Signal processing for measurement of physiological analysis

A method is provided for continually or continuously measuring the concentration of target chemical analytes present in a biological system, and processing analyte-specific signals to obtain a measurement value that is closely correlated with the concentration of the target chemical analyte in the biological system. One important application of the invention involves a method for signal processing in a system for monitoring blood glucose values.

FIELD OF THE INVENTION
 The invention relates generally to methods for continually or continuously
 measuring the concentration of target chemical analytes present in a
 biological system. More particularly, the invention relates to methods for
 processing signals obtained during measurement of physiological analytes.
 One important application of the invention involves a method for
 monitoring blood glucose concentrations.
 BACKGROUND OF THE INVENTION
 A number of diagnostic tests are routinely performed on humans to evaluate
 the amount or existence of substances present in blood or other body
 fluids. These diagnostic tests typically rely on physiological fluid
 samples removed from a subject, either using a syringe or by pricking the
 skin. One particular diagnostic test entails self-monitoring of blood
 glucose levels by diabetics.
 Diabetes is a major health concern, and treatment of the more severe form
 of the condition, Type I (insulin-dependent) diabetes, requires one or
 more insulin injections per day. Insulin controls utilization of glucose
 or sugar in the blood and prevents hyperglycemia which, if left
 uncorrected, can lead to ketosis. On the other hand, improper
 administration of insulin therapy can result in hypoglycemic episodes,
 which can cause coma and death. Hyperglycemia in diabetics has been
 correlated with several long-term effects of diabetes, such as heart
 disease, atherosclerosis, blindness, stroke, hypertension and kidney
 failure.
 The value of frequent monitoring of blood glucose as a means to avoid or at
 least minimize the complications of Type I diabetes is well established.
 Patients with Type II (non-insulin-dependent) diabetes can also benefit
 from blood glucose monitoring in the control of their condition by way of
 diet and exercise.
 Conventional blood glucose monitoring methods generally require the drawing
 of a blood sample (e.g., by fingerprick) for each test, and a
 determination of the glucose level using an instrument that reads glucose
 concentrations by electrochemical or colorimetric methods. Type I
 diabetics must obtain several fingerprick blood glucose measurements each
 day in order to maintain tight glycemic control. However, the pain and
 inconvenience associated with this blood sampling, along with the fear of
 hypoglycemia, has led to poor patient compliance, despite strong evidence
 that tight control dramatically reduces long-term diabetic complications.
 In fact, these considerations can often lead to an abatement of the
 monitoring process by the diabetic. See, e.g., The Diabetes Control and
 Complications Trial Research Group (1993) New Engl. J. Med. 0329:977-1036.
 Recently, various methods for determining the concentration of blood
 analytes without drawing blood have been developed. For example, U.S. Pat.
 No. 5,267,152 to Yang et al. describes a noninvasive technique of
 measuring blood glucose concentration using near-IR radiation
 diffuse-reflection laser spectroscopy. Similar near-IR spectrometric
 devices are also described in U.S. Pat. No. 5,086,229 to Rosenthal et al.
 and U.S. Pat. No. 4,975,581 to Robinson et al.
 U.S. Pat. Nos. 5,139,023 to Stanley et al., and U.S. Pat. No. 5,443,080 to
 D'Angelo et al. describe transdermal blood glucose monitoring devices that
 rely on a permeability enhancer (e.g., a bile salt) to facilitate
 transdermal movement of glucose along a concentration gradient established
 between interstitial fluid and a receiving medium. U.S. Pat. No. 5,036,861
 to Sembrowich describes a passive glucose monitor that collects
 perspiration through a skin patch, where a cholinergic agent is used to
 stimulate perspiration secretion from the eccrine sweat gland. Similar
 perspiration collection devices are described in U.S. Pat. No. 5,076,273
 to Schoendorfer and U.S. Pat. No. 5,140,985 to Schroeder.
 In addition, U.S. Pat. No. 5,279,543 to Glikfeld et al. describes the use
 of iontophoresis to noninvasively sample a substance through skin into a
 receptacle on the skin surface. Glikfeld teaches that this sampling
 procedure can be coupled with a glucose-specific biosensor or
 glucose-specific electrodes in order to monitor blood glucose. Finally,
 International Publication No. WO 96/00110, published Jan. 4, 1996,
 describes an iontophoretic apparatus for transdermal monitoring of a
 target substance, wherein an iontophoretic electrode is used to move an
 analyte into a collection reservoir and a biosensor is used to detect the
 target analyte present in the reservoir.
 SUMMARY OF THE INVENTION
 The present invention provides a method for continually or continuously
 measuring the concentration of an analyte present in a biological system.
 The method entails continually or continuously detecting an analyte from
 the biological system and deriving a raw signal therefrom, wherein the raw
 signal is related to the analyte concentration. A number of signal
 processing steps are then carried out in order to convert the raw signal
 into an initial signal output that is indicative of an analyte amount. The
 converted signal is then further converted into a value indicative of the
 concentration of analyte present in the biological system.
 The raw signal can be obtained using any suitable sensing methodology
 including, for example, methods which rely on direct contact of a sensing
 apparatus with the biological system; methods which extract samples from
 the biological system by invasive, minimally invasive, and non-invasive
 sampling techniques, wherein the sensing apparatus is contacted with the
 extracted sample; methods which rely on indirect contact of a sensing
 apparatus with the biological system; and the like. In preferred
 embodiments of the invention, methods are used to extract samples from the
 biological sample using minimally invasive or non-invasive sampling
 techniques. The sensing apparatus used with any of the above-noted methods
 can employ any suitable sensing element to provide the raw signal
 including, but not limited to, physical, chemical, electrochemical,
 photochemical, spectrophotometric, polarimetric, colorimetric,
 radiometric, or like elements. In preferred embodiments of the invention,
 a biosensor is used which comprises an electrochemical sensing element.
 In one particular embodiment of the invention, the raw signal is obtained
 using a transdermal sampling system that is placed in operative contact
 with a skin or mucosal surface of the biological system. The sampling
 system transdermally extracts the analyte from the biological system using
 any appropriate sampling technique, for example, iontophoresis. The
 transdermal sampling system is maintained in operative contact with the
 skin or mucosal surface of the biological system to provide for such
 continual or continuous analyte measurement.
 The analyte can be any specific substance or component that one is desirous
 of detecting and/or measuring in a chemical, physical, enzymatic, or
 optical analysis. Such analytes include, but are not limited to, amino
 acids, enzyme substrates or products indicating a disease state or
 condition, other markers of disease states or conditions, drugs of abuse,
 therapeutic and/or pharmacologic agents, electrolytes, physiological
 analytes of interest (e.g., calcium, potassium, sodium, chloride,
 bicarbonate (CO.sub.2), glucose, urea (blood urea nitrogen), lactate,
 hematocrit, and hemoglobin), lipids, and the like. In preferred
 embodiments, the analyte is a physiological analyte of interest, for
 example glucose, or a chemical that has a physiological action, for
 example a drug or pharmacological agent.
 Accordingly, it is an object of the invention to provide a method for
 continually or continuously measuring an analyte present in a biological
 system, wherein raw signals are obtained from a suitable sensing
 apparatus, and then subjected to signal processing techniques. More
 particularly, the raw signals undergo a data screening method in order to
 eliminate outlier signals and/or poor (incorrect) signals using a
 predefined set of selection criteria. In addition, or alternatively, the
 raw signal can be converted in a conversion step which (i) removes or
 corrects for background information, (ii) integrates the raw signal over a
 sensing time period, (iii) performs any process which converts the raw
 signal from one signal type to another, or (iv) performs any combination
 of steps (i), (ii) and/or (iii). In preferred embodiments, the conversion
 step entails a baseline background subtraction method to remove background
 from the raw signal and an integration step. In other embodiments, the
 conversion step can be tailored for use with a sensing device that
 provides both active and reference (blank) signals; wherein mathematical
 transformations are used to individually smooth active and reference
 signals, and/or to subtract a weighted reference (blank) signal from the
 active signal. In still further embodiments, the conversion step includes
 correction functions which account for changing conditions in the
 biological system and/or the biosensor system (e.g., temperature
 fluctuations in the biological system, temperature fluctuations in the
 sensor element, skin conductivity fluctuations, or combinations thereof).
 The result of the conversion step is an initial signal output which
 provides a value which can be correlated with the concentration of the
 target analyte in the biological sample.
 It is also an object of the invention to provide a signal processing
 calibration step, wherein the raw or initial signals obtained as described
 above are converted into an analyte-specific value of known units to
 provide an interpretation of the signal obtained from the sensing device.
 The interpretation uses a mathematical transformation to model the
 relationship between a measured response in the sensing device and a
 corresponding analyte-specific value. Such mathematical transformations
 can entail the use of linear or nonlinear regressions, or neural network
 algorithms. In one embodiment, the calibration step entails calibrating
 the sensing device using a single- or multi-point calibration, and then
 converting post-calibration data using correlation factors, time
 corrections and constants to obtain an analyte-specific value. Further
 signal processing can be used to refine the information obtained in the
 calibration step, for example, where a signal processing step is used to
 correct for signal differences due to variable conditions unique to the
 sensor element used to obtain the raw signal. In one embodiment, this
 further step is used to correct for signal time-dependence, particularly
 signal decline. In another embodiment, a constant offset term is obtained,
 which offset is added to the signal to account for a non-zero signal at an
 estimated zero analyte concentration.
 Further, the methods of the present invention include enhancement of skin
 permeability by pricking the skin with micro-needles. In addition, the
 sampling system can be programed to begin execution of sampling and
 sensing at a defined time(s).
 It is yet a further object of the invention to provide a monitoring system
 for continually or continuously measuring an analyte present in a
 biological system. The monitoring system comprises, in operative
 combination: (a) a sampling means for continually or continuously
 extracting the analyte from the biological system, (b) a sensing means in
 operative contact with the analyte extracted by the sampling means, and
 (c) a microprocessor means in operative communication with the sensing
 means. The sampling means is adapted for extracting the analyte across a
 skin or mucosal surface of a biological system. The sensing means is used
 to obtain a raw signal from the extracted analyte, wherein the raw signal
 is specifically related to the analyte. The microprocessor means is used
 to subject the raw signal to a conversion step, thereby converting the
 same into an initial signal output which is indicative of the amount of
 analyte extracted by the sampling means, and then perform a calibration
 step which correlates the initial signal output with a measurement value
 indicative of the concentration of analyte present in the biological
 system at the time of extraction. In one embodiment, the monitoring system
 uses iontophoresis to extract the analyte from the biological system. In
 other embodiments, the monitoring system is used to extract a glucose
 analyte from the biological system. Further, the microprocessor can be
 programed to begin execution of sampling and sensing at a defined time(s).
 Additional objects, advantages and novel features of the invention will be
 set forth in part in the description which follows, and in part will
 become apparent to those skilled in the art upon examination of the
 following, or may be learned by practice of the invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
 Before describing the present invention in detail, it is to be understood
 that this invention is not limited to particular compositions or
 biological systems as such may, of course, vary. It is also to be
 understood that the terminology used herein is for the purpose of
 describing particular embodiments only, and is not intended to be
 limiting.
 It must be noted that, as used in this specification and the appended
 claims, the singular forms "a", "an" and "the" include plural referents
 unless the content clearly dictates otherwise. Thus, for example,
 reference to "a time-dependent variable" includes a mixture of two or more
 such variables, reference to "an electrochemically active species"
 includes two or more such species, reference to "an analyte" includes
 mixtures of analytes, and the like.
 All publications, patents and patent applications cited herein, whether
 supra or infra, are hereby incorporated by reference in their entirety.
 Unless defined otherwise, all technical and scientific terms used herein
 have the same meaning as commonly understood by one of ordinary skill in
 the art to which the invention pertains. Although any methods and
 materials similar or equivalent to those described herein can be used in
 the practice for testing of the present invention, the preferred materials
 and methods are described herein.
 In describing and claiming the present invention, the following terminology
 will be used in accordance with the definitions set out below.
 Definitions
 The terms "analyte" and "target analyte" are used herein to denote any
 physiological analyte of interest that is a specific substance or
 component that is being detected and/or measured in a chemical, physical,
 enzymatic, or optical analysis. A detectable signal (e.g., a chemical
 signal or electrochemical signal) can be obtained, either directly or
 indirectly, from such an analyte or derivatives thereof. Furthermore, the
 terms "analyte" and "substance" are used interchangeably herein, and are
 intended to have the same meaning, and thus encompass any substance of
 interest. In preferred embodiments, the analyte is a physiological analyte
 of interest, for example, glucose, or a chemical that has a physiological
 action, for example, a drug or pharmacological agent.
 A "sampling device" or "sampling system" refers to any device for obtaining
 a sample from a biological system for the purpose of determining the
 concentration of an analyte of interest. As used herein, the term
 "sampling" means invasive, minimally invasive or non-invasive extraction
 of a substance from the biological system, generally across a membrane
 such as skin or mucosa. The membrane can be natural or artificial, and can
 be of plant or animal nature, such as natural or artificial skin, blood
 vessel tissue, intestinal tissue, and the like. Typically, the sampling
 means are in operative contact with a "reservoir," or "collection
 reservoir," wherein the sampling means is used for extracting the analyte
 from the biological system into the reservoir to obtain the analyte in the
 reservoir. A "biological system" includes both living and artificially
 maintained systems. Examples of minimally invasive and noninvasive
 sampling techniques include iontophoresis, sonophoresis, suction,
 electroporation, thermal poration, passive diffusion, microfine
 (miniature) lances or cannulas, subcutaneous implants or insertions, and
 laser devices. Sonophoresis uses ultrasound to increase the permeability
 of the skin (see, e.g., Menon et al. (1994) Skin Pharmacology 7:130-139).
 Suitable sonophoresis sampling systems are described in International
 Publication No. WO 91/12772, published Sep. 5, 1991. Passive diffusion
 sampling devices are described, for example, in International Publication
 Nos.: WO 97/38126 (published Oct. 16, 1997); WO 97/42888, WO 97/42886, WO
 97/42885, and WO 97/42882 (all published Nov. 20, 1997); and WO 97/43962
 (published Nov. 27, 1997). Laser devices use a small laser beam to burn a
 hole through the upper layer of the patient's skin (see, e.g., Jacques et
 al. (1978) J. Invest. Dermatology 88:88-93). Examples of invasive sampling
 techniques include traditional needle and syringe or vacuum sample tube
 devices.
 The term "collection reservoir" is used to describe any suitable
 containment means for containing a sample extracted from a biological
 system. For example, the collection reservoir can be a receptacle
 containing a material which is ionically conductive (e.g., water with ions
 therein), or alternatively, it can be a material, such as, a sponge-like
 material or hydrophilic polymer, used to keep the water in place. Such
 collection reservoirs can be in the form of a hydrogel (for example, in
 the form of a disk or pad). Hydrogels are typically referred to as
 "collection inserts." Other suitable collection reservoirs include, but
 are not limited to, tubes, vials, capillary collection devices, cannulas,
 and miniaturized etched, ablated or molded flow paths.
 A "housing" for the sampling system can further include suitable
 electronics (e.g., microprocessor, memory, display and other circuit
 components) and power sources for operating the sampling system in an
 automatic fashion.
 A "monitoring system," as used herein, refers to a system useful for
 continually or continuously measuring a physiological analyte present in a
 biological system. Such a system typically includes, but is not limited
 to, sampling means, sensing means, and a microprocessor means in operative
 communication with the sampling means and the sensing means.
 The term "artificial," as used herein, refers to an aggregation of cells of
 monolayer thickness or greater which are grown or cultured in vivo or in
 vitro, and which function as a tissue of an organism but are not actually
 derived, or excised, from a pre-existing source or host.
 The term "subject" encompasses any warm-blooded animal, particularly
 including a member of the class Mammalia such as, without limitation,
 humans and nonhuman primates such as chimpanzees and other apes and monkey
 species; farm animals such as cattle, sheep, pigs, goats and horses;
 domestic mammals such as dogs and cats; laboratory animals including
 rodents such as mice, rats and guinea pigs, and the like. The term does
 not denote a particular age or sex. Thus, adult and newborn subjects, as
 well as fetuses, whether male or female, are intended to be covered.
 As used herein, the term "continual measurement" intends a series of two or
 more measurements obtained from a particular biological system, which
 measurements are obtained using a single device maintained in operative
 contact with the biological system over the time period in which the
 series of measurements is obtained. The term thus includes continuous
 measurements.
 The term "transdermal," as used herein, includes both transdermal and
 transmucosal techniques, i.e., extraction of a target analyte across skin
 or mucosal tissue. Aspects of the invention which are described herein in
 the context of "transdermal," unless otherwise specified, are meant to
 apply to both transdermal and transmucosal techniques.
 The term "transdermal extraction," or "transdermally extracted" intends any
 noninvasive, or at least minimally invasive sampling method, which entails
 extracting and/or transporting an analyte from beneath a tissue surface
 across skin or mucosal tissue. The term thus includes extraction of an
 analyte using iontophoresis (reverse iontophoresis), electroosmosis,
 sonophoresis, microdialysis, suction, and passive diffusion. These methods
 can, of course, be coupled with application of skin penetration enhancers
 or skin permeability enhancing technique such as tape stripping or
 pricking with micro-needles. The term "transdermally extracted" also
 encompasses extraction techniques which employ thermal poration,
 electroporation, microfine lances, microfine canulas, subcutaneous
 implants or insertions, and the like.
 The term "iontophoresis" intends a method for transporting substances
 across tissue by way of an application of electrical energy to the tissue.
 In conventional iontophoresis, a reservoir is provided at the tissue
 surface to serve as a container of material to be transported.
 Iontophoresis can be carried out using standard methods known to those of
 skill in the art, for example, by establishing an electrical potential
 using a direct current (DC) between fixed anode and cathode "iontophoretic
 electrodes," alternating a direct current between anode and cathode
 iontophoretic electrodes, or using a more complex waveform such as
 applying a current with alternating polarity (AP) between iontophoretic
 electrodes (so that each electrode is alternately an anode or a cathode).
 The term "reverse iontophoresis" refers to the movement of a substance from
 a biological fluid across a membrane by way of an applied electric
 potential or current. In reverse iontophoresis, a reservoir is provided at
 the tissue surface to receive the extracted material.
 "Electroosmosis" refers to the movement of a substance through a membrane
 by way of an electric field-induced convective flow. The terms
 iontophoresis, reverse iontophoresis, and electroosmosis, will be used
 interchangeably herein to refer to movement of any ionically charged or
 uncharged substance across a membrane (e.g., an epithelial membrane) upon
 application of an electric potential to the membrane through an ionically
 conductive medium.
 The term "sensing device," "sensing means," or "biosensor device"
 encompasses any device that can be used to measure the concentration of an
 analyte, or derivative thereof, of interest. Preferred sensing devices for
 detecting blood analytes generally include electrochemical devices and
 chemical devices. Examples of electrochemical devices include the Clark
 electrode system (see, e.g., Updike, et al., (1967) Nature 214:986-988),
 and other amperometric, coulometric, or potentiometric electrochemical
 devices. Examples of chemical devices include conventional enzyme-based
 reactions as used in the Lifescan.RTM. glucose monitor (Johnson and
 Johnson, New Brunswick, N.J.) (see, e.g., U.S. Pat. No. 4,935,346 to
 Phillips, et al.).
 A "biosensor" or "biosensor device" includes, but is not limited to, a
 "sensor element" which includes, but is not limited to, a "biosensor
 electrode" or "sensing electrode" or "working electrode" which refers to
 the electrode that is monitored to determine the amount of electrical
 signal at a point in time or over a given time period, which signal is
 then correlated with the concentration of a chemical compound. The sensing
 electrode comprises a reactive surface which converts the analyte, or a
 derivative thereof, to electrical signal. The reactive surface can be
 comprised of any electrically conductive material such as, but not limited
 to, platinum-group metals (including, platinum, palladium, rhodium,
 ruthenium, osmium, and iridium), nickel, copper, silver, and carbon, as
 well as, oxides, dioxides, combinations or alloys thereof. Some catalytic
 materials, membranes, and fabrication technologies suitable for the
 construction of amperometric biosensors were described by Newman, J. D.,
 et al. (Analytical Chemistry 67(24), 4594-4599, 1995).
 The "sensor element" can include components in addition to a biosensor
 electrode, for example, it can include a "reference electrode," and a
 "counter electrode." The term "reference electrode" is used herein to mean
 an electrode that provides a reference potential, e.g., a potential can be
 established between a reference electrode and a working electrode. The
 term "counter electrode" is used herein to mean an electrode in an
 electrochemical circuit which acts as a current source or sink to complete
 the electrochemical circuit. Although it is not essential that a counter
 electrode be employed where a reference electrode is included in the
 circuit and the electrode is capable of performing the function of a
 counter electrode, it is preferred to have separate counter and reference
 electrodes because the reference potential provided by the reference
 electrode is most stable when it is at equilibrium. If the reference
 electrode is required to act further as a counter electrode, the current
 flowing through the reference electrode may disturb this equilibrium.
 Consequently, separate electrodes functioning as counter and reference
 electrodes are most preferred.
 In one embodiment, the "counter electrode" of the "sensor element"
 comprises a "bimodal electrode." The term "bimodal electrode" as used
 herein typically refers to an electrode which is capable of functioning
 non-simultaneously as, for example, both the counter electrode (of the
 "sensor element") and the iontophoretic electrode (of the "sampling
 means").
 The terms "reactive surface," and "reactive face" are used interchangeably
 herein to mean the surface of the sensing electrode that: (1) is in
 contact with the surface of an electrolyte containing material (e.g. gel)
 which contains an analyte or through which an analyte, or a derivative
 thereof, flows from a source thereof; (2) is comprised of a catalytic
 material (e.g., carbon, platinum, palladium, rhodium, ruthenium, or nickel
 and/or oxides, dioxides and combinations or alloys thereof) or a material
 that provides sites for electrochemical reaction; (3) converts a chemical
 signal (e.g. hydrogen peroxide) into an electrical signal (e.g., an
 electrical current); and (4) defines the electrode surface area that, when
 composed of a reactive material, is sufficient to drive the
 electrochemical reaction at a rate sufficient to generate a detectable,
 reproducibly measurable, electrical signal that is correlatable with the
 amount of analyte present in the electrolyte.
 The term "collection reservoir" and "collection insert" are used to
 describe any suitable containment means for containing a sample extracted
 from a biological system. The reservoir can include a material which is
 tonically conductive (e.g., water with ions therein), wherein another
 material such as a sponge-like material or hydrophilic polymer is used to
 keep the water in place. Such collection reservoirs can be in the form of
 a hydrogel (for example, in the shape of a disk or pad). Other suitable
 collection reservoirs include, but are not limited to, tubes, vials,
 capillary collection devices, cannulas, and miniaturized etched, ablated
 or molded flow paths.
 An "ionically conductive material" refers to any material that provides
 ionic conductivity, and through which electrochemically active species can
 diffuse. The ionically conductive material can be, for example, a solid,
 liquid, or semi-solid (e.g., in the form of a gel) material that contains
 an electrolyte, which can be composed primarily of water and ions (e.g.,
 sodium chloride), and generally comprises 50% or more water by weight. The
 material can be in the form of a gel, a sponge or pad (e.g., soaked with
 an electrolytic solution), or any other material that can contain an
 electrolyte and allow passage therethrough of electrochemically active
 species, especially the analyte of interest.
 The term "physiological effect" encompasses effects produced in the subject
 that achieve the intended purpose of a therapy. In preferred embodiments,
 a physiological effect means that the symptoms of the subject being
 treated are prevented or alleviated. For example, a physiological effect
 would be one that results in the prolongation of survival in a patient.
 A "laminate", as used herein, refers to structures comprised of at least
 two bonded layers. The layers may be bonded by welding or through the use
 of adhesives. Examples of welding include, but are not limited to, the
 following: ultrasonic welding, heat bonding, and inductively coupled
 localized heating followed by localized flow. Examples of common adhesives
 include, but are not limited to, pressure sensitive adhesives, thermoset
 adhesives, cyanocrylate adhesives, epoxies, contact adhesives, and heat
 sensitive adhesives.
 A "collection assembly", as used herein, refers to structures comprised of
 several layers, where the assembly includes at least one collection
 insert, for example a hydrogel. An example of a collection assembly of the
 present invention is a mask layer, collection inserts, and a retaining
 layer where the layers are held in appropriate, functional relationship to
 each other but are not necessarily a laminate, i.e., the layers may not be
 bonded together. The layers may, for example, be held together by
 interlocking geometry or friction.
 An "autosensor assembly", as used herein, refers to structures generally
 comprising a mask layer, collection inserts, a retaining layer, an
 electrode assembly, and a support tray. The autosensor assembly may also
 include liners. The layers of the assembly are held in appropriate,
 functional relationship to each other.
 The mask and retaining layers are preferably composed of materials that are
 substantially impermeable to the analyte (chemical signal) to be detected
 (e.g., glucose); however, the material can be permeable to other
 substances. By "substantially impermeable" is meant that the material
 reduces or eliminates chemical signal transport (e.g., by diffusion). The
 material can allow for a low level of chemical signal transport, with the
 proviso that chemical signal that passes through the material does not
 cause significant edge effects at the sensing electrode.
 "Substantially planar" as used herein, includes a planar surface that
 contacts a slightly curved surface, for example, a forearm or upper arm of
 a subject. A "substantially planar" surface is, for example, a surface
 having a shape to which skin can conform, i.e., contacting contact between
 the skin and the surface.
 By the term "printed" as used herein is meant a substantially uniform
 deposition of an electrode formulation onto one surface of a substrate
 (i.e., the base support). It will be appreciated by those skilled in the
 art that a variety of techniques may be used to effect substantially
 uniform deposition of a material onto a substrate, e.g., Gravure-type
 printing, extrusion coating, screen coating, spraying, painting, or the
 like.
 The term "enzyme" intends any compound or material which catalyzes a
 reaction between molecules to produce one or more reaction products. The
 term thus includes protein enzymes, or enzymatically active portions
 (fragments) thereof, which proteins and/or protein fragments may be
 isolated from a natural source, or recombinantly or synthetically
 produced. The term also encompasses designed synthetic enzyme mimetics.
 The term "time-dependent signal decline" refers to a detectable decrease in
 measured signal over time when no decrease or change in analyte
 concentration is actually occurring. The decrease in signal over time may
 be due to a number of different phenomena.
 The term "signal-to-noise ratio" describes the relationship between the
 actual signal intended to be measured and the variation in signal in the
 absence of the analyte. The terms "S/N" and "SNR" are also used to refer
 to the signal-to-noise ratio. "Noise," as used herein, refers to any
 undesirable signal which is measured along with the intended signal.
 General Methods
 The present invention relates to use of a device for transdermally
 extracting and measuring the concentration of a target analyte present in
 a biological system. In preferred embodiments, the sensing device
 comprises a biosensor. In other preferred embodiments, a sampling device
 is used to extract small amounts of a target analyte from the biological
 system, and then sense and/or quantify the concentration of the target
 analyte. Measurement with the biosensor and/or sampling with the sampling
 device can be carried out in a continual or continuous manner. Continual
 or continuous measurements allow for closer monitoring of target analyte
 concentration fluctuations.
 The analyte can be any specific substance or component that one is desirous
 of detecting and/or measuring in a chemical, physical, enzymatic, or
 optical analysis. Such analytes include, but are not limited to, amino
 acids, enzyme substrates or products indicating a disease state or
 condition, other markers of disease states or conditions, drugs of abuse,
 therapeutic and/or pharmacologic agents (e.g., theophylline, anti-HIV
 drugs, lithium, anti-epileptic drugs, cyclosporin, chemotherapeutics),
 electrolytes, physiological analytes of interest (e.g., urate/uric acid,
 carbonate, calcium, potassium, sodium, chloride, bicarbonate (CO.sub.2),
 glucose, urea (blood urea nitrogen), lactate/lactic acid, hydroxybutyrate,
 cholesterol, triglycerides, creatine, creatinine, insulin, hematocrit, and
 hemoglobin), blood gases (carbon dioxide, oxygen, pH), lipids, heavy
 metals (e.g., lead, copper), and the like. In preferred embodiments, the
 analyte is a physiological analyte of interest, for example glucose, or a
 chemical that has a physiological action, for example a drug or
 pharmacological agent.
 In order to facilitate detection of the analyte, an enzyme can be disposed
 in the collection reservoir, or, if several collection reservoirs are
 used, the enzyme can be disposed in several or all of the reservoirs. The
 selected enzyme is capable of catalyzing a reaction with the extracted
 analyte (in this case glucose) to the extent that a product of this
 reaction can be sensed, e.g., can be detected electrochemically from the
 generation of a current which current is detectable and proportional to
 the concentration or amount of the analyte which is reacted. A suitable
 enzyme is glucose oxidase which oxidizes glucose to gluconic acid and
 hydrogen peroxide. The subsequent detection of hydrogen peroxide on an
 appropriate biosensor electrode generates two electrons per hydrogen
 peroxide molecule which create a current which can be detected and related
 to the amount of glucose entering the device. Glucose oxidase (GOx) is
 readily available commercially and has well known catalytic
 characteristics. However, other enzymes can also be used, so long as they
 specifically catalyze a reaction with an analyte or substance of interest
 to generate a detectable product in proportion to the amount of analyte so
 reacted.
 In like manner, a number of other analyte-specific enzyme systems can be
 used in the invention, which enzyme systems operate on much the same
 general techniques. For example, a biosensor electrode that detects
 hydrogen peroxide can be used to detect ethanol using an alcohol oxidase
 enzyme system, or similarly uric acid with urate oxidase system, urea with
 a urease system, cholesterol with a cholesterol oxidase system, and
 theophylline with a xanthine oxidase system.
 In addition, the oxidase enzyme (used for hydrogen peroxide-based
 detection) can be replaced with another redox system, for example, the
 dehydrogenase-enzyme NAD-NADH, which offers a separate route to detecting
 additional analytes. Dehydrogenase-based sensors can use working
 electrodes made of gold or carbon (via mediated chemistry). Examples of
 analytes suitable for this type of monitoring include, but are not limited
 to, cholesterol, ethanol, hydroxybutyrate, phenylalanine, triglycerides,
 and urea. Further, the enzyme can be eliminated and detection can rely on
 direct electrochemical or potentiometric detection of an analyte. Such
 analytes include, without limitation, heavy metals (e.g., cobalt, iron,
 lead, nickel, zinc), oxygen, carbonate/carbon dioxide, chloride, fluoride,
 lithium, pH, potassium, sodium, and urea. Also, the sampling system
 described herein can be used for therapeutic drug monitoring, for example,
 monitoring anti-epileptic drugs (e.g., phenytion), chemotherapy (e.g.,
 adriamycin), hyperactivity (e.g., ritalin), and anti-organ-rejection
 (e.g., cyclosporin).
 The methods for measuring the concentration of a target analyte can be
 generalized as follows. An initial step (Step A) entails obtaining a raw
 signal from a sensing device, which signal is related to a target analyte
 present in the biological system. The raw signal can be obtained using any
 suitable sensing methodology including, for example, methods which rely on
 direct contact of a sensing apparatus with the biological system; methods
 which extract samples from the biological system by invasive, minimally
 invasive, and non-invasive sampling techniques, wherein the sensing
 apparatus is contacted with the extracted sample; methods which rely on
 indirect contact of a sensing apparatus with the biological system; and
 the like. In preferred embodiments of the invention, methods are used to
 extract samples from the biological sample using minimally invasive or
 non-invasive sampling techniques. The sensing apparatus used with any of
 the above-noted methods can employ any suitable sensing element to provide
 the signal including, but not limited to, physical, chemical,
 electrochemical, photochemical, spectrophotometric, polarimetric,
 colorimetric, radiometric, or like elements. In preferred embodiments of
 the invention, a biosensor is used which comprises an electrochemical
 sensing element.
 After the raw signal has been obtained, the signal can undergo a data
 screening method (Step B) in order to eliminate outlier signals and/or
 poor (incorrect) signals using a predefined set of selection criteria. In
 addition, or alternatively, the raw signal can be converted in a
 conversion step (Step C) which can (i) remove or correct for background
 information, (ii) integrate the signal over a sensing time period, (iii)
 perform any process which converts the signal from one signal type to
 another, or (iv) perform any combination of steps (i), (ii) and/or (iii).
 In preferred embodiments, the conversion step entails a baseline
 background subtraction method to remove background from the raw signal and
 an integration step. In other embodiments, the conversion step can be
 tailored for use with a sensing device that provides both active and
 reference (blank) signals; wherein mathematical transformations are used
 to individually smooth active and reference signals, and/or to subtract a
 weighted reference (blank) signal from the active signal. In still further
 embodiments, the conversion step includes correction functions which
 account for changing conditions in the biological system and/or the
 biosensor system (e.g., temperature fluctuations in the biological system,
 temperature fluctuations in the sensor element, skin conductivity
 fluctuations, or combinations thereof). The result of the conversion step
 is an initial signal output which provides a value which can be correlated
 with the concentration of the target analyte in the biological sample.
 In a calibration step (Step D), the raw signal obtained from Step A, or the
 initial signal obtained from Step B and/or Step C, is converted into an
 analyte-specific value of known units to provide an interpretation of the
 signal obtained from the sensing device. The interpretation uses a
 one-to-one mathematical transformation to model the relationship between a
 measured response in the sensing device and a corresponding
 analyte-specific value. Thus, the calibration step is used herein to
 relate, for example, an electrochemical signal (detected by a biosensor)
 with the concentration of a target analyte in a biological system. In one
 embodiment, the calibration step entails calibrating the sensing device
 using a single- or multi-point calibration, and then converting
 post-calibration data using correlation factors, time corrections and
 constants to obtain an analyte-specific value. Further signal processing
 can be used to refine the information obtained in the calibration step,
 for example, where a signal processing step is used to correct for signal
 differences due to variable conditions unique to the sensor element used
 to obtain the raw signal. In one embodiment, this further step is used to
 correct for signal time-dependence, particularly signal decline. In
 another embodiment, a constant offset term is obtained, which offset is
 added to the signal to account for a non-zero signal at an estimated zero
 analyte concentration.
 The analyte value obtained using the above techniques can optionally be
 used in a subsequent step (Step E) to predict future (time forecasting) or
 past (calibration) measurements of the target analyte concentration in the
 biological system. For example, a series of analyte values are obtained by
 performing any combination of Steps A, B, C, and/or D in an iterative
 manner. This measurement series is then used to predict unmeasured analyte
 values at different points in time, future or past. In this manner, lag
 times inherent in certain sampling and/or sensing techniques can be
 reduced or eliminated to provide real time measurement predictions.
 In another optional step, analyte values obtained using the above
 techniques can be used in a subsequent step (Step F) to control an aspect
 of the biological system. In one embodiment, the analyte value obtained in
 Step D is used to determine when, and at what level, a constituent should
 be added to the biological system in order to control an aspect of the
 biological system. In a preferred embodiment, the analyte value can be
 used in a feedback control loop to control a physiological effect in the
 biological system.
 The above general methods (Steps A through F) are each independently useful
 in analyte sensing systems and can, of course, be used in a wide variety
 of combinations selected for a particular biological system, target
 analyte, and/or sensing technique. For example, in certain applications, a
 measurement sequence can include Steps A, C, D, E and F, in other
 applications, a measurement sequence can include Steps A, B, C and D, and
 the like. The determination of particularly suitable combinations is
 within the skill of the ordinarily skilled artisan when directed by the
 instant disclosure. Furthermore, Steps C through F are preferably embodied
 as one or more mathematical functions as described herein below. These
 functions can thus be carried out using a microprocessor in a monitoring
 system. Although these methods are broadly applicable to measuring any
 chemical analyte and/or substance in a biological system, the invention is
 expressly exemplified for use in a non-invasive, transdermal sampling
 system which uses an electrochemical biosensor to quantify or qualify
 glucose or a glucose metabolite.
 Step A
 Obtaining the Raw Signal
 The raw signal can be obtained using any sensing device that is operatively
 contacted with the biological system. Such sensing devices can employ
 physical, chemical, electrochemical, spectrophotometric, polarimetric,
 colorimetric, radiometric, or like measurement techniques. In addition,
 the sensing device can be in direct or indirect contact with the
 biological system, or used with a sampling device which extracts samples
 from the biological system using invasive, minimally invasive or
 non-invasive sampling techniques. In preferred embodiments, a minimally
 invasive or non-invasive sampling device is used to obtain samples from
 the biological system, and the sensing device comprises a biosensor with
 an electrochemical sensing element. In particularly preferred embodiments,
 a sampling device is used to obtain continual transdermal or transmucosal
 samples from a biological system, and the analyte of interest is glucose.
 More specifically, a non-invasive glucose monitoring device is used to
 measure changes in glucose levels in an animal subject over a wide range
 of glucose concentrations. The sampling method is based on transdermal
 glucose extraction and the sensing method is based on electrochemical
 detection technology. The device can be contacted with the biological
 system continuously, and automatically obtains glucose samples in order to
 measure glucose concentration at preprogrammed intervals.
 Sampling is carried out continually by non-invasively extracting glucose
 through the skin of the patient. More particularly, an iontophoretic
 current is applied to a surface of the skin of a subject. When the current
 is applied, ions or charged molecules pull along other uncharged molecules
 or particles such as glucose which are drawn into a collection reservoir
 placed on the surface of the skin. The collection reservoir may comprise
 any ionically conductive material and is preferably in the form of a
 hydrogel which is comprised of a hydrophilic material, water and an
 electrolyte.
 The collection reservoir may further contain an enzyme which catalyzes a
 reaction of glucose to form an easily detectable species. The enzyme is
 preferably glucose oxidase (GOx) which catalyzes the reaction between
 glucose and oxygen and results in the production of hydrogen peroxide. The
 hydrogen peroxide reacts at a catalytic surface of a biosensor electrode,
 resulting in the generation of electrons which create a detectable
 biosensor current (raw signal). Based on the amount of biosensor current
 created over a given period of time, a measurement is taken, which
 measurement is related to the amount of glucose drawn into the collection
 reservoir over a given period of time. In a preferred embodiment, the
 reaction is allowed to continue until substantially all of the glucose in
 the collection reservoir has been subjected to a reaction and is therefore
 no longer detectable, and the biosensor current generated is related to
 the concentration of glucose in the subject at the approximate time of
 sample collection.
 When the reaction is complete, the process is repeated and a subsequent
 measurement is obtained. More specifically, the iontophoretic current is
 again applied, glucose is drawn through the skin surface into the
 collection reservoir, and the reaction is catalyzed in order to create a
 biosensor current. These sampling (extraction) and sensing operations are
 integrated such that glucose is extracted into the hydrogel collection pad
 where it contacts the GOx enzyme. The GOx enzyme converts glucose and
 oxygen in the hydrogel to hydrogen peroxide which diffuses to the sensor
 and is catalyzed by the sensor to regenerate oxygen and form electrons.
 The electrons generate an electrical signal that can be measured,
 analyzed, and correlated to blood glucose.
 Optionally, one or more additional "active" collection reservoirs (each
 containing the GOx enzyme) can be used to obtain measurements. In one
 embodiment, two active collection reservoirs are used, and an average is
 taken between signals from the reservoirs for each measurement time point.
 Obtaining multiple signals, and then averaging reads from each signals,
 allows for signal smoothing of unusual data points from a sensor that
 otherwise may not have been detected by data screening techniques.
 Furthermore, skin site variability can be detected, and "lag" and/or
 "lead" differences in blood glucose changes relative to extracted glucose
 changes can be mitigated. In another embodiment, a second collection
 reservoir can be provided which does not contain the GOx enzyme. This
 second reservoir can serve as an internal reference (blank) for the
 sensing device, where a biosensor is used to measure the "blank" signal
 from the reference reservoir which signal is then used in a blank
 subtraction step as described below.
 A generalized method for continual monitoring of a physiological analyte is
 disclosed in International Publication No. WO 97/24059, published Jul. 10,
 1997, which publication is incorporated herein by reference. As noted in
 that publication, the analyte is extracted into a reservoir containing a
 hydrogel which is preferably comprised of a hydrophilic material of the
 type described in International Publication No. WO 97/02811, published
 Jan. 30, 1997, which publication is incorporated herein by reference.
 Suitable hydrogel materials include polyethylene oxide, polyacrylic acid,
 polyvinylalcohol and related hydrophilic polymeric materials combined with
 water to form an aqueous gel.
 In the above non-invasive glucose monitoring device, a biosensor electrode
 is positioned on a surface of the hydrogel opposite the surface contacting
 the skin. The sensor electrode acts as a detector which detects current
 generated by hydrogen peroxide in the redox reaction, or more specifically
 detects current which is generated by the electrons generated by the redox
 reaction catalyzed by the platinum surface of the electrode. The details
 of such electrode assemblies and devices for iontophoretic extraction of
 glucose are disclosed in International Publication No. WO 96/00110,
 published Jan. 4, 1996, and International Publication No. WO 97/10499,
 published Mar. 2, 1997, which publications are also incorporated herein by
 reference.
 Referring now to FIGS. 1A and 1B, an iontophoretic collection reservoir and
 electrode assembly for use in a transdermal sensing device is generally
 indicated at 2. The assembly comprises two iontophoretic collection
 reservoirs, 4 and 6, each having a conductive medium 8, and 10 (preferably
 cylindrical hydrogel pads), respectively disposed therein. First (12) and
 second (14) ring-shaped iontophoretic electrodes are respectively
 contacted with conductive medium 8 and 10. The first iontophoretic
 electrode 12 surrounds three biosensor electrodes which are also contacted
 with the conductive medium 8, a working electrode 16, a reference
 electrode 18, and a counter electrode 20. A guard ring 22 separates the
 biosensor electrodes from the iontophoretic electrode 12 to minimize noise
 from the iontophoretic circuit. Conductive contacts provide communication
 between the electrodes and an associated power source and control means as
 described in detail below. A similar biosensor electrode arrangement can
 be contacted with the conductive medium 10, or the medium can not have a
 sensor means contacted therewith.
 Referring now to FIG. 2, an exploded view of the key components from a
 preferred embodiment of an iontophoretic sampling system is presented. In
 FIG. 2, the iontophoretic collection reservoir and electrode assembly 2 of
 FIGS. 1A and 1B is shown in exploded view in combination with a suitable
 iontophoretic sampling device housing 32. The housing can be a plastic
 case or other suitable structure which preferably is configured to be worn
 on a subjects arm in a manner similar to a wrist watch. As can be seen,
 conductive media 8 and 10 (hydrogel pads) are separable from the assembly
 2; however, when the assembly 2 and the housing 32 are assembled to
 provide an operational iontophoretic sampling device 30, the media are in
 contact with the electrodes to provide a electrical contact therewith.
 In one embodiment, the electrode assemblies can include bimodal electrodes
 as shown in FIG. 3.
 Referring now to FIG. 5, an exploded view of the key components from one
 embodiment of an iontophoretic sampling system (e.g., one embodiment of an
 autosensor assembly) is presented. The sampling system components include
 two biosensor/iontophoretic electrode assemblies, 504 and 506, each of
 which have an annular iontophoretic electrode, respectively indicated at
 508 and 510, which encircles a biosensor 512 and 514. The electrode
 assemblies 504 and 506 are printed onto a polymeric substrate 516 which is
 maintained within a sensor tray 518. A collection reservoir assembly 520
 is arranged over the electrode assemblies, wherein the collection
 reservoir assembly comprises two hydrogel inserts 522 and 524 retained by
 a gel retaining layer 526 and a mask layer 528.
 In one embodiment, the electrode assemblies can include bimodal electrodes
 as shown in FIG. 3. Modifications and additions to the embodiment of FIG.
 5 will be apparent to those skilled in the art in light of the teachings
 of the present specification.
 The components described herein are intended for use in a automatic
 sampling device which is configured to be worn like an ordinary
 wristwatch. As described in International Publication No. WO 96/00110,
 published Jan. 4, 1996, the wristwatch housing (not shown) contains
 conductive leads which communicate with the iontophoretic electrodes and
 the biosensor electrodes to control cycling and provide power to the
 iontophoretic electrodes, and to detect electrochemical signals produced
 at the biosensor electrode surfaces. The wristwatch housing can further
 include suitable electronics (e.g., microprocessor, memory, display and
 other circuit components) and power sources for operating the automatic
 sampling system.
 Modifications and additions to the embodiment of FIG. 2 will be apparent to
 those skilled in the art in light of the teachings of the present
 specification.
 A power source (e.g., one or more rechargeable or nonrechargeable
 batteries) can be disposed within the housing 32 or within the straps 34
 which hold the device in contact with a skin or mucosal surface of a
 subject. In use, an electric potential (either direct current or a more
 complex waveform) is applied between the two iontophoretic electrodes 12
 and 14 such that current flows from the first iontophoretic electrode 12,
 through the first conductive medium 8 into the skin or mucosal surface,
 and then back out through the second conductive medium 10 to the second
 iontophoretic electrode 14. The current flow is sufficient to extract
 substances including an analyte of interest through the skin into one or
 both of collection reservoirs 4 and 6. The electric potential may be
 applied using any suitable technique, for example, the applied current
 density may be in the range of about 0.01 to 0.5 mA/cm.sup.2. In a
 preferred embodiment, the device is used for continual or continuous
 monitoring, and the polarity of iontophoretic electrodes 12 and 14 is
 alternated at a rate of about one switch every 10 seconds to about one
 switch every hour so that each electrode is alternately a cathode or an
 anode. The housing 32 can further include an optional temperature sensing
 element (e.g., a thermistor, thermometer, or thermocouple device) which
 monitors the temperature at the collection reservoirs to enable
 temperature correction of sensor signals as described in detail below. The
 housing can also include an optional conductance sensing element (e.g., an
 integrated pair of electrodes) which monitors conductance at the skin or
 mucosal surface to enable data screening correction or invalidation of
 sensor signals as also described in detail below.
 After a suitable iontophoretic extraction period, one or both of the sensor
 electrode sets can be activated in order to detect extracted substances
 including the analyte of interest. Operation of the iontophoretic sampling
 device 30 is controlled by a controller 36 (e.g., a microprocessor), which
 interfaces with the iontophoretic electrodes, the sensor electrodes, the
 power supply, the optional temperature and/or conductance sensing
 elements, a display and other electronics. For example, the controller 36
 can include a programmable a controlled circuit source/sink drive for
 driving the iontophoretic electrodes. Power and reference voltage are
 provided to the sensor electrodes, and signal amplifiers can be used to
 process the signal from the working electrode or electrodes. In general,
 the controller discontinues the iontophoretic current drive during sensing
 periods. A sensor confidence loop can be provided for continually
 monitoring the sampling system to insure proper operations.
 In a further aspect, the sampling device can operate in an alternating
 polarity mode using first and second bimodal electrodes (FIGS. 4, 40 and
 41) and two collection reservoirs (FIGS. 4, 47 and 48). Each bi-modal
 electrode (FIGS. 3, 30; FIGS. 4, 40 and 41) serves two functions depending
 on the phase of the operation: (1) an electro-osmotic electrode (or
 iontophoretic electrode) used to electrically draw analyte from a source
 into a collection reservoir comprising water and an electrolyte, and to
 the area of the electrode subassembly; and (2) as a counter electrode to
 the first sensing electrode at which the chemical compound is
 catalytically converted at the face of the sensing electrode to produce an
 electrical signal.
 The reference (FIGS. 4, 44 and 45; FIGS. 3, 32) and sensing electrodes
 (FIGS. 4, 42 and 43; FIGS. 3, 31), as well as, the bimodal electrode
 (FIGS. 4, 40 and 41; FIGS. 3, 30) are connected to a standard potentiostat
 circuit during sensing. In general, practical limitations of the system
 require that the bimodal electrode will not act as both a counter and
 iontophoretic electrode simultaneously.
 The general operation of an iontophoretic sampling system is the cyclical
 repetition of two phases: (1) a reverse-iontophoretic phase, followed by a
 (2) sensing phase. During the reverse iontophoretic phase, the first
 bimodal electrode (FIGS. 4, 40) acts as an iontophoretic cathode and the
 second bimodal electrode (FIGS. 4, 41) acts as an iontophoretic anode to
 complete the circuit. Analyte is collected in the reservoirs, for example,
 a hydrogel (FIGS. 4, 47 and 48). At the end of the reverse iontophoretic
 phase, the iontophoretic current is turned off. During the sensing phase,
 in the case of glucose, a potential is applied between the reference
 electrode (FIGS. 4, 44) and the sensing electrode (FIGS. 4, 42). The
 chemical signal reacts catalytically on the catalytic face of the first
 sensing electrode (FIGS. 4, 42) producing an electrical current, while the
 first bi-modal electrode (FIGS. 4, 40) acts as a counter electrode to
 complete the electrical circuit.
 The electrode described is particularly adapted for use in conjunction with
 a hydrogel collection reservoir system for monitoring glucose levels in a
 subject through the reaction of collected glucose with the enzyme glucose
 oxidase present in the hydrogel matrix.
 The bi-modal electrode is preferably comprised of Ag/AgCl. The
 electrochemical reaction which occurs at the surface of this electrode
 serves as a facile source or sink for electrical current. This property is
 especially important for the iontophoresis function of the electrode.
 Lacking this reaction, the iontophoresis current could cause the
 hydrolysis of water to occur at the iontophoresis electrodes causing pH
 changes and possible gas bubble formation. The pH changes to acidic or
 basic pH could cause skin irritation or burns. The ability of an Ag/AgCl
 electrode to easily act as a source of sink current is also an advantage
 for its counter electrode function. For a three electrode electrochemical
 cell to function properly, the current generation capacity of the counter
 electrode should not limit the speed of the reaction at the sensing
 electrode. In the case of a large sensing electrode, the counter electrode
 should be able to source proportionately larger currents.
 The design of the sampling system provides for a larger sensing electrode
 (see for example, FIG. 3) than previously designed. Consequently, the size
 of the bimodal electrode should be sufficient so that when acting as a
 counter electrode with respect to the sensing electrode the counter
 electrode does not become limiting the rate of catalytic reaction at the
 sensing electrode catalytic surface.
 Two methods exist to ensure that the counter electrode does not limit the
 current at the sensing electrode: (1) the bi-modal electrode is made much
 larger than the sensing electrode, or (2) a facile counter reaction is
 provided.
 During the reverse iontophoretic phase, the power source provides a current
 flow to the first bi-modal electrode to facilitate the extraction of the
 chemical signal into the reservoir. During the sensing phase, the power
 source is used to provide voltage to the first sensing electrode to drive
 the conversion of chemical signal retained in reservoir to electrical
 signal at the catalytic face of the sensing electrode. The power source
 also maintains a fixed potential at the electrode where, for example
 hydrogen peroxide is converted to molecular oxygen, hydrogen ions, and
 electrons, which is compared with the potential of the reference electrode
 during the sensing phase. While one sensing electrode is operating in the
 sensing mode it is electrically connected to the adjacent bimodal
 electrode which acts as a counter electrode at which electrons generated
 at the sensing electrode are consumed.
 The electrode sub-assembly can be operated by electrically connecting the
 bimodal electrodes such that each electrode is capable of functioning as
 both an iontophoretic electrode and counter electrode along with
 appropriate sensing electrode(s) and reference electrode(s), to create
 standard potentiostat circuitry.
 A potentiostat is an electrical circuit used in electrochemical
 measurements in three electrode electrochemical cells. A potential is
 applied between the reference electrode and the sensing electrode. The
 current generated at the sensing electrode flows through circuitry to the
 counter electrode (i.e., no current flows through the reference electrode
 to alter its equilibrium potential). Two independent potentiostat circuits
 can be used to operate the two biosensors. For the purpose of the present
 sampling system, the electrical current measured at the sensing electrode
 subassembly is the current that is correlated with an amount of chemical
 signal.
 With regard to continual operation for extended periods of time, Ag/AgCl
 electrodes are provided herein which are capable of repeatedly forming a
 reversible couple which operates without unwanted electrochemical side
 reactions (which could give rise to changes in pH, and liberation of
 hydrogen and oxygen due to water hydrolysis). The Ag/AgCl electrodes of
 the present sampling system are thus formulated to withstand repeated
 cycles of current passage in the range of about 0.01 to 1.0 mA per
 cm.sup.2 of electrode area. With regard to high electrochemical purity,
 the Ag/AgCl components are dispersed within a suitable polymer binder to
 provide an electrode composition which is not susceptible to attack (e.g.,
 plasticization) by components in the collection reservoir, e.g., the
 hydrogel composition. The electrode compositions are also formulated using
 analytical- or electronic-grade reagents and solvents, and the polymer
 binder composition is selected to be free of electrochemically active
 contaminants which could diffuse to the biosensor to produce a background
 current.
 Since the Ag/AgCl iontophoretic electrodes must be capable of continual
 cycling over extended periods of time, the absolute amounts of Ag and AgCl
 available in the electrodes, and the overall Ag/AgCl availability ratio,
 can be adjusted to provide for the passage of high amounts of charge.
 Although not limiting in the sampling system described herein, the Ag/AgCl
 ratio can approach unity. In order to operate within the preferred system
 which uses a biosensor having a geometric area of 0.1 to 3 cm.sup.2, the
 iontophoretic electrodes are configured to provide an approximate
 electrode area of 0.3 to 1.0 cm.sup.2, preferably about 0.85 cm.sup.2.
 These electrodes provide for reproducible, repeated cycles of charge
 passage at current densities ranging from about 0.01 to 1.0 mA/cm.sup.2 of
 electrode area. More particularly, electrodes constructed according to the
 above formulation parameters, and having an approximate electrode area of
 0.85 cm.sup.2, are capable of a reproducible total charge passage (in both
 anodic and cathodic directions) of 270 mC, at a current of about 0.3 mA
 (current density of 0.35 mA/cm.sup.2) for 48 cycles in a 24 hour period.
 Once formulated, the Ag/AgCl electrode composition is affixed to a suitable
 rigid or flexible nonconductive surface as described above with respect to
 the biosensor electrode composition. A silver (Ag) underlayer is first
 applied to the surface in order to provide uniform conduction. The Ag/AgCl
 electrode composition is then applied over the Ag underlayer in any
 suitable pattern or geometry using various thin film techniques, such as
 sputtering, evaporation, vapor phase deposition, or the like, or using
 various thick film techniques, such as film laminating, electroplating, or
 the like. Alternatively, the Ag/AgCl composition can be applied using
 screen printing, pad printing, inkjet methods, transfer roll printing, or
 similar techniques. Preferably, both the Ag underlayer and the Ag/AgCl
 electrode are applied using a low temperature screen print onto a
 polymeric substrate. This low temperature screen print can be carried out
 at about 125 to 160.degree. C., and the screening can be carried out using
 a suitable mesh, ranging from about 100-400 mesh.
 User control can be carried out using push buttons located on the housing
 32, and an optional liquid crystal display (LCD) can provide visual
 prompts, readouts and visual alarm indications. The microprocessor
 generally uses a series of program sequences to control the operations of
 the sampling device, which program sequences can be stored in the
 microprocessor's read only memory (ROM). Embedded software (firmware)
 controls activation of measurement and display operations, calibration of
 analyte readings, setting and display of high and low analyte value
 alarms, display and setting of time and date functions, alarm time, and
 display of stored readings. Sensor signals obtained from the sensor
 electrodes are processed before storage and display by one or more signal
 processing functions or algorithms which are described in detail below.
 The microprocessor can also include an electronically erasable,
 programmable, read only memory (EEPROM) for storing calibration parameters
 (as described in detail below), user settings and all downloadable
 sequences.
 Step B
 Data Screening Methodologies
 The raw signal obtained from the above-described glucose monitoring device
 can be screened to detect deviations from expected behavior which are
 indicative of poor or incorrect signals that will not correlate with blood
 glucose. Signals that are identified as poor or incorrect in this data
 screen may be discarded or otherwise corrected for prior to any signal
 processing and/or conversion in order to maintain data integrity. In the
 method of the invention, an objective set of selection criteria is
 established which can then be used to accept or discard signals from the
 sensing device. These selection criteria are device- and analyte-specific,
 and can be arrived at empirically by way of testing various devices in
 particular applications.
 In the particular context of transdermal blood glucose monitoring using
 iontophoretic extraction and electrochemical detection, the following data
 screens can be employed. As discussed above, the iontophoretic extraction
 device can include two collection reservoirs. Thus, in active/blank
 systems, wherein one reservoir is active (contains the GOx enzyme) and one
 reservoir is blank, each reservoir contains an iontophoretic electrode and
 a sensing electrode. Signals from both the active and the blank reservoirs
 are screened, and an error in either the active, or the active and blank
 signal can be used to invalidate or correct the measurement from the
 cycle. In multiple active systems (wherein two or more reservoirs contain
 the GOx enzyme and iontophoretic and sensing electrodes), signals from one
 or more of the active reservoirs are screened, and an error can be used to
 invalidate or correct the measurement from the cycle.
 As with any chemical sensing method, transient changes in temperature
 during or between measurement cycles, or between measurements of blank and
 active signals, can alter background signal, reaction constants and/or
 diffusion coefficients. Accordingly, a temperature sensor is used to
 monitor changes in temperature over time. A maximum temperature change
 over time (d(temp)/d(time)) threshold value can then be used in a data
 screen to invalidate a measurement. Such a threshold value can, of course,
 be set at any objective level, which in turn can be empirically determined
 depending upon the particular extraction/sensing device used, how the
 temperature measurement is obtained, and the analyte being detected.
 Absolute temperature threshold criteria can also be employed, wherein
 detection of high and/or low temperature extremes can be used in a data
 screen to invalidate a measurement. Temperature monitoring can be carried
 out using a separate, associated temperature sensing device, or,
 preferably using a temperature sensor that is integral with the sensing
 device. A large number of temperature sensing elements are known in the
 art (e.g., thermometers, thermistors, thermocouples, and the like) which
 can be used to monitor the temperature in the collection reservoirs.
 Another data screen entails monitoring physiological conditions in the
 biological system, particularly monitoring for a perspiration threshold.
 In this regard, perspiration contains glucose, and perspiration occurring
 rapidly and in sufficient quantities may affect the detected signal either
 before or during biosensor measurement. Accordingly, a sensor can be used
 to monitor perspiration levels for a given measurement cycle at time
 points before, during, and/or after iontophoresis, and before, during,
 and/or after glucose sensing. Detection of perspiration levels that exceed
 an objective threshold is then used in a data screen to invalidate poor
 measurements. Although a number of different mechanisms can be used, skin
 conductance can be readily measured with a device contacted with the skin.
 Skin conductivity is related to perspiration. In one embodiment, if skin
 conductance as measured by a conductivity detector is greater than a
 predetermined level, then the corresponding measurement is invalidated.
 Yet further data screens which are used in the practice of the invention
 take into consideration the expected behavior of the sampling/sensing
 device. In iontophoretic sampling, for example, there is a skin
 equilibration period before which measurements will generally be less
 accurate. During this equilibration period, the system voltage can be
 assessed and compared against an objective high voltage threshold. If this
 high voltage limit is exceeded, a data screen is used to exclude the
 corresponding analyte measurement, since the iontophoretic current was not
 at a target value due to high skin resistance (as indicted by the high
 voltage level).
 In addition, the electrochemical signal during each sensing cycle is
 expected to behave as a smooth, monotonically decreasing signal which
 represents depletion of the hydrogen peroxide by the sensor electrode.
 Significant departure from this expected behavior is indicative of a poor
 or incorrect measurement (e.g., a non-monotonically decreasing signal is
 indicative of excessive noise in the biosensor signal), and thus
 monitoring signal behavior during sensing operations provides yet a
 further data screen for invalidating or correcting measurements.
 Raw signal thresholds can also be used in the data screening method of the
 present invention. For example, any sensor reading that is less than some
 minimum threshold can indicate that the sampling/sensing device is not
 operating correctly, for example, where the biosensor electrode is
 disconnected. In addition, any chemical sensor will have a maximum range
 in which the device can operate reliably. A reading greater than some
 maximal value, then, indicates that the measurement is off-scale, and thus
 possibly invalid. Accordingly, minimum and maximum signal thresholds are
 used herein as data screens to invalidate or correct measurements. Such
 minimum and maximum thresholds can likewise be applied to background
 measurements.
 A general class of screens can be applied that detect changes in signal,
 background, or voltage measurements. These screens are useful to assess
 the consistency of measurements and can detect problems or inconsistencies
 in the measurements. Error messages can be relayed to a display screen on
 the monitoring device, and/or, recorded to a log. Examples of such screens
 include the following:
 (i) signal--Peak Stability. A large change in the peak of a sensor reading
 indicates a noisy signal. The peak of any given cathodal half cycle is
 defined as the difference between the first biosensor point and the
 temperature corrected average of the last two points from the previous
 anodal half cycle. If the percentage difference between successive peaks
 from the same sensor is greater than a predetermined value, for example,
 30%, then an error is indicated.
 (ii) background--Background Precision. Divergent readings at the end of
 biosensing indicate an unstable biosensor signal. Because these readings
 are used to assess background current for a particular cycle, an unstable
 signal may lead to an erroneous data point. If the difference between the
 last two anodal points (where the last two anodal points are typically the
 last two biosensor currents measured after anodal extraction) used to
 calculate the baseline is greater than or equal to a predetermined value,
 for example, 6 nA (or, e.g., a percentage of the first anodal point
 relative to the second anodal point), then an error is indicated.
 (iii) background--Background Stability. This check is to determine if the
 background current is changing too excessively, which indicates a noisy
 signal and can result in inaccurate glucose readings. If the percentage
 difference between successive background measurements is greater than or
 equal to a predetermined value, for example, 15%, then an error is
 indicated.
 (iv) voltage--Voltage Stability. If the glucose monitoring device is
 mechanically disturbed, there can be a larger change (e.g., larger
 relative to when the monitor is functioning under normal conditions) in
 iontophoresis voltage. This could lead to an aberrant reading. If the
 percentage difference between successive cathodal or anodal iontophoresis
 voltages is grater than a predetermined value, for example, 15%, then an
 error is indicated.
 (v) voltage--Reference Electrode Check. When the electrode assembly
 includes a reference electrode (as when, for example, a bimodal electrode
 is employed) this check establishes the connectivity of the reference
 electrode to the sampling device and to the working electrode. The
 biosensor is activated such that a current should flow from the working
 electrode to the reference electrode. If the current measured is less than
 a threshold value, then an error is indicated and the measurement sequence
 can be terminated.
 As will be appreciated by one of ordinary skill in the art upon reading
 this specification, a large number of other data screens can be employed
 without departing from the spirit of the present invention.
 Step C
 The Conversion Step
 Continuing with the method of the invention, the above-described
 iontophoretic sampling device is used to extract the analyte from the
 biological system, and a raw amperometric signal (e.g., nanoampere (nA)
 signal) is generated from the associated electrochemical biosensor device.
 This raw signal can optionally be subjected to a data screening step (Step
 B) to eliminate poor or incorrect signals, or can be entered directly into
 a conversion step to obtain an initial signal output which is indicative
 of the amount of analyte extracted by the sampling system.
 I. Ways of Obtaining Integrated Signals
 1. Baseline Background
 In one embodiment, the raw or screened raw signal is processed in the
 conversion step in order to remove or correct for background information
 present in the signal. For example, many sensor devices will have a signal
 whether or not an analyte of interest is present, i.e., the background
 signal. One such background signal is the "baseline background," which, in
 the context of electrochemical detection, is a current (nA) generated by
 the sensing device independent of the presence or absence of the analyte
 of interest. This baseline background interferes with measurement of
 analyte of interest, and the amount of baseline background can vary with
 time, temperature and other variable factors. In addition,
 electrochemically active interfering species and/or residual analyte can
 be present in the device which will further interfere with measurement of
 the analyte of interest.
 This background can be transient background, which is a current generated
 independent of the presence or absence of the analyte of interest and
 which decreases over the time of sensor activation on the time scale of a
 measurement, eventually converging with the baseline background signal.
 Accordingly, in one embodiment of the invention, a baseline background
 subtraction method is used during the conversion step in order to reduce
 or eliminate such background interferences from the measured initial
 signal output. The subtraction method entails activation of the
 electrochemical sensor for a sufficient period of time to substantially
 reduce or eliminate residual analyte and/or electrochemical signal that is
 not due to the analyte (glucose). After the device has been activated for
 a suitable period of time, and a stable signal is obtained, a measurement
 is taken from the sensor which measurement can then be used to establish a
 baseline background signal value. This background signal value is
 subtracted from an actual signal measurement value (which includes both
 analyte-specific and background components) to obtain a corrected
 measurement value. This baseline background subtraction method can be
 expressed using the following function:
EQU i(.tau.)=i.sub.raw (.tau.)-i.sub.bkgnd (.tau.)
 wherein: (i.sub.raw (.tau.)) is the current measured by the sensor (in nA)
 at time .tau.; (.tau.) is the time after activation of the sensor;
 (i.sub.bkgnd (.tau.)) is the background current (in nA); and (i(.tau.)) is
 the corrected current (in nA). Measurement of the baseline background
 signal value is taken close in time to the actual signal measurement in
 order to account for temperature fluctuations, background signal drift,
 and like variables in the baseline background subtraction procedure. The
 baseline background signal value can be integrated for use with
 coulometric signal processing, or used as a discrete signal value in
 amperometric signal processing. In particular embodiments of the
 invention, continual measurement by the iontophoretic sampling device
 provides a convenient source for the baseline background measurement, that
 is, after an initial measurement cycle has be completed, the baseline
 background measurement can be taken from a previous measurement (sensing)
 cycle.
 2. Temperature Correcting Baseline Background
 In yet another embodiment of the invention, the conversion step is used to
 correct for changing conditions in the biological system and/or the
 biosensor system (e.g., temperature fluctuations in the biological system,
 temperature fluctuations in the biosensor element, or combinations
 thereof). Temperature can affect the signal in a number of ways, such as
 by changing background, reaction constants, and/or diffusion coefficients.
 Accordingly, a number of optional temperature correction functions can be
 used in order to reduce these temperature-related effects on the signal.
 In order to correct for the effect that temperature fluctuations or
 differences may have on the baseline background subtracted signal, the
 following temperature correction step can be carried out. More
 particularly, to compensate for temperature fluctuations, temperature
 measurements can be taken at each measurement time point within the
 measurement cycle, and this information can be used to base a temperature
 correction algorithm which adjusts the background current at every time
 point depending on the difference in temperature between that time point
 and the temperature when the previous background current was measured.
 This particular temperature correction algorithm is based on an Arrhenius
 relationship between the background current and temperature.
 The temperature correction algorithm assumes an Arrhenius-type temperature
 dependence on the background current, such as:
 ##EQU1##
 wherein: (i.sub.bkgnd) is the background current; (A) is a constant; (K1)
 is termed the "Arrhenius slope" and is an indication of how sensitive the
 current is to changes in temperature; and (T) is the temperature in
 .degree. K.
 Plotting the natural log of the background current versus the reciprocal of
 temperature provides a linear function having a slope of (-K1). Using a
 known or derived value of K1 allows the baseline current at any time
 (.tau.) to be corrected using the following function (which is referred to
 herein as the "K1 temperature correction"):
 ##EQU2##
 wherein: (i.sub.bkgnd,corrected) is the temperature corrected baseline
 current; (i.sub.bkgnd,.tau.0) is the baseline current at some reference
 temperature T.sub..tau.0, for example, the baseline background measurement
 temperature; (K1) is the temperature correction constant; and
 (T.sub..tau.) is the temperature at time .tau.. For the purposes of the
 invention, (i.sub.bkgnd,.tau.0) is usually defined as the "previous"
 baseline current. As can be seen, instead of making a time-independent
 estimation of the baseline current, the K1 temperature correction adjusts
 the baseline current in an Arrhenius fashion depending upon whether the
 temperature increases or decreases during or between biosensor cycles.
 Determination of the constant K1 can be obtained by plotting the natural
 log of the background current versus the reciprocal of the temperature for
 a learning set of data, and then using a best fit analysis to fit this
 plot with a line having a slope (-K1).
 Raw or screened amperometric signals from Step A or Step B, respectively
 (whether or not subjected to the above-described baseline background
 subtraction and/or K1 temperature correction), can optionally be refined
 in the conversion step to provide integrated coulometric signals. In one
 particular embodiment of the invention, any of the above amperometric
 signals (e.g., the current generated by the sensor) can be converted to a
 coulometric signal (nanocoulombs (nC)), which represents the integration
 of the current generated by the sensor over time to obtain the charge that
 was produced by the electrochemical reaction.
 In one embodiment, integration is carried out by operating the biosensor in
 a coulometric (charge-measuring) mode. Measuring the total amount of
 charge that passes through the biosensor electrode during a measurement
 period is equivalent to mathematically integrating the current over time.
 By operating in the coulometric mode, changes in diffusion constants
 resulting from temperature fluctuations, possible changes in the diffusion
 path length caused by uneven or non-uniform reservoir thickness, and
 changes in sensor sensitivity, have little effect on the integrated
 signal, whereas these parameters may have a greater effect on single point
 (current) measurements. Alternatively, a functionally equivalent
 coulometric measurement can be mathematically obtained in the method of
 the invention by taking discrete current measurements at selected,
 preferably small, time intervals, and then using any of a number of
 algorithms to approximate the integral of the time-current curve. For
 example, integrated signal can be obtained as follows:
 ##EQU3##
 wherein: (Y) is the integrated signal (in nC); and (i(.tau.)) is a current
 at time .tau., and can be equal to i.sub.raw (.tau.) for an uncorrected
 raw signal, or i.sub.raw (.tau.)-i.sub.bkgnd (.tau.) for a baseline
 background subtracted signal, or i.sub.raw (.tau.)-i.sub.bkgnd,corrected
 (.tau.) for a baseline background subtracted and temperature corrected
 signal.
 3. Temperature Correction of Active Versus Blank Integrals
 An additional temperature correction algorithm can be used herein to
 compensate for temperature dependence of a transient background (blank)
 signal. That is, in the active/blank sampling system exemplified
 hereinabove, the analyte measurement (blood glucose) is generated by
 integrating an active signal and subtracting therefrom a blank signal (see
 the blank subtraction method, infra). The blank integral may be
 "artifactually" high or low depending upon whether blank signal was
 measured at a higher or lower temperature than the active signal. In order
 to normalize the blank integral to the temperature at which the active
 signal was measured, the following function can be used (which is referred
 to herein as the "K2 temperature correction"):
 ##EQU4##
 wherein: (Y.sub.blank,corrected) is the corrected blank integral;
 (Y.sub.blank) is the uncorrected blank integral (in nC); (K2) is the
 "blank integral correction constant"; and (T.sup.n.sub.act) and
 (T.sup.n.sub.blank) are the average temperature of the active and blank
 signal, respectively. The average temperature is obtained from averaging
 the first n temperatures, such that (n) is also an adjustable parameter.
 Determination of the constant K2 can be obtained from an Arrhenius plot of
 the log of the blank integral against 1/T.sup.n.sub.blank, using the
 reciprocal of the average of the first n temperature values, and then
 using a best fit analysis to fit this plot with a line having a slope
 (-K2).
 Alternative temperature corrections which can be performed during the
 conversion step are as follows. In one embodiment, an integral average
 temperature correction is used wherein, for each measurement cycle, the
 integral average temperature is determined by the function:
 ##EQU5##
 and then correcting for the temperature at subsequent time points using the
 function:
 ##EQU6##
 wherein: (Y.sub.t) is the uncorrected signal at time t; (Y.sub.t,corrected)
 is the corrected signal at time t; (&lt;T.sub.t &gt;) is the integral average
 temperature at time t; (&lt;T.sub.ref &gt;) is the integral average temperature
 at the reference time (e.g., the calibration time); (t) is the time after
 sensor measurement is first initiated; and (a) is an adjustable parameter
 which is fit to the data.
 In other embodiments, temperature correction functions can be used to
 correct for temperature differences between multiple active signals, or
 between active and blank signals. For example, in the active/blank sensing
 device exemplified herein, blank subtraction is used to cancel out much of
 the temperature-dependence in the active signal. However, temperature
 transients during the monitoring period will result in varying background
 currents, which can result in signal errors when the current is multiplied
 by the total integration time in the instant conversion step. This is
 particularly true where the active and blank integrals are disjointed in
 time, and thus possibly comprised of sets of background current values
 that occurred at different temperatures.
 4. Anodal Subtraction
 In yet another alternative temperature correction, temperature measurements
 taken in the active and blank reservoirs at alternating anodal and
 cathodal phases during a measurement cycle are used in a subtraction
 method in order to reduce the impact of temperature fluctuations on the
 signals. In this regard, the active/blank reservoir iontophoretic sampling
 system can be run under conditions which alternate the active and blank
 reservoirs between anodal and cathodal phases during a measurement cycle.
 This allows the blank anodal signal to be measured at the same time as the
 active cathode signal, and temperature variations will likely have similar
 impact on the two signals. The temperature correction function thus
 subtracts an adjusted anodal signal (taken at the same time as the
 cathodal signal) from the cathodal signal in order to account for the
 effect of temperature on the background. More particularly, a number of
 related temperature correction functions which involve fractional
 subtraction of blank anode signals can be summarized as follows:
 ##EQU7##
 wherein: (Y.sub.act, cath) is the active signal in the cathodal phase (in
 nC); (Y.sub.blank, an) is the blank signal in the anodal phase (in nC);
 (Y.sub.act, an) is the active signal in the anodal phase (in nC);
 (Y.sub.blank, cath) is the blank signal in the cathodal phase (in nC); (Y)
 is the "blank anode subtracted" signal; (ave t.sub.1, t.sub.2) is the
 average of signals taken at two time points t.sub.1 and t.sub.2 ; (ave
 t.sub.1 -t.sub.2) is the average of signals taken over the time period of
 t.sub.1 -t.sub.2 ; (d) is a universal fractional weight and is generally a
 function of time; and (AOS) is a universal anodal offset which can be
 empirically obtained using standard mathematical techniques, and
 optionally adjusted using data taken from two previous time points,
 t.sub.1 and t.sub.2 (i.e., ave t.sub.1, t.sub.2) or using the average of
 data taken over the time period of t.sub.1 -t.sub.2 (i.e., ave t.sub.1
 -t.sub.2).
 In still further embodiments of the invention, the conversion step can
 include a blank subtraction step, combined data from two active
 reservoirs, and/or a smoothing step.
 The blank subtraction step is used to subtract the blank signal from the
 active signal in order to remove signal components that are not related to
 the analyte, thus obtaining a cleaner analyte signal. When raw signal is
 obtained from two active reservoirs the two raw signals can be averaged or
 a summed value of the two raw signals can be used. In the smoothing step,
 mathematical transformations are carried out which individually smooth
 signals obtained from the active and blank collection reservoirs. These
 smoothing algorithms help improve the signal-to-noise ratio in the
 biosensor, by allowing one to correct the signal measurements obtained
 from the device to reduce unwanted noise while maintaining the actual
 signal sought.
 More particularly, a blank subtraction step is used in the active-blank
 iontophoretic sampling system of the invention as follows. Signals from
 the blank (second) reservoir, taken at, or about the same time as signals
 from the active (first) reservoir, are used to substantially eliminate
 signal components from the active signal that are not specifically related
 to the analyte. In this regard, the blank reservoir contains all of the
 same components as the active reservoir except for the GOx enzyme, and the
 blank signal should thus exhibit similar electrochemical current to the
 active signal, except for the signal associated with the analyte.
 Accordingly, the following function can be used to subtract the blank
 signal from the active signal:
EQU Y.sub.t =Y.sub.t,act -d*Y.sub.t,blank
 wherein: (Y.sub.t,act) is the active signal (in nC) at time t;
 (Y.sub.t,blank) is the blank signal (in nC) at time t; (Y.sub.t) is the
 "blank subtracted" signal at time t; and (d) is the time-dependent
 fractional weight for the blank signal, and d preferably=1. In relation to
 the equation shown above that is used to subtract the blank signal from
 the active signal, when two active reservoirs are used d preferably=-1,
 or, more generally, as shown in the equation below, the summed signal can
 be "weighted" to account for different contributions of signal from each
 reservoir.
 In the case of two active reservoirs, each reservoir is capable of
 generating raw signal and each contains all of the same components. For
 example, where two collection reservoirs are used for detecting glucose
 both reservoirs contain glucose oxidase. Accordingly, the following
 function can be used:
EQU Y.sub.t,.epsilon. =aY.sub.t,act1 +bY.sub.t,act2
 wherein: "a" is the time-dependent fractional weight for the first active
 signal; (Y.sub.t,act1) is the first active signal (in nC) at time t; "b"
 is the time-dependent fractional weight for the second active signal;
 (Y.sub.t,act2) is the second active signal (in nC) at time t;
 (Y.sub.t,.epsilon.) is the summed signal at time t.
 II. General Procedures for Smoothing Integrated Signals
 In the smoothing step, the active signal obtained from the first (active)
 reservoir can be smoothed using a smoothing function. In multiple active
 systems, the same smoothing can be applied to each signal before summing.
 In one embodiment, the function can be expressed as a recursive function
 as follows:
EQU E.sub.t,act =w.sub.act Y.sub.t,act +(1-w.sub.act)(E.sub.t-1,act)
 wherein: (Y.sub.t,act) is the measurement of the active signal (in nC) at
 time t; (E.sub.t,act) is the estimate of the active signal (in nC) at time
 t for t&gt;1 (at t=1, E.sub.t,act =Y.sub.t,act); and (w.sub.act) is the
 "estimate weight" for the active biosensor, wherein
 0.ltoreq.w.sub.act.ltoreq.1.
 The reference (blank) signal obtained from the second reservoir can also be
 smoothed using a similar recursive smoothing function. This function can
 be expressed as follows:
EQU E.sub.t,blank =w.sub.blank Y.sub.t,blank +(1-w.sub.blank)(E.sub.t-1,blank)
 wherein: (Y.sub.t,blank) is the measurement of the blank signal (in nC) at
 time t; (E.sub.t,blank) is the estimate of the blank signal (in nC) at
 time t for t&gt;1 (at t=1, E.sub.t,blank =Y.sub.t,blank); and (w.sub.blank)
 is the "estimate weight" for the blank biosensor, wherein
 0.ltoreq.w.sub.blank.ltoreq.1.
