SENSOR FOR MEASURING pH

Cross-Reference to Related Applications

[0001] This application claims priority to U.S. Provisional Application No. 61/772,233 titled "IMPLEMENTATION OF A CALIBRATION-FREE ABSORBANCE SