Patent Application
20070299617
The following detailed description illustrates the invention by way of example, not by way of limitation of the principles of the invention. This description will clearly enable one skilled in the art to make and use the invention, and describes several embodiments, adaptations, variations, alternatives and uses of the invention, including what we presently believe is the best mode of carrying out the invention. It is to be understood that this invention is not limited to the particular embodiments described, as such may, of course, vary.
In general, symbols without a subscript refer to a continuous variable, such as the continuous biosensing current i, the continuous transient time t, or the continuous run-time Tr.
Symbols with the subscript n are discretely sampled variables that correspond or are indexed to a discretely sampled value of the run-time [Tr]n, such as [ip]n, a discretely sampled value of the current of an nth biosensing current transient that is indexed to a discretely sampled value of the run-time [Tr]n.
Symbols with both the subscript n and the subscript j are discretely sampled variables that correspond or are indexed to both a discretely sampled value of the run-time [Tr]n and a discretely sampled transient time tj. For example, [ij]Tr or [ij]n is the value of the transient current that is discretely sampled, at a transient time tj of an nth biosensing current transient, indexed to a discretely sampled value of the run-time [Tr]n.
Symbols with a subscript other than n, j or k identify a variable to a particular value, characteristic, property or definition, such as: the use of the subscript Tr to identify a bracketed variable to the run-time, e.g., [RD1]Tr, or to emphasize the dependence of a discretely sampled transient current on the run-time, e.g., [ij]Tr; or, the use of the subscript, t, to identify variables within the transient time of an individual current transient, e.g., [RTt]Tr. The meaning of subscripts other than n, j or k will be apparent from the context in which such subscripts are used.
It is to be understood that the terminology used herein is for describing particular embodiments only, and is not intended to be limiting, since the scope of the present invention will be limited only by the appended claims.
As used herein and in the appended claims, the singular indefinite forms “a”, “an”, and the singular definite form, “the”, include plural referents unless the context clearly dictates otherwise. Thus, for example, reference to a current transient includes a plurality of such current transients and reference to an analyte includes reference to one or more analytes and equivalents thereof known to those skilled in the art, and so forth.
As used herein, the term computing system means a system comprising a micro-processor, an input device coupled to the micro-processor, an output device coupled to the micro-processor, and memory devices coupled to the micro-processor. The input device may be, inter alia, a touchpad or a miniature keyboard, etc. The output device may be, inter alia, a printer, a plotter, a computer screen, a wireless data transmitter, a data transmission cable (e.g., a USB cable) etc. The memory devices may be, inter alia, dynamic random access memory (DRAM), or read-only memory (ROM), etc. The memory device includes computer code. The computer code includes drift adjustment functions invented herein. The micro-processor executes the computer code. The memory device includes input data. The input data includes input required by the computer code. The output device displays output from the computer code. Memory devices may be used as a computer usable medium (or a computer readable medium or a program storage device) having a computer readable program code embodied therein and/or having other data stored therein, wherein the computer readable program code comprises the computer code. A computer program product (or, alternatively, an article of manufacture) of the computer system may comprise the computer usable medium or the program storage device. Any configuration of hardware and software, as would be known to a person of ordinary skill in the art, may be utilized to configure the computer system.
As used herein, the term sensitivity (S) is defined as the change in the response of the biosensor per unit change in concentration of an analyte. In the case of a glucose oxidase (“GOx”) amperometric enzyme biosensor, the biosensor response current is directly proportional to the glucose concentration. As indicated, supra, sensitivity S is expressed as the change in biosensor response current per unit of change in concentration, e.g. nA/mg/dL or nA/mM, where mM is an abbreviation for millimolar (millimoles/Liter) or (mmol L−1) and nA is an abbreviation for nanoamps. The sensitivity may be determined by linear regression of the biosensor response current v. analyte concentration. The slope of such a plot is the sensitivity S.
Continuous run-time refers to time points within the period that an in vivo biosensor is operated or implanted in a subject, and is symbolized Tr. In addition, run-time represented as [Tr]n may be measured or sampled discretely instead of continuously. For example, if a series of n square-wave voltage pulses is applied to an electrochemical cell, a point in run-time [Tr]n may be recorded and cross-indexed to the beginning of each voltage step or the beginning of each entrained biosensing current transient that it generates, so that each voltage step or entrained biosensing current transient is associated with an increasing value of the run-time [Tr]n.
Discretely sampled values of the run-time Tr cross-indexed to a specific biosensing current transient, [ij]Tr are symbolized Tr or [Tr]n, (n=1, 2, 3, . . . ). With respect to recurring biosensing current transients, entrained within a series of square wave voltage pulses, if, for example, the total period Pτ of each biosensing current transient is 5 seconds, there will be a corresponding run-time point [Tr]n recorded at multiples of 5 seconds. The first value of [Tr]n is at run-time 5 seconds [Pτ] and is denoted as [Tr]1. Following [Tr]1, the next run-time value [Tr]2 occurs at 10 seconds, 2(Pτ); and, following [Tr]2, the next run-time value [Tr]3 occurs at 15 seconds, 3(Pτ), etc. In the figures, the continuous run-time points [Tr]n may be denoted as Tr.
The terms Implantation time or implantation period are synonymous with run-time.
Continuous transient time is symbolized with a lower-case t and refers to time points within any biosensing current transient, generated by a periodic voltage waveform.
Discretely sampled transient times tj(j=1, 2, 3, . . . ) are indexed to time points within a current transient and may, in turn, be indexed to any value of a discretely sampled run-time point [ij]Tr.
Biofouling induction period: Although the body's immune system immediately recognizes a foreign body, there is a biofouling induction period before the foreign body response has an adverse impact on the response of an in vivo biosensor. Evidence has shown biofouling begins to affect a biosensor's response within approximately 30-180 minutes post-implantation. The duration of the biofouling induction period is dependent on the size, biocompatibility and the magnitude of the inflammatory response to the in vivo biosensor. The induction period may last for approximately 1-3 hours post implantation. If necessary, drift adjustments may be applied to the biosensing current at times greater than the induction period. The term induction period is synonymous with biofouling induction period, and is symbolized [Tr]induction.
Baseline data collection time: If baseline data is obtained during a time period within the induction period [Tr]induction, it is possible to adjust biosensing currents for the effect of biofouling at run-times greater than the induction period, i.e., Tr>[Tr]induction. For example, a period within which to collect the baseline data (“baseline data collection time” [Tr]baseline) may be between 60 and 180 minutes post-implantation. Any time range within 60 to 180 minutes may be used to measure baseline data (e.g. 60-80 min). The term baseline period is synonymous with baseline data collection period, and is symbolized [Tr]baseline.