 Once the active and blank signals have been individually smoothed, the
 blank signal can be subtracted from the active signal in order to obtain a
 signal that is indicative of the glucose reaction only. As discussed
 above, the blank signal should exhibit a similar electrochemical current
 to the active signal, except for the signal associated with the glucose
 analyte. In the practice of the invention, this blank subtraction step can
 subtract the value of the smoothed blank signal per se, or a weighted
 blank signal can be subtracted from the active signal, using the following
 function to obtain a fractional subtraction:
EQU E.sub.t =E.sub.t,act -d*E.sub.t,blank
 wherein: (E.sub.t,act) is the estimate of the active signal (in nC) at time
 t; (E.sub.t,blank) is the estimate of the blank signal (in nC) at time t;
 (E.sub.t) is the "blank subtracted" smoothed sensor signal at time t; and
 (d) is the time-dependent fractional weight for the blank signal.
 The same recursive function can be used wherein the order of the smoothing
 and blank subtraction steps are reversed such that: (Y.sub.t,act) is the
 integral of the active signal (in nC) at time t; (Y.sub.t,blank) is the
 integral of the blank signal (in nC) at time t; (Y.sub.t) is the "blank
 subtracted" sensor signal (in nC) at time t; (d) is the time-dependent
 fractional weight for the blank signal; and
EQU Y.sub.t =Y.sub.t,act -d*Y.sub.t,blank
EQU E.sub.t =wY.sub.t +(1-w)(E.sub.t-1)
 This smoothing can alternatively be carried out on discrete (nA) sensor
 signals, with or without temperature and/or background subtraction
 corrections. Smoothing can also be carried out on active signals or on
 averages of two or more active signals. Further modifications to these
 functions will occur to those of ordinary skill in the art, in light of
 the present enabling disclosure.
 Step D
 The Calibration Step
 Continuing with the method of the invention, any of the raw signals
 obtained from Step A, the screened raw signal obtained from Step B, or the
 initial output signal obtained from Step C (or from Steps B and C), can be
 converted into an analyte-specific value using a calibration step which
 correlates the signal obtained from the sensing device with the
 concentration of the analyte present in the biological system. A wide
 variety of calibration techniques can be used to interpret such signals.
 These calibration techniques apply mathematical, statistical and/or
 pattern recognition techniques to the problem of signal processing in
 chemical analyses, for example, using neural networks, genetic algorithm
 signal processing, linear regression, multiple-linear regression, partial
 linear regression, deconvolution, or principal components analysis of
 statistical (test) measurements.
 One method of calibration involves estimation techniques. To calibrate an
 instrument using estimation techniques, it is necessary to have a set of
 exemplary measurements with known concentrations referred to as the
 calibration set (e.g., reference set). This set consists of m samples,
 each with n instrument variables contained in an m by n matrix (X), and an
 m by 1 vector (y), containing the concentrations. If a priori information
 indicates the relationship between the measurement and concentration is
 linear, the calibration will attempt to determine an n by 1 transformation
 or mapping (b), such that
EQU y=Xb
 is an optimal estimate of y according to a predefined criteria. Numerous
 suitable estimation techniques useful in the practice of the invention are
 known in the art. These techniques can be used to provide constant
 parameters, which can then be used in a mathematical transformation to
 obtain a measurement value indicative of the concentration of analyte
 present in the biological system at the times of measurement.
 In one particular embodiment, the calibration step may be carried out using
 artificial neural networks or genetic algorithms. The structure of a
 particular neural network algorithm used in the practice of the invention
 can vary widely; however, the network should contain an input layer, one
 or more hidden layers, and one output layer. Such networks can be
 optimized on training data set, and then applied to a population. There
 are an infinite number of suitable network types, transfer functions,
 training criteria, testing and application methods, which will occur to
 the ordinarily skilled artisan upon reading the instant specification.
 In the context of the iontophoretic glucose sampling device described
 hereinabove (which can contain an active collection reservoir--with the
 GOx enzyme, and a blank collection reservoir; or alternately, two active
 reservoirs with the GOx enzyme), a preferred neural network algorithm
 would use, for example, inputs selected from the following to provide a
 blood glucose measurement: elapsed time since calibration; signal from the
 active reservoir; signal from the blank reservoir; signal from two active
 reservoirs (either averaged or summed); calibration time; measured
 temperature; applied iontophoretic voltage; skin conductance; blood
 glucose concentration, determined by an independent means, at a defined
 calibration point; background; background referenced to calibration; and,
 when operating in the training mode, measured glucose.
 Whether or not the calibration step is carried out using conventional
 statistical techniques or neural network algorithms, the calibration step
 can include a universal calibration process, a single-point calibration
 process, or a multi-point calibration process. In one embodiment of the
 invention, a universal calibration process is used, wherein the above
 mathematical techniques are used to derive a correlation factor (or
 correlation algorithm) that allows for accurate, dependable quantification
 of analyte concentration by accounting for varying backgrounds and signal
 interferences irrespective of the particular biological system being
 monitored. In this regard, the universal calibrant is selected to provide
 a close correlation (i.e., quantitative association) between a particular
 instrument response and a particular analyte concentration, wherein the
 two variables are correlated.
 In another embodiment, a single-point calibration is used. More
 particularly, the single-point calibration process can be used to
 calibrate measurements obtained by iontophoretic sampling methodologies
 using a reference measurement obtained by conventional (invasive) methods.
 Single-point calibration allows one to account for variables that are
 unique to the particular biological system being monitored, and the
 particular sensing device that is being used. In this regard, the
 transdermal sampling device is generally contacted with the biological
 system (placed on the surface of a subject's skin) upon waking. After the
 device is put in place, it is preferable to wait a period of time in order
 allow the device to begin normal operations.
 Further, the sampling system can be pre-programmed to begin execution of
 its signal measurements (or other functions) at a designated time. One
 application of this feature is to have the sampling system in contact with
 a subject and to program the sampling system to begin sequence execution
 during the night so that it is available for calibration immediately upon
 waking. One advantage of this feature is that it removes any need to wait
 for the sampling system to warm-up before calibrating it.
 In the context of glucose monitoring, a blood sample can be extracted when
 the device has attained normal operations, such that the invasive blood
 sample extraction is taken in a corresponding time period with a
 measurement cycle. Actual blood glucose levels can then be determined
 using any conventional method (e.g., colorimetric, electrochemical,
 spectrophotometric, or the like) to analyze the extracted sample. This
 actual value is then used as a reference value in the single-point
 calibration process, wherein the actual value is compared against the
 corresponding measured value obtained with the transdermal sampling
 device. In yet another embodiment, a multi-point calibration process is
 used, wherein the above-described single-point calibration process is
 repeated at least once to provide a plurality of point calibrations. For
 example, the multi-point calibration process can be carried out at various
 time intervals over the course of a continual or continuous measuring
 period.
 Continuing with the calibration step, the signals obtained from Step B
 and/or Step C, supra, can be subjected to further signal processing prior
 to calibration as follows. Referring particularly to the baseline
 background subtraction method of the conversion step (Step C), the
 corrected signal should theoretically be directly proportional to the
 amount of analyte (glucose) present in the iontophoretically extracted
 sample. However, sometimes a non-zero intercept is obtained in the
 correlation between signal and reference glucose value. Accordingly, a
 constant offset term (which can be positive or negative) is obtained which
 can be added to the converted signal to account for a non-zero signal at
 an estimated zero blood glucose concentration. The offset can be added to
 the active sensor signal; or, in the case of an iontophoretic sampling
 system that obtains both active and blank signals, the offset can be added
 to the blank-subtracted active signal.
 The calibration step can be carried out using, for example, the
 single-point calibration method described hereinabove. The reference blood
 glucose concentration thus obtained can then be used in the following
 conversion factor:
 ##EQU8##
 wherein: (E.sub.cal) is the blank-subtracted smoothed sensor signal (in nC)
 at calibration; (BG.sub.cal) is the reference blood glucose concentration
 (in mg/dL) at calibration; (b.sub.gain) is the conversion factor [(mg/dL)
 /nC]; (OS) is the offset calibration factor constant (in nC) which can be
 calculated using standard regression analysis; and (.rho.) is the
 calibration offset (in mg/dL). Post calibration data can then be converted
 using the following function:
EQU EG.sub.t =b.sub.gain [E.sub.t +OS]-.rho.
 wherein (EG.sub.t) is the estimated blood glucose concentration (in mg/dL).
 Other signal values, such as Y.sub.t, can be substituted for E.sub.t and
 E.sub.cal depending upon the amount of prior signal processing performed
 (see, e.g., Step C, supra).
 Further signal processing can also be used to correct for time-dependent
 behavior related to the particular sensor element that is used in the
 sensing operation. In this regard, signal measurements of certain types
 (such as the electrochemical signal measurements described herein) exhibit
 change over time for reasons which are not fully understood. The present
 invention is not premised on any particular theory with respect to why
 such time-dependent change occurs. Rather, the invention recognizes that
 time-dependent behavior can occur, and corrects for this behavior using
 one or more mathematical functions.
 Thus, in one embodiment, a corrected measurement can be calculated using a
 mathematical function which compensates for time-dependent decline in the
 biosensor signal between measurements during the period of continual or
 continuous measuring of the analyte concentration. The correction function
 uses one or more additive decay parameters (.alpha..sub.i) and one or more
 multiplicative decay parameters (.epsilon..sub.i), (both of which are
 empirically determined for the biosensor), and can be expressed as
 follows:
EQU EG.sub.t =b.sub.gain [E.sub.t (1+.epsilon..sub.i t)+OS]+.alpha..sub.i
 t-.rho.
 wherein:
 ##EQU9##
 and (t.sub.cal) is the calibration point; (EG.sub.t) is the estimated blood
 glucose concentration at time t; (E.sub.t) is the analyte signal at time
 t; (OS) is the constant offset term which accounts for a non-zero signal
 at an estimated zero blood glucose concentration (as described above);
 (.epsilon.) is a gain term for time-dependent signal decline and can have
 multiple time segments (e.g., i=1, 2, or 3); (.alpha.) is a correction
 term for a linear time-dependent signal decline in the time segments and
 can have multiple time segments (e.g., i=1, 2, or 3); (t) is the elapsed
 time, and (.rho.) is the calibration offset (in mg/dl).
 In an alternative embodiment, a corrected measurement can be calculated
 using a mathematical function which compensates for time-dependent decline
 in the biosensor signal between measurements, during the period of
 continual or continuous measuring of the analyte concentration, by
 correlating signal at the beginning of the measurement series to a unit of
 decay. The correction function uses an additive decay parameter (.alpha.)
 and a decay correction factor (.gamma.). This equation allows a
 time-dependent multiplicative correction to be applied to the integrated
 signal in a manner that amplifies, to a greater extent, those signals that
 have been observed to decay at a greater rate (e.g., empirically, signals
 that give lower BGain tend to decay faster). Use of the BGAIN factor, as
 described herein, can insure that a reasonable calibration factor is
 obtained.
 In this embodiment, EG.sub.t, the calculated value of blood glucose at the
 measurement time, is computed as follows:
 ##EQU10##
 wherein: BG.sub.cal is the true blood glucose at the calibration point;
 E.sub.cal is the analyte signal at calibration; (t.sub.cal) is the elapsed
 time of the calibration point; (EG.sub.t) is the estimated blood glucose
 concentration at time t; (E.sub.t) is the analyte signal at time t; (OS)
 is the constant offset term which accounts for a non-zero signal at an
 estimated zero blood glucose concentration (as described above); (.gamma.)
 is a time-dependent correction term for signal decline; (.alpha.) is a
 time-dependent correction term for signal decline; and (t) is the elapsed
 time.
 Employing these equations a "time segmentation" can be performed as
 follows:
 ##EQU11##
 if t.sub.23 &lt;t.sub.cal
EQU EG.sub.t =(BGAIN.sub.1 +.gamma..sub.1 t)*(E.sub.t +OS)+.alpha..sub.1 t
 if t&lt;t.sub.12
 EG.sub.t =(BGAIN.sub.2 +.gamma..sub.1 t.sub.12 +.gamma..sub.2
 (t-t.sub.12))*(E.sub.t +OS)+.alpha..sub.1 t.sub.12 +.alpha..sub.2
 (t-t.sub.12)
 if t.sub.12 &lt;t&lt;t.sub.23
EQU EG.sub.t =(BGAIN.sub.3 +.gamma..sub.1 t.sub.12 +.gamma..sub.2 (t.sub.23
 -t.sub.12)+.gamma..sub.3 (t-t.sub.23))*(E.sub.t +OS)+.alpha..sub.1
 t.sub.12 +.alpha..sub.2 (t.sub.23 -t.sub.12)+.alpha..sub.3 (t-t.sub.23)
 if t.sub.23 &lt;t
 wherein: EG.sub.t is the calculated value of blood glucose at the
 measurement time; BG.sub.cal is the true blood glucose at the calibration
 point, t is the elapsed time (hence t.sub.cal is the elapsed time at the
 calibration point), OS is the offset parameter, .alpha..sub.i and
 .gamma..sub.i are the time dependent correction terms to account for the
 declining signal with time. To avoid a dominant time correction term as
 the elapsed time increases, the time correction parameters .alpha..sub.i
 and .gamma..sub.i are distinct for three different time intervals ("i"): 0
 to 6 hours (e.g., i=1), 6 to 10 hours (e.g., i=2), and 10 to 14 hours
 (e.g., i=3), as shown above. Therefore, t.sub.12 =6 hours and t.sub.23 =10
 hours.
 The time segmentation allows for greater flexibility in predicting
 non-linear signal decay terms.
