over a period of (illustratively) five 
times constants to yield a weighting function at the output of the 
cross-correlator 260. A process reaction curve is produced by integrating 
the weighting function in the integrator 262, and the control parameters 
(K.sub.C, T.sub.I and T.sub.D) are determined by the method of Cohen and 
Coon within the element 266. These new controller settings for each 
process variable are substituted into the four PID controllers and the 
process is repeated for another five time constants. The procedure is 
performed independently for each of the four PID controllers and 
simultaneously for all four controllers during each experimental run. 
This process of controller tuning is initially performed independently 
(and/or in combination with one or more of the other process variables) 
for each process variable to obtain initial estimates of controller 
settings for each controller. In the course of an actual run, the 
controllers for each of the four process variables operate together in 
parallel and are returned periodically (every 5 time constants, 
illustratively) simultaneously to provide new updated values for the 
controller settings. Controller setting values obtained by his adaptive 
control procedure during the course of an experimental run are rejected, 
and previous values retained, if the proposed values are outside of a 
range of values for each setting which had been found to induce 
instability in the operation of one or more of the loops. 
Although the invention has been described in terms of selected preferred 
embodiments and improvements to these embodiments, the invention should 
not be deemed limited thereto, since other embodiments and modifications 
will readily occur to one skilled in the art. It is therefore to be 
understood that the appended claims are intended to cover all such 
modifications as fall within the true spirit and scope of the invention.