Equilibration period, equilibration time, or break-in period: When a biosensor is implanted within a subject or used in vitro within a test cell, a period is required for equilibration of the biosensor's response to the conductive fluid surrounding the implanted biosensor. The period required for the biosensor's response to reach its steady-state value is called the equilibration period [Tr]eq. The term equilibration time or break-in period is synonymous with equilibration period, and is symbolized [Tr]eq.
The induction period is the sum of the equilibration period and
the baseline period.
[Tr]induction=[Tr]eq+[Tr]baseline (7)
As used herein, the term applied voltage or applied potential refers to a variable or floating electric potential difference between:
(a) a working electrode; and,
(b) a counter electrode of a biosensor, and is represented as Ewc.
As used herein, the term poise voltage, poise potential or bias potential refers to a fixed electric potential difference between a working electrode and a reference electrode of a biosensor, and is represented as Ewr.
A potentiostat is used to supply a voltage between the working and counter electrodes. By means of a feedback circuit, the potentiostat varies the applied potential Ewc to maintain a constant poise potential Ewr.
As indicated above, when one or more electrodes of an electrochemical biosensor are implanted within a subject or used in vitro within a test cell, a period is required for equilibration of the biosensor's biosensing current to the conductive fluid surrounding the biosensor. The time required for the biosensing current to reach its steady-state value is called the equilibration period [Tr]eq of the biosensor. An equilibration period exists even in the absence of target analyte.
The equilibration time [Tr]eq is a function, inter alia, of the thickness and chemical complexity of the catalytic surface (sensing element) of the working electrode. For example, if the enzyme layer that forms the catalytic surface of the working electrode is relatively thin, the equilibration time [Tr]eq may be less than 30 minutes. If however, the enzyme layer that forms the catalytic surface of the working electrode is relatively thick or covered with non-enzymatic materials, such as polymers or proteins, then the equilibration time [Tr]eq may be greater than 30 minutes, approaching hours. In either case, a high response current is initially observed that decreases over time to a steady state value consistent with the quantity of the target analyte being measured.
The equilibration time [Tr]eq is also a function of the density and thickness of a biosensor's membrane(s). The greater the density or the thicker the membrane(s) encapsulating a biosensor, the longer it may take for the biosensing current to reach equilibrium. When using GOx and oxygen dissolved in an aqueous fluid as a mediator, to prevent oxygen limitation, the barrier membrane is usually dense; consequently, currents in the range of 10-100 nA (nanoamp, 10−9) are normally observed. The density and thickness of the membrane may also cause a lag by increasing the response time of a biosensor to changes in a target analyte's concentration. If however, a metallo-organic or synthetic mediator is present within the biosensor's active zone, oxygen limitation is of less concern, so that less dense, thinner membranes will decrease the response time and equilibration time.
When a steady-state voltage is applied to an in vitro GOx biosensor, the biosensing current, even in the absence of glucose, is initially high and decays to a steady-state value over the course of time comprising the equilibration period. Thereafter, the biosensing current remains at a steady-state value until there is a change in the concentration of a target analyte such as glucose. When glucose is present, the biosensing current will increase due to oxidation of hydrogen peroxide generated by the reaction of GOx with glucose (see
When an electrochemical biosensor is implanted in vivo, a steady-state may not exist, as shown in
In the absence of target analyte, the biosensor response over [Tr]eq, is called the “background response” or the “intercept at zero analyte concentration,” or simply, the “intercept.” In aqueous buffer solutions, the intercept should be nearly zero; however, there may be other electroactive species present, called “interferants” that are oxidized or reduced at the same poise potential as the analyte of interest. If a mediator is used, the poise potential may be lowered to the point where interferants are not electrochemically active, resulting in background responses that approach zero. Even in the absence of analyte, a small current flows due to the charging current required to maintain the electrical double layer at the working electrode surface. When implanted in vivo, amperometric biosensing background currents may become significant and must be taken into account when calculating analyte concentrations.
In configuring a biosensor for in vivo use, the distance between its reference electrode and working electrode should preferably be as small as possible without causing shielding effects. Such placement will reduce the uncompensated resistance Ru between the reference electrode and the working electrode. Additionally, the reference electrode should preferably be small and symmetrically disposed between the working electrode and the counter electrode. The counter electrode should preferably have a surface area larger than the working electrode.
With respect to implanted biosensors, an observer or witness sensor (O) may be used to measure or monitor changes in the physical properties of an in vivo biosensor such as resistance, impedance, conductance, diffusion, pressure, admittance, capacitance, optical, magnetic or other physical property. The observer sensor may be utilized in vivo, close to the implanted biosensor. Changes in electrical, optical, magnetic or other physical property on the surface of an implanted biosensor, may be measured through space by the implanted observer sensor and used to track changes occurring on the surface of the implanted biosensor. The data so obtained, can be correlated with changes in sensitivity of the biosensor. The in vivo, observer sensor may be used independently to measure changes in a physical property of itself that correlates with changes in sensitivity of the implanted biosensor.
Additionally, a combination of an implanted observer sensor and an external or ex vivo observer sensor can be used to measure relative changes in the properties of an implanted observer sensor. In the case of two observer sensors, they may or may not be in direct communication with one another; however, temporal changes in one or more physical properties of the in vivo observer sensor, relative to the ex vivo observer sensor, may be correlated to temporal changes in sensitivity of the in vivo biosensor. In the case of an ex vivo observer sensor, it may be situated in an environment not subject to varying degrees of biofouling. A convenient location for the ex vivo observer sensor is the skin surface of a mammal.
In the descriptions of biosensor configurations that follow, dashed lines interrupted with resistor symbols in accompanying
Implanting all electrodes together is the most optimal configuration; theoretically, for electrochemical sensors and results in the least amount of electrical resistance in the form of the solution resistance between the counter electrode and the working electrode Rs and the uncompensated electrical resistance Ru that has been earlier defined to equal the resistance between the working electrode and the reference electrode.
By keeping the reference and counter electrodes close to the working electrode, the magnitude of Rs and Ru is minimized.
Within the active zone, the magnitude of Rs and Ru are represented as follows:
R
s
=R
w
+R
Fi
+R
c (8)
R
u
=R
w
+R
Fi
+R
r (9)
In Equations 8 and 9, RFi refers to the electrical resistance of the conductive fluid contained within the active zone of the biosensor and may consist of ISF 11 minus cells and high molecular weight proteins due to their exclusion by a barrier membrane. In
In first illustrative biosensor configuration 50, the magnitude of resistive components Rs and Ru are relatively small; and may have a minor IR drop effect on the potential difference Rs, between counter, 12 and working electrode 14 or Ru between reference 13 and working electrode 14.