 The signal processing methods and techniques described in Steps A through D
 can be combined in a variety of ways to provide for improved signal
 processing during analyte measurement. In one embodiment, an active/blank
 sampling system is used to obtain the raw signal in Step A. These raw
 signals are then screened in Step B to obtain screened data. These
 screened data are then subjected to a temperature correction using the K1
 temperature correction, and then converted using the baseline subtraction
 and integration methods of Step C. The converted data are also smoothed
 (both active and blank) using the smoothing functions of Step C, the
 smoothed data are temperature corrected using the K2 temperature
 correction, and a blank subtraction is carried out. The smoothed and
 corrected data are then converted to the analyte concentration in the
 biological system using the calibration methods of Step D to perform a
 single-point calibration, wherein the data is also refined using the
 offset and time-dependent behavior corrections to obtain a highly accurate
 analyte concentration value.
 In another embodiment, if two active reservoirs (A.sub.1 /A.sub.2) are
 used, a "sensor consistency check" can be employed that detects whether
 the signals from the reservoirs are changing in concert with one another.
 This check compares the percentage change from the calibration signal for
 each reservoir, then calculates the difference in percentage change in
 signal between the two reservoirs. If this difference is greater than some
 threshold, then the signals are not "tracking" one another and this data
 point can be screened as in Step B. This check verifies consistency
 between the two sensors. A large difference can indicate noise in the
 signals.
 In yet another embodiment of the present invention a "Calibration Factor
 Check" may be employed. This check provides control over unreasonable
 finger prick measurements or incorrect entries and provides additional
 assurance that a reasonable calibration slope has been generated.
 Typically, there are two calibration factors that are calculated at
 calibration: BGAIN and CAL RATIO. If BGAIN is less than or equal to a
 predetermined threshold value, or if the CAL RATIO is greater than or
 equal to a predetermined threshold value, then a calibration error is
 indicated. Such an error can be displayed to the user, for example, a
 calibration window can appear on the monitor's display appear. Such an
 error indicates to the users that the user must perform the calibration
 again. For the Calibration Factor Check, CAL RATIO can be calculated as
 follows:
 ##EQU12##
 wherein, BG.sub.cal is the true blood glucose at the calibration point;
 E.sub.cal is the analyte signal at calibration; and (OS) is the constant
 offset term which accounts for a non-zero signal at an estimated zero
 blood glucose concentration.
 Step E
 Time Forecasting Measurements
 The corrected analyte value obtained using the above techniques can be used
 to predict future (e.g., time forecasting) or past (e.g., calibration)
 target analyte concentrations in the biological system. In one embodiment,
 a series of analyte values are obtained by performing any combination of
 Steps A, B, C, and/or D, supra, in an iterative manner. These measurements
 are then used to predict unmeasured analyte values at different points in
 time, future or past.
 More particularly, the above-described iontophoretic sampling process is
 carried out in order to obtain three or more measurements of the target
 analyte. Using these measurements, an additional measurement can be
 calculated. The additional measurement is preferably calculated using a
 series function.
 In the context of blood glucose monitoring, it has been found that the
 actual (real-time) glucose level in a subject differs from the measured
 glucose level obtained using a sampling device that extracts glucose from
 the subject using iontophoresis. The difference is due, in part, to a lag
 time between extracting the glucose analyte and obtaining a measurement
 from the extracted glucose. This lag time can vary depending on factors
 such as the particular subject using the device, the particular area of
 skin from which glucose is extracted, the type of collection reservoir
 used, and the amount of current applied. In order to compensate for this
 inherent lag time, the method of the present invention can utilize data
 obtained from previous measurements and a mathematical function in order
 to predict what a future analyte concentration will be. In this case, the
 predicted future reading can be used as a "real-time value" of the analyte
 level.
 In another embodiment, mathematical methods can be used to predict past
 measurements, such as in the context of making a calibration. More
 particularly, measurements obtained using the above-described transdermal
 sampling device can be calibrated against one or more reference
 measurements obtained by conventional (blood extraction) methods. In such
 calibration processes, actual blood glucose levels are determined using
 conventional analytical methods (e.g., colorimetric, electrochemical,
 spectrophotometric, or the like) to analyze an extracted blood sample.
 These actual measurements are then compared with corresponding
 measurements obtained with the transdermal sampling device, and a
 conversion factor is then determined. In normal operations, the
 transdermal sampling device is generally first contacted with the
 biological system (placed on the surface of a subject's skin) upon waking.
 After the device is put in place, it is preferable to wait a period of
 time in order allow the device to attain normal operating parameters,
 after which time the device can be calibrated. However, if a blood sample
 is extracted at the time when the device is first applied (as would
 normally be most convenient), there may not be a corresponding signal from
 the transdermal sampling system which can be compared with the reference
 value obtained from the extracted blood sample. This problem can be
 overcome using prediction methods which allow one to perform a
 conventional blood glucose test (via a blood sample extraction) when the
 device is first applied, and then calibrate the device at a later time
 against the results of the conventional glucose test.
 A number of mathematical methods for predicting future or past measurements
 can be used in the practice of the invention. For example, linear or
 nonlinear regression analyses, time series analyses, or neural networks
 can be used to predict such measurements. However, it is preferred that a
 novel combination of exponential smoothing and a Taylor series analysis be
 used herein to predict the future or past measurement.
 A number of other physiological variables may be predicted using the above
 techniques. For example, these prediction methods can be used to time
 forecast those physiological variables that cannot be measured in
 real-time, or that demonstrate frequent fluctuations in their data.
 Examples of physiological functions and the variables that characterize
 them include, but are not limited to, cerebral blood flow (in the
 treatment of stroke patients) which is related to blood viscosity and the
 concentrations of plasma proteins and clotting factors in the blood stream
 (Hachinski, V. and Norris, J. W., "The Acute Stroke," Philadelphia, F. A.
 Davis, 1985); pulmonary function (in asthma patients) as measured by lung
 volumes in the different phases of respiration (Thurlbeck, W. M. (1990)
 Clin. Chest Med. 11:389); and heart activity (in recurrent cardiac arrest)
 as measured by electrical activity of the heart (Marriott, H. J. L.,
 "Practical Electrocardiography", 8th Ed., Baltimore, Williams & Wilkins,
 1983). Other examples of physiological variables that can be predicted,
 include renal dialysis, where blood concentrations of urea and blood gases
 are followed (Warnock, D. G. (1988) Kidney Int. 34:278); and anesthesia
 treatment, where various parameters (e.g., heart rate, blood pressure,
 blood concentration of the anesthesia) are monitored to determine when the
 anesthesia will stop functioning (Vender, J. S., and Gilbert, H. C.,
 "Monitoring the Anesthetized Patient," in Clinical Anesthesia, 3rd Ed., by
 Barash et al., Lippincott-Raven Publishers, Philadelphia, 1996).
 Step F
 Controlling a Physiological Effect
 The analyte value obtained using the above techniques can also be used to
 control an aspect of the biological system. e.g., a physiological effect.
 In one embodiment, an analyte value obtained as described above is used to
 determine when, and at what level, a constituent should be added to the
 biological system in order to control the concentration of the target
 analyte.
 More particularly, in the context of blood glucose monitoring, use of
 prediction techniques (Step E, supra) allows for accurate predictions of
 either real-time or future blood glucose values. This is of particular
 value in predicting hypoglycemic episodes which can lead to diabetic
 shock, or even coma. Having a series of measurements obtained from the
 continual iontophoretic sampling device, and the capability to predict
 future values, allows a subject to detect blood glucose swings or trends
 indicative of hypoglycemic or hyperglycemic episodes prior to their
 reaching a critical level, and to compensate therefor by way of exercise,
 diet or insulin administration.
 A feedback control application of the present invention entails using a
 function to predict real-time blood glucose levels, or measurement values
 of blood glucose levels at a different time, and then the same to control
 a pump for insulin delivery to treat hyperglycemia.
 EXAMPLES
 The following examples are put forth so as to provide those of ordinary
 skill in the art with a complete disclosure and description of how to make
 and use the devices, methods, and formulae of the present invention, and
 are not intended to limit the scope of what the inventors regard as their
 invention. Efforts have been made to ensure accuracy with respect to
 numbers used (e.g., amounts, temperature, etc.) but some experimental
 errors and deviations should be accounted for. Unless indicated otherwise,
 parts are parts by weight, molecular weight is weight average molecular
 weight, temperature is in degrees Centigrade, and pressure is at or near
 atmospheric.
 Example 1
 Signal Processing for Measurement of Blood Glucose
 In order to assess the signal processing methods of the present invention,
 an iontophoretic sampling device was used to extract a series of 525 blood
 glucose samples from an experimental population of human subjects, and
 non-processed measurement values were compared against measurement values
 obtained using the data screening and correction algorithm of the present
 invention.
 More particularly, iontophoretic sampling was performed on subjects using a
 GlucoWatch.TM. (Cygnus, Inc., Redwood City, Calif.) iontophoretic sampling
 system. This transdermal sampling device, which is designed to be worn
 like a wrist watch, uses iontophoresis (electroosmosis) to extract glucose
 analyte into a collection pad worn beneath the watch. Glucose collected
 into the GlucoWatch.TM. sampling system triggers an electrochemical
 reaction with a reagent in the pad, giving rise to a current which is
 sensed, measured, and converted to a blood glucose concentration.
 Measurements are taken on a continual basis, wherein combined extraction
 and sensing (measurement cycles) were set at 30 minutes. Iontophoresis was
 carried out using two collection pads contacted with Ag/AgCl iontophoretic
 electrodes, an iontophoretic current density of 0.3 mA/cm.sup.2, and the
 electrical polarity of the electrodes was switched halfway through the 30
 minute measurement cycle. Sensing was carried out using platinum-based
 biosensor electrodes which were contacted with the collection pads. A
 description of the GlucoWatch.TM. sampling system can be found in
 publication to Conn, T. E. (Jan. 15, 1997) "Evaluation of a Non-Invasive
 Glucose Monitoring System for People with Diabetes," given at the
 Institute of Electrical and Electronics Engineers (IEEE) meeting entitled
 "Engineering in Medicine & Biology," Stanford, Calif., which publication
 is incorporated herein by reference.
 Concurrent with obtaining the calculated blood glucose values (from the
 GlucoWatch.TM. sampling system), blood samples (finger sticks) were
 obtained and analyzed for use as reference measurements. As a result, 525
 sets of paired measurements (reference and calculated measurements) were
 obtained. A comparison was then made between the reference measurements
 and the calculated measurements (either raw, or signal processed using the
 methods of the invention). Two different sets of data screens were used as
 follows: (a) maximum temperature change over time (d(temp)/d(time)),
 perspiration threshold, and a threshold departure from monotonicity (this
 set of temperature screens is indicated as (+) in Table 1 below); or (b)
 maximum temperature change over time (d(temp)/d(time)), perspiration
 threshold, a threshold departure from monotonicity, and a threshold
 baseline background change over time (this set of temperature screens is
 indicated as (++) in Table 1 below). The correction algorithm that was
 used is as follows:
EQU EG.sub.t =b.sub.gain [E.sub.t (1+.epsilon..sub.i t)+OS]+.alpha..sub.i
 t-.rho.
 wherein:
 ##EQU13##
 and (t.sub.cal) is the calibration point; (EG.sub.t) is the estimated blood
 glucose concentration at time t; (E.sub.t) is the analyte signal at time
 t; (OS) is the constant offset term which accounts for a non-zero signal
 at an estimated zero blood glucose concentration (as described above);
 (.epsilon.) is a gain term for time-dependent signal decline and can have
 multiple time segments (e.g., i=1, 2, or 3); (.alpha.) is a correction
 term for a linear time-dependent signal decline in the time segments and
 can have multiple time segments (e.g., i=1, 2, or 3); (t) is the elapsed
 time, and (.rho.) is the calibration offset (in mg/dl).
 In the comparison, an Error Grid Analysis (Clarke et al. (1987) Diabetes
 Care 10:622-628) was used to assess device effectiveness, wherein
 calculated measurements were plotted against the corresponding reference
 measurements. An effective blood glucose monitoring device should have
 greater than approximately 85-90% of the data in the A and B regions of
 the Error Grid Analysis, with a majority of the data in the A region
 (Clark et al., supra). The results of the Error Grid Analysis are
 presented below in Table 1 as (A+B%). As can be seen, the combination of
 data screening methods and the correction algorithm of the present
 invention met this effective criteria.
 Another measure of device accuracy is the mean absolute % error (MPE(%))
 which is determined from the mean of individual % error (PE) given by the
 following function:
 ##EQU14##
 wherein BG.sub.t is the reference glucose measurement and EG.sub.t is the
 calculated glucose measurement. Effective measurements should have a
 MPE(%) of about 25% or less. The results of the MPE(%) are also depicted
 in Table 1. As can be seen, the combination of data screening methods and
 the correction algorithm of the present invention met this effective
 criteria.
 The correlation between calculated and measured blood glucose values was
 also assessed. The correlation coefficient values (R) are also presented
 in Table 1 below. Effective measurements should have R values of greater
 than about 0.85. As can be seen, the combination of data screening methods
 and the correction algorithm of the present invention provide for
 increased correlation between actual and measured values.
 TABLE 1
 525 Total Paired Data
 Algorithm Screen No. pts. MPE (%) A + B (%) Other (%) R
 0 0 525 54 73 27 0.54
 + + 467 24 90 10 0.87
 + ++ 308 20 91 9 0.90