The fluid volume within the active zone of first biosensor configuration 50 is small; and, as the glucose concentration within this fluid volume increases, the resistance components (Rs and Ru) may increase because glucose is a neutral molecule. However, in the case of an amperometric GOx biosensor, the products of the chemical and electrochemical processes are charged, so the effect of increasing glucose concentration on the electrical resistance of the fluid, within the active zone, may be minimal.
The drawback to using first illustrative biosensor configuration 50 is that if cells, proteins, fibrin or other cellular materials adhere to the outside surface of a barrier membrane covering a biosensor, there is no convenient way to compensate for the decrease in diffusion or mass transport of a target analyte into the active zone other than by recalibration.
Due to the phenomenon of biofouling, in vivo glucose biosensors of first illustrative biosensor configuration 50 require frequent recalibration using blood samples taken from the subject. The resulting blood glucose value(s) must be manually entered into the in vivo sensor monitor or wirelessly transmitted to the monitor so that new calibration parameters may be calculated. The recalibration process is time consuming, inconvenient and expensive.
(a) the counter electrode 12 is in contact with the skin of a subject;
(b) the working electrode 14 is implanted within a subject; and,
(c) the reference electrode 13 is implanted within the subject.
In the case of a two-electrode second illustrative biosensor configuration, reference electrode 13 and counter electrode 12 are the same and together referred to as a reference-counter electrode. Since the counter electrode 12 is outside barrier membrane 40, in a relatively stable environment, it can also serve as an observer sensor (O) and provide a means of indirectly measuring the effect of biofouling, of barrier membrane 40, on working electrode responses.
As in first illustrative biosensor configuration 50, the value of Ru, the resistance between working electrode 14 and reference electrode 13 may be relatively small because reference electrode 13 is close to the working electrode 14. However, Rs, the resistance between counter electrode 12 on the skin surface and working electrode 14 may be significant.
The resistive components of Rs in the second illustrative biosensor configuration are:
R
s
=R
c
+R
w
+R
skin
+R
Fo
+R
Fi
+R
mem (10)
The inherent resistances of the counter Rc and working Rw electrodes are constant and the resistance across the skin, Rskin, although it may be high (e.g., Kilo-ohms), remains relatively constant once the biosensor has equilibrated, because a conductive, hydrophilic adhesive is used between the skin and counter electrode 12. Once the skin equilibrates with the conductive adhesive, the resistance across the skin stabilizes. The value of Rs can be in the meg ohm (106) range.
Owing to homeostasis, the resistance or ionic strength of the fluid surrounding the outer aspect of membrane 40 and defined as RFo remains relatively constant once the biosensor has equilibrated. Although the resistance of the fluid RFi within the active zone may vary, it remains low so that its contribution to Rs, the resistance between the counter electrode and the working electrode, is relatively small.
The total electrical resistance across the membrane Rmem includes Rmem intrinsic, the electrical resistance across the inner and outer aspect of membrane 40, and a variable contribution from the electrical resistance of adsorbed protein, cells and fibrinous tissue, Rbiofouling that may adhere to the outer aspect of membrane 40 during the biofouling process, so that:
R
mem
=R
mem intrinsic
+R
biofouling (11)
The value of Rmem intrinsic during the induction period [Tr]induction of an electrochemical biosensor may be higher than at a later stage because membrane 40 must “wet-up” and establish fluid equilibrium between its inner and outer surfaces. This process contributes to the aforementioned equilibration time [Tr]eq of the electrochemical biosensor, which must transpire before useful measurements can be made. Because most of the terms in equation 10 are either small or relatively constant, the Rbiofouling term is the variable component and therefore the total resistance Rs may be used to track the extent of biofouling.
Following implantation, there are stages to the biofouling process. First, proteins, such as albumin and fibrinogen, adhere to the outside surface of membrane 40, this may be followed by the attachment of different proteins and cell types. As the biosensor's implantation period increases, biofouling may increase, depending on the extent of the inflammatory response to the implanted biosensor. As Rbiofouling increases, the resultant increase in Rmem can produce a significant voltage drop in the applied potential between working electrodes 14 and counter electrode 12.
The voltage drop in the applied potential between working electrode 14 and counter electrode 12 could exceed the compliance voltage (e.g. ±10 volts) of a compensating potentiostat feedback circuit, such that, the biosensor's response saturates; and/or, the fixed poise potential between the working electrode 14 and the reference electrode 13 shifts to a lower value, resulting in a change in the biosensor's response characteristics such as sensitivity and mass transfer across the barrier membrane.
If counter electrode 12 is close to working electrode 14, the value of Rs is small, as in the first illustrative biosensor configuration. However, the resistance Ru of the resistive path between reference electrode 13 on the skin and the implanted working electrode 14 may be significant. With this type of electrode configuration, wherein the reference electrode is remote from the working electrode, there may exist a significant voltage (IR) drop, between the reference electrode and the working electrode. This configuration goes against the theoretical optimum where the reference electrode is as close as possible to the working electrode without causing shielding effects. In addition, the reference electrode is not disposed between the counter and working electrodes. For these reasons, third illustrative biosensor configuration 90 is not as favorable as second illustrative biosensor configuration 70. Nonetheless, with third illustrative biosensor configuration 90, the effect of changes in Ru, due to biofouling, can be measured and used to compensate for biofouling.
The resistive components of Ru are:
(a) the inherent electrical resistance of the working and reference electrodes Rw, Rr, respectively;
(b) the electrical resistance across the skin Rskin;
(c) the electrical resistance within the bodily fluid/tissue outside the barrier membrane RFo;
(d) the electrical resistance across membrane 40 Rmem; and,
(e) the electrical resistance of the body fluid within the active zone is RFi; and, similar to equation 11, the total uncompensated resistance, Ru, is expressed as:
R
u
=R
r
+R
skin
+R
Fo
+R
mem
+R
Fi
+R
w (12)
In third illustrative biosensor configuration 90, the reference electrode on the skin surface is far removed from the working electrode; therefore, a high value for Ru may have an adverse effect on the time constant RuCdl for the rise in poise potential. If the rise time, [RT]t, of the working electrode voltage exceeds the pulse width period τ1 of a periodically applied voltage waveform such as a square wave, the poise potential will not attain its maximum value within τ1. This will cause a decrease in the biosensor response, leading to inaccuracy of the computed analyte concentration. As in the case of second biosensor illustrative configuration 70, most of the terms in equation 12 are either small or relatively constant; thus, the Rbiofouling term is the variable component and therefore the total uncompensated resistance Ru, and its effect on the poise potential, may be used to track the extent of biofouling.
Prior to reaching the desired poise potential [Ewr]1, the observed potential ascends exponentially through a rise time [RT]t, proportional to the time constant “RuCdl”, in accordance with:
[Ewr]obs=[Ewr]1(1−e−t/RuCdl) (13);
where [Ewr]obs represents the observed potential on the exponentially rising part of the curve in
Although resistance and current magnitude play an important role in defining the applied voltage limitations of a potentiostat and the time constants of the applied working electrode voltage and the decay of current time transients, a major advantage is the implanted working electrode can be much smaller than either a biosensor wherein two or more electrodes are implanted. A smaller implanted sensor can reduce the inflammatory response and provide a sensor with less susceptibility to biofouling.
In
The advantage of fifth illustrative biosensor configuration 110 is that resistance (Rs) between the counter and working electrode and between the reference and working electrode (Ru) are minimized while electrode 15 provides a means for monitoring the resistance or impedance across membrane 40. This measurement provides a means for compensating for the effects of biofouling on analyte mass transfer across membrane 40. The disadvantage is that a larger sensor is implanted which may lead to an increased inflammatory response. Regardless of the size of the biosensor, if the inflammatory response is limited to an acute phase, changes in sensor signal outputs, and their impact on accuracy and sensitivity can be minimized.
In
(a) the open circuit potential defined as [E]oc; or,
(b) any potential less than or greater than [Ewr]1; or,
(c) the value of the potential difference that is operative during a disconnect period between pulses when no current flows.
A disconnect period is defined as the time over which there is a break in the electrical contact between the working and reference electrodes, or between the working and counter electrodes. The difference between an open circuit period and a disconnect period is that at open circuit, the working and reference electrodes remain connected with no external voltage applied with little current flowing; however, there is still a potential difference between the working and reference electrode. The potential difference during open circuit is attributable to the redox behavior of half-cells or “battery effects” due to differences in material comprising the working and reference electrodes and the electrolyte solution(s) surrounding the electrodes.
In
i
j
=nFAC
o
D
o
1/2/(πtj)1/2 (14)
where,
ij=the biosensing current on the falling portion of the current transient in Amps
n=number of electrons transferred, equivalents/mol (1, 2, 3 . . . )
F=Faraday constant, 96,485 Coulombs/equivalent
A=electrode area, cm2
Co=initial mass concentration of the analyte, mol/cm3 (molality)
Do=initial diffusion coefficient of the analyte, cm2/sec
tj=transient time, sec.
The transient current is inversely proportional to the square root of transient time tj; and, for a diffusion-controlled reaction at a planar electrode, the product ij*(tj1/2) should be constant. In addition, there is a linear portion of the exponentially declining current transient that begins at the peak current i1 and ends at a time tj where the current becomes non-linear. This linear region exists for approximately 2-100 msec after the peak current.
Biosensing currents referred to herein may consist of discrete single transient currents [ij]n, the difference between two transient currents [i2−i1]n, an average transient current, the rate of change of the transient current or integrated transient current expressed as charge in coulombs, in accordance with Faraday's Laws where charge is expressed as a change in current multiplied by a corresponding change in time.
In order to obtain calibrated values of an analyte concentration, each discretely sampled indexed transient current [ij]n, integrated transient current or function of the transient current used as a biosensing output response, for the calculation of an analyte concentration, must be calibrated against known analyte concentrations so that calibration parameters such as sensitivity and intercept may be determined.
In
If the magnitude of the square wave voltage pulse [Ewr]1, the total period Pτ and the pulse width period τ1 are judiciously chosen, the concentration of an analyte species, such as hydrogen peroxide, can be controlled so that when the pulsed voltage [Ewr]1 is applied, the analyte concentration within the active zone temporarily falls to zero within the pulse width period, τ1 and increases again during the inter-pulse period τ2.
The final current value [if], may be a function of the final current, such as an averaged or integrated transient current immediately preceding the final transient current value. In some cases, the final current function may be used as the y-intercept bk in equation 4, supra, and with appropriate substitution of subscripts, equation 4 becomes:
[C]Tr={[ij]−[if]}Tr/Sk (15),
where:
(a) [C]Tr is the concentration of glucose corresponding to a function of the run-time indexed transient current, in this case a run-time indexed current difference;
(b) [ij] is any current, preferably the peak current, on the declining portion of the run-time indexed current transient and [if] is the final current within the same run-time indexed current transient and,
(c) Sk represents the sensitivity determined at a run-time other than the run-time indexed transient currents.
In
The number of discrete time points tj is determined by a sampling rate and pulse width τ1. For example, if the sampling rate is 500 Hz, then the number of time points tj within a pulse width, τ1, of 0.3 sec is (0.3)(500)=150, with intervening increments of 2 msec. In this case, the final current if would be designated i150. If an average final current is used, then the average should be taken within a time range immediately preceding ij150 such as, for example, between i140 and i150, which equates to the average of 6 current values. The same holds true for integration of the final current.
As indicated, supra, the biosensing transient current declines exponentially and can be described as:
i
j=([Ewr]1/Rs)(e−tj/RsCdl) (16)
By rearranging terms in equation 16 and taking the natural log(Ln) of both sides of equation 16:
Ln[i
j]=−[1/(RsCdl)]tj+Ln{[Ewr]1/Rs} (17)
Equation 17 is in the form of y=mx+b, where m is the slope and b is the y-intercept. In equation 17, the term [−(1/RsCdl)] is the slope; and the term Ln{[Ewr]1/Rs} is the y-intercept.
Since the poise potential [Ewr]1 is either known or measured, a determination of Rs from the y-intercept Ln{[Ewr]i/Rs} is possible. Relative changes in the slope [−(1/RsCdl)] with run-time may be used to calculate gain adjustment functions that may be used to adjust drifting biosensing signal outputs, as more fully described, below.
As capacitance Cdl, and/or resistance Rs increases, the value of 1/RsCdl decreases and, as indicated above in connection with
The transient peak width [Pw]n of biosensing current transients, such as those shown in
When studied under controlled laboratory conditions such as with aqueous buffer solutions, the behavior of electrochemical biosensors is well defined. However, the behavior of electrochemical biosensors under non-laboratory conditions may be unpredictable. This is particularly true for electrochemical biosensors implanted within mammals.
When implanted in vivo, biosensors are affected, to varying degrees, by the body's foreign body response. The effect the foregoing process has on biosensor signal outputs is termed biofouling. Heretofore, there were no real-time algorithms, derived from information contained within biosensing currents, to account for drifting biosensor signal output caused by biofouling. As described below, a number of methods and gain adjustment functions are presented that can be used, on a real-time basis, to adjust drifting biosensor responses for the effects of biofouling.
The calculation of relative gain adjustment functions is based on information contained within current transients generated by the application of a voltage waveform, such as a square wave voltage pulse applied to the working electrode of an implanted biosensor. Relative changes in gain functions measured at run-times greater than an induction period versus gain functions measured during a baseline period, are used to compensate for biofouling. The calculation and application of gain adjustments occurs, on a real-time basis. For example, if the information contained within a series of voltage pulses is used to calculate baseline values of relative gain adjustment functions, within a baseline period, and if the change in these baseline values and those measured at run-times greater than the induction period exceed certain limits, a gain adjustment may be applied to biosensing signal output, sensitivity or both at run-time points greater than the induction period.
Referring to the second illustrative biosensor configuration of
The applied potential gain adjustment equation is a function of the applied voltage [Ewc]Tr between the working electrode and the counter electrode. The applied voltage [Ewc]Tr varies to maintain a constant poise potential [Ewr]1 and constant inter-pulse potential [Ewr]2 between the working electrode and the reference electrode. If the resistance Rs between a counter electrode and a working electrode changes, the applied voltage from a potentiostat will also change in order to maintain a constant poise or inter-pulse potential between the working electrode and counter electrode.
Since the resistance Rs between a skin surface observer sensor (O) and an in vivo working electrode includes a contribution from biofouling, then [Ewc]Tr, the voltage applied across the working electrode and the counter electrode will indirectly reflect increases in resistance Rs caused by biofouling of the barrier membrane. Accordingly, relative changes in applied potential due to changes in Rs between a skin surface counter electrode and working electrode of an in vivo biosensor may be used to calculate an applied potential gain adjustment function.
A mathematical expression for an applied potential gain adjustment function [Gwc]Tr at any time Tr, greater than the induction period, may be computed as follows:
[GEwc]Tr=1+{([Ewc]Tr−[Ewc]0)/[Ewc]0} (18)
where, [Ewc]0 refers to an average of the applied potential taken over the baseline period, [Ewc]Tr is the run-time indexed applied voltage between the working electrode and the counter electrode at any time Tr greater than the induction period; and, by definition, when [Ewc]Tr=[Ewc]0, then from equation 18, [GEwc]Tr=1. The second term in equation 19 is a relative difference function of [Ewc]Tr and [Ewc]0.
For measurements taken on a continuous basis, the applied potential gain adjustment function [GEwc]Tr may be used to adjust a single, discretely sampled transient current [ij]Tr; multiple, discretely sampled, transient currents; a difference between two discretely sampled transient currents; an integrated transient current between two transient time points or integration over a range of multiple, discretely sampled transient currents at any time Tr greater than the induction period. The measured value of [GEwc]Tr or its reciprocal may be used, such that,
f{[i
j]Tr}A=[GEwc]Tr*f{[ij]Tr} (19);
where the subscript, A, represents an adjusted function of the transient current(s) proportional to the analyte concentration and f{[ij]Tr} represents the unadjusted function of the transient current(s) as a function of analyte concentration.
The applied voltage gain adjustment function [GEwc]Tr may be used to adjust the sensitivity Sk of the biosensor by multiplying or dividing the sensitivity Sk by [GEwc]Tr:
[S]Tr=[Sk]/[GEwc]Tr (20),
where [Sk] is a previous sensitivity value and [S]Tr is the adjusted sensitivity at the same run-time point were [GEwc]Tr and the analyte concentration dependent transient current function were measured.
Referring again to the second illustrative biosensor configuration of
[GRs]Tr=1+{([RS]Tr−[RS]0)/[RS]0} (21);
where [RS]Tr is the resistance between the implanted working electrode and the skin surface counter electrode at any time Tr greater than the induction period; and, [RS]0 refers to an average taken over the baseline period. By definition, when [RS]Tr=[RS]0, then from equation 21, [GRs]Tr=1. As in equation 18, supra, the second term in equation 21 is a relative difference function of [RS]Tr.
For measurements taken on a continuous basis, the Rs resistance gain adjustment function [GRs]Tr may be used to adjust a single, discretely sampled transient current [ij]Tr; multiple, discretely sampled transient currents; a difference between two discretely sampled transient currents; an integrated transient current between two transient time points or integration over a range of multiple, discretely sampled transient currents at any time Tr greater than the induction period. The value of [GRs]Tr or its reciprocal may be used:
f{[i
j]Tr}A=[GRs]Tr·f{[ij)]Tr} (22);
where the subscript, A, represents an adjusted function of the transient current(s) proportional to the analyte concentration and f{[ij]Tr} represents the unadjusted function of the transient current(s) as a function of the analyte concentration.
The resistive gain adjustment function [GRs]Tr may be used to adjust the sensitivity Sk of the biosensor by multiplying or dividing the sensitivity as follows:
[S]Tr=[Sk]/[GRs]Tr (23),
where [Sk] is a previous sensitivity value and [S]Tr is the adjusted sensitivity at the same run-time point where [GRs]Tr and the analyte concentration dependent current function were measured.
Again referring again to the second illustrative biosensor configuration of
[GPw]Tr=1+{([Pw]Tr−[Pw]0)/[Pw]0} (24);
where [Pw]Tr is the transient peak width at any time Tr greater than the induction period; and, [Pw]0 refers to an average transient peak width taken over the baseline period. By definition, when [Pw]Tr=[Pw]0, then from equation 24, [Pw]Tr=1.
For measurements taken on a continuous basis, the transient peak width gain adjustment function [GPw]Tr may be used to adjust a single, discretely sampled transient current [ij]Tr; multiple, discretely sampled, transient currents; a difference in transient currents; an integrated transient current between two transient time points or integration over a range of multiple, sampled transient currents at any time Tr greater than the induction period. Accordingly,
f{[i
j]Tr}A=[GPw]Tr·f{[ij]Tr} (25);
where the subscript, A, represents an adjusted function of the transient current(s) proportional to the analyte concentration and f{[ij]Tr} represents the unadjusted function of the transient current(s) as a function of analyte concentration.
The transient peak width gain adjustment function [GPw]Tr may be used to adjust the sensitivity Sk of the biosensor by multiplying or dividing the sensitivity as follows:
[S]Tr=[Sk]/[GPw]Tr (26),
where [Sk] is a previous sensitivity value and [S]Tr is the adjusted initial sensitivity at the same run-time point where
Referring to the third illustrative biosensor configuration of
For example, if the desired poise potential, [Ewr]1, is 0.500 volts with respect to a reference electrode, such as silver/silver chloride, then measuring the relative difference between the desired poise potential and the observed poise potential provides a means of applying a poise potential gain adjustment to the measured biosensing current. The poise potential is measured near the end of the pulse width period, τ1, and the relative difference between the measured value and the desired value is used in a poise potential gain adjustment function represented by the following equation:
[GEwr]Tr=1+{([Ewr]Tr−[Ewr]0}/[Ewr]0} (27),
Where [GEwr]Tr is the measured poise potential indexed to any time Tr after the induction period and [Ewr]0 is the average measured poise potential within the baseline period. Each discretely sampled output biosensing current value [ij]Tr, beyond the induction period is multiplied by [GEwr]Tr to obtain an adjusted biosensing current value:
{[ij]Tr}A=[GEwr]Tr*[ij]Tr (28)
where the subscript, A, represents an adjusted function of the transient current(s) proportional to the analyte concentration and f{[ij]Tr} represents the unadjusted function of the transient current. By definition, when [Ewr]Tr=[Ewc]0, then from equation 28, [GEwr]Tr=1. The poise potential gain adjustment function [GEwr]Tr may be used to adjust the sensitivity Sk, by multiplying or dividing the sensitivity as follows:
[S]Tr=[Sk]/[GEwr]Tr (29)
where [Sk] is a previous sensitivity value and [S]Tr is the adjusted sensitivity at the same run-time point were [GEwr]Tr and the analyte concentration dependent current(s), were measured.
In the following examples, biosensing current transients were generated by periodically applying a 0.500-volt voltage pulse versus a silver-silver chloride reference electrode, across an implanted working electrode and a counter electrode of an intradermal glucose oxidase biosensor. The total pulse period PT was 5 sec and the pulse width period τ1 was 300 msec and by difference τ2 equals 4.7 sec.
Pulse-widths from milliseconds to seconds may be used; however, it is preferable to select a pulse-width that allows consumption of the bulk of an electroactive species (e.g., hydrogen peroxide) created during the ensuing inter-pulse period, τ2. This is especially true for an amperometric, GOx biosensors, wherein excess accumulation of hydrogen peroxide may have a deleterious effect on enzyme stability. A preferred range of pulse widths is 0.050-100 sec., with pulse widths of 0.050-10.0 sec more preferable.
The inter-pulse period τ2 must be longer than the pulse width period τ1 (e.g. τ2=10τ1). It is preferable to provide an inter-pulse period τ2 sufficient to allow accumulation of the electroactive species (e.g., hydrogen peroxide) between pulses. The resulting peak current ip of the biosensing current transient will yield an enhanced biosensor response with a higher signal to noise ratio compared with shorter inter-pulse periods. Inter-pulse periods of 1 to 600 seconds are preferable, with inter-pulse periods of 1-60 seconds being more preferable.
In the following calculations, two data points from each current transient in response to a square wave voltage pulse are selected to compute a relative difference function defined as:
[RD1]Tr=[(i1−i2)/i1]Tr (30)
where i1 and i2 are two discretely sampled transient currents within a run-time indexed biosensing current transient where i1>i2. Preferably:
(a) [i1]Tr is the transient peak current or a transient current value near the peak value; and,
(b) [i2]Tr is the value of a biosensing transient current ij within the linear portion of the declining transient current where [i2]Tr is less than [i1]Tr and the transient time between the two currents is held constant during the run-time period.
(c) the subscript Tr indicates that each value of [RD1] and ij are indexed to the same run-time point.
In
Using at least the foregoing two data points [i1]Tr and [i2]Tr, respectively selected from the same run-time indexed biosensing current transient and shown plotted against the run-time Tr in
Tr[RD1]Tr=0.240Tr−0.885 (31);
represented by the solid straight line in
(a) slope mTr of 0.240; and,
(b) y-intercept of −0.885
(a) The “meas” graph (also shown in
(b) The “calc” graph was obtained by: (1) performing linear regression on the measured values of Tr[RD1]Tr, as in
So as not to introduce unwanted noise into the adjusted values of the biosensing signal output or sensitivity, smooth gain adjustment functions are preferred. The natural log(Ln) of the calculated values of Tr[RD1]Tr from
Theoretically, the y-intercept of the regression line within the baseline period in
In order to determine the gain adjustment functions for biosensing currents at run-time points beyond the induction period, the natural log of calculated values of Tr[RD]Tr is taken for each Tr value greater than the induction period:
Ln{Tr[RD1]Tr}=Ln[mTr*Tr] (32)
Y
Tr=(0.0143*Tr)+1.813 (33);
with a slope of 0.0143 and a y-intercept, Yo, of 1.813 that identifies a straight dashed line labeled YTr. The linear regression period used to derive equation 33 was performed within the vertical bars delineating the selected run-time range of 60-80 minutes, within the baseline period. In performing linear regression within the 60-80 minute window, linearity of the Ln[mTr*Tr] data points was assumed over the selected run-time range of 60-80 minutes. This is a valid assumption because the linear correlation coefficient for the data, within the selected run-time range, was 0.999. The y-intercept of the YTr line is non-zero and is defined as Yo.
In
({Ln[mTr*Tr]}60+{Ln[mTr*Tr]}80)*0.5=M60-80 (34)
The notation M60-80 represents the median value of the function Ln[mTr*Tr] at 60 and 80 minutes. The normalized values of Ln[mTr*Tr] are denoted by the lower curve, labeled:
G1=Ln[mTr*Tr]/M60-80 (35)
In
G2=Ln[mTr*Tr]/Yo (36)
There are numerous ways G1 and G2 may be used to adjust a biosensor's signal response to compensate for the effects of drift and biofouling. G1 and G2 values alone may be used as well as functions of G1 and G2 such as the ratio G1/G2, average (G1+G2)/2, difference (G2−G1), etc., determined at each run-time point, Tr.
Whether to apply a gain adjustment, beyond the induction period, can be predicated on information obtained within the baseline period or in other cases, data measured after the induction period. For example, certain biofouling parameters calculated within the baseline period, e.g. mTr, may be above or below a certain threshold limit and biofouling parameters outside threshold values may be used to trigger a gain correction that is applied to all biosensor signal outputs beyond the induction period. Several types of threshold values are discussed below.
The graph to the left labeled A:
(a) is associated with a time constant [RsCdl]A;
(b) is labeled “non-drifting”; and,
(c) shows the decline in transient current from [i1]A to [i2]A, after a fixed period, dtj, of 10 msec.;
(d) shows the value of the biosensing current at half of the peak value labeled “[i1]A/2=[Pw]A”.
The graph to the right labeled B:
(a) is associated with a time constant [RsCdl]B
(b) is labeled “drifting”; and,
(c) shows the decline in transient current from [i1]B to [i2]B, after a fixed period of 10 msec.;
(d) shows the value of the biosensing current at half of the peak value labeled “[i1]B/2=[Pw]B”.
The relative difference function [RD1] is defined from equation 30 as [RD1]=(i1−i2)/i1. In comparing the graph on the left (A) to the graph on the right (B):
[RsCdl]A<[RsCdl]B;
[RD1]A>[RD1]B;
[i2]A<[i2]B; and,
[Pw]A<[Pw]B
(a) RsCdl increases (graph B): and,
(b) the peak width of the current-time transient within the 10 msec window also increases; and,
(c) broadening of the current transient leads to values of [RD1] that may be less than that of a non-drifting sensor, i.e., [RD1]B<[RD1]A; and,
(d) establishing threshold values for parameters obtained from biosensor output signals, within the baseline period, may be used to determine whether drift adjustments are necessary to biosensing output signals beyond the induction period.
The graphs in
The lower graph in
The slope of [G2−G1]Tr, obtained from linear regression data within the 60-80 run-time range, within a baseline period, for a drifting biosensor (m2=0.00281) is greater than for a non-drifting biosensor (m1=0.00217). Setting a threshold limit for this slope value provides another means of distinguishing drifting from non-drifting in vivo biosensor responses. For example, if the threshold slope value was set at 0.00250, then slope values greater than 0.00250 would indicate biofouling. In
Additionally shown in
Drift adjustment functions [Dx]Tr are derived from functions of both G1 and G2. Although a number of gain adjustment functions are possible, one example is discussed below.
Drift adjustment functions [Dx]Tr are functions of both G1 and G2, indexed to run-time Tr. An example of such a function is the average of the gain adjustment functions G1 and G2 at each run-time point, denoted as:
[D1]Tr=[(G1+G2)/2]Tr for Tr>induction period (37)
In the graphs shown in
(a) the left ordinate, reflecting reference glucose values, obtained by fingerstick measurements of blood samples from a subject wearing an intradermal, amperometric GOx biosensor is labeled “ref glu mg/dl” and is scaled in units of 20 mg/dl.
(b) the right ordinate reflecting unadjusted glucose values calculated from unadjusted biosensor output currents recorded from the same intradermal glucose biosensor is labeled “meas glu mg/dl’ and is scaled in units of 20 mg/dl, it is further labeled “unadjusted”;
(c) the common abscissa, reflecting run-time, is labeled “Tr, min” and is scaled in 100-minute units;
(d) the graph of reference glucose values, obtained by fingerstick measurements is identified by open circles; and,
(e) the graph of unadjusted, calculated glucose values, measured by an intradermal glucose biosensor is represented by the solid black, jagged line.
(f) the graph is further labeled “drift begins at 150 min” and “unadjusted”.
As shown in
(a) the graph is labeled in the box above by a linear equation: Y=0.0196*Glu+3.529; r=0.948 and r=0.589 (all data)”;
(b) the graph is labeled below as “Unadjusted [i2]Tr Data”;
(c) an elliptical circle is drawn around certain points and labeled “inaccuracy caused by drift”;
(d) the left ordinate, reflecting unadjusted biosensing current values [i2]Tr obtained from a drifting, in vivo biosensor, is labeled “[i2]Tr, μA” and is scaled in units of 1 μA;
(e) the abscissa, reflecting reference glucose values, is labeled reference glu mg/dL,” and is scaled in 25-mg/dL units.
The solid line in
To apply [D1]Tr, the drifting, unadjusted biosensor response current at each run-time point greater than the induction period was multiplied by the corresponding [D1]Tr value. The unadjusted, measured biosensing currents [i2]Tr in
{[i2]Tr}A=[D1]Tr*[i2]Tr (38)
(a) the graph is labeled above by: “Y=0.0441*Glu+3.117; r=0.910 (all data)”;
(b) the graph is labeled below by “[D1]Tr Adjusted [i2]Tr Data”;
(c) the left ordinate, reflecting drift adjusted biosensing current values obtained from equation 38, at run-times greater than an induction period, is labeled “{[i2]Tr}A, uA” and is scaled in units of 2 μA.
The solid line in
In the graphs in
(a) the left ordinate, reflecting reference glucose values, obtained by fingerstick measurements in mg per deciliter, is labeled “ref glu mg/dl” and is scaled in units of 25 mg/dl;
(b) the right ordinate reflecting both adjusted and unadjusted glucose values, measured by a drifting intradermal glucose biosensor in mg per deciliter, is labeled “meas glu mg/dl’ and is scaled in units of 25 mg/dl;
(c) the common abscissa, reflecting run-time, is labeled “Tr, min” and is scaled in 100-minute units;
(d) the graph of reference glucose values, obtained by fingerstick measurements is identified by open circles within vertical error bars of +/−10%;
(e) the lower graph of unadjusted glucose values, measured by a drifting intradermal glucose biosensor is represented by a solid gray jagged line and labeled “unadjusted MAB=42%”;
(f) the upper graph of adjusted, calculated glucose values, measured by the intradermal glucose biosensor is also represented by a solid black, jagged line and further labeled “[D1]Tr adjusted MAB=7%”.
The Mean Absolute Bias Percent (MAB) is the average of all the values of the Absolute Bias Percent (AB %) calculated for each run-time indexed computed value of glucose versus the run-time indexed measured reference glucose value, where AB %=ABS{(meas−ref)/ref}*100, where the absolute value is denoted as ABS.
The improvement in the adjusted calculated glucose values in
Referring now to
BG processing system 12 includes: a potentiostat incorporating a waveform generator for generating and applying periodic or non-periodic voltage waveforms to the biosensor; a current sampling system 22 for sampling the response current 18 from application of the voltage waveforms; a biofouling analysis system 24 for determining if any biofouling is occurring and, if so, providing a drift adjustment; a BG calculation system 32 for calculating a BG reading; and a BG output system 34 for outputting the BG reading to the display device 38. BG processing system 12 can calculate a BG reading using currents generated from the application of any applied voltage waveform 16 (square waveform shown) as often as desirable. Moreover, some or all of BG processing system 12 may be integrated with the sensor 14 or reside apart from the sensor 14 (e.g., within display 38).
In response to a voltage pulse 36, a response current is sampled by current sampling system 22 at three or more transient time points tj such as i1, i2, and i3. Current values i1, and i2 are utilized by biofouling analysis system 24. Current values, i1, i2 or i3 can be utilized by BG calculation system 32.
Biofouling analysis system 24 includes a drift adjustment calculation system 26 that determines if biofouling has occurred, and if so, calculates a drift adjustment [Dx]Tr, where x=1, 2, 3 . . . and x values represent different gain functions. In addition, a calculation system 30 is provided along with induction period data 28 (e.g., collected during the first 30-60 minutes of use) to calculate biofouling threshold values, as well as, gains G1 and G2 used in the drift adjustment function [D1]Tr.
As described herein, a relative difference [RD1] is computed at S1, e.g., using equation 30 where [RD1]Tr=[(i1−i2)/i1]Tr. The regression slope, mTr, of a plot of Tr[RD1]Tr versus Tr is determined within a baseline period (e.g. 60-80 min). The value of mTr is compared to a threshold limit at S2. If mTr is less than the threshold limit, a run-time indexed drift adjustment function [Dx]Tr is calculated for use by BG calculation system 32. To obtain adjusted response values, each run-time indexed current function(s) is multiplied by the run-time indexed drift adjustment function [Dx]Tr to yield a drift adjusted current function for each run-time point [Tr]n.
As noted above, functions f of discrete sampled currents (e.g. i1, i2 or i3) may be used to calculate the BG. If no biofouling has occurred then [Dx]Tr is not used in the function f, and if biofouling has occurred then [Dx]Tr is used within the function to compensate for biofouling. BG concentrations are calculated from the adjusted or unadjusted current functions using the sensitivity Sk or [S]Tr and intercept bk. Note that a new BG reading can be provided at any time Tr, where a function of the response current is captured in response to the application of a voltage waveform 16.
Once the BG is calculated, it can be sent by BG output system 34 to an output device 38. Output device 38 may comprise any device capable of receiving and displaying data (e.g., an insulin pump, a cell phone, a Bluetooth device, a watch, etc.).
Referring to
(a) The biosensor housing containing the biosensor working electrode and at least one other electrode is attached to the skin of a subject using an adhesive pad on the underside of the housing. The liner over the pad is removed and the biosensor housing pressed against the skin.
(c) The biosensor within the biosensor housing is activated by insertion into the subject, at which time, a potentiostat is triggered to begin an applied voltage regime.
(d) The applied voltage regime may consist of the application of a series of periodic voltage waveforms, such as a square wave voltage pulse between a counter and working electrode. The initial potential, prior to the first voltage step, may be zero volts with respect to the reference electrode; greater or less than zero volts with respect to the reference electrode; or, an open circuit potential Eoc. Either the entire current transient generated from the application of the square-wave voltage or a series of sampled transient currents are stored in the memory of the in vivo biosensor's microprocessor controlled monitoring unit.
(e) A period is required for the in vivo biosensor to equilibrate to its surroundings. An example of such an equilibrium period is 60-120 minutes from the time of implantation. Throughout the run-time period Tr, each application of a voltage waveform creates a characteristic current transient response. Within each transient, there are j values of current after the peak current ip. The maximum value of j is determined by the pulse width and the data sampling rate.
(f) Following the equilibration period, there is a period called the baseline period, within which, biofouling is assumed to be minimal. During this baseline period, an “in vivo” sensitivity may be determined by an in vitro reference glucose method using blood samples from the subject. For example, the baseline period may be 60-180 minutes in length; however, any range within that period (e.g. 60-80 min) may be used as the baseline collection period or calibration period.
(g) The data obtained within the baseline period is used to calculate a biofouling drift parameter which is compared to a software encoded threshold value to determine whether a drift adjustment is necessary at run-times greater than an induction period. Also, during the baseline period, other baseline parameters such as [Ewc]0, [GPw]0, [Ewr]0, [Rs]0 or [Ru]0 may be calculated. These baseline values may be compared, via relative difference functions, to calculated values of [Ewc]Tr, [Ewr]Tr, [GPw]Tr, [Rs]Tr or [Ru]Tr beyond the induction period. For example, if the drift determining parameter is outside a software encoded threshold limit, then gain adjustments are calculated and applied, on a point-by-point basis at run-times greater than an induction period, using gain adjustment functions such as [GEwc]Tr (eq. 18); [GRs]Tr (eq. 21); [GPw]Tr (eq. 24); [GEwr]Tr (eq. 27); or [D1]Tr (eq. 37).
(h) If the calculated value of a drift parameter, e.g. mTr, is outside a threshold limit, then a gain adjustment function [Gx], encoded within the software of the monitoring unit, is used to calculate the value of the drift adjustment function [Dx]Tr at each run-time point greater than an induction period;
(i) If the calculated value of the drift parameter is within the threshold range limit, no drift adjustment is necessary.
(j) If the drift parameter is outside the threshold limit, then point-by-point, run-time indexed, calculated values of the drift adjustment function are applied to each run-time indexed biosensing current function at run-times greater than a threshold period. Adjusting the biosensing current may require a similar adjustment in the sensitivity in order to compensate for changes in the magnitude of the biosensing current due to application of the drift adjustment function.
(k) Analyte concentrations at run-times greater than the induction period are calculated from the drift-adjusted values of the initial sensitivity S0 and biosensing currents.
(l) If no drift is detected, analyte concentrations at run-times greater than the induction period are calculated from computer encoded calibration constants or from an adjusted calibration constants.
The foregoing description of the specific embodiments will so fully reveal the general nature of the invention that others can, by applying knowledge within the skill of the art (including the contents of the references cited herein), readily modify and/or adapt for various applications such specific embodiments, without undue experimentation, without departing from the general concept of the present invention.
While this invention has been described in connection with specific embodiments thereof, it will be understood that it is capable of further uses, variations modifications or adaptations. Such uses, variations, modifications and adaptations are intended to be within the meaning and range of equivalents of the disclosed embodiments, based on the teaching and guidance presented herein.
Having fully described this invention, it will be appreciated by those skilled in the art that the same can be performed, within a wide range of equivalent parameters, concentrations, and conditions without departing from the spirit and scope of the invention, and without undue experimentation. It is to be understood that the phraseology or terminology herein is for the purpose of description and not of limitation, such that the terminology or phraseology of the present specification is to be interpreted by the skilled artisan in light of the teachings and guidance presented herein, in combination with the knowledge of one of ordinary skill in the art.
It is believed that the disclosure set forth above encompasses multiple distinct inventions with independent utility. While each of these inventions has been disclosed in its preferred form, the specific embodiments thereof as disclosed and illustrated herein are not to be considered in a limiting sense as numerous variations are possible. No single feature, function, element or property of the disclosed embodiments is essential to all of the disclosed inventions. Similarly, where the claims recite “a” or “a first” element or the equivalent thereof, such claims should be understood to include incorporation of one or more such elements, neither requiring nor excluding two or more such elements.
The subject matter of the inventions includes all novel and non-obvious combinations and sub-combinations of the various elements, features, functions and/or properties disclosed herein. Inventions embodied in other combinations and sub-combinations of features, functions, elements and/or properties may be claimed through amendment of the present claims or presentation of new claims in this or a related application. Such amended or new claims, whether they are directed to a different invention or directed to the same invention, whether different, broader, narrower or equal in scope to the original claims, are also regarded as included within the subject matter of the inventions of the present disclosure.
This application claims priority of co-pending provisional application 60/816,608 filed on Jun. 27, 2006, entitled “Biofouling self-compensating biosensor,” the contents of which are hereby incorporated by reference.
| Number | Date | Country | |
|---|---|---|---|
| 60816608 | Jun 2006 | US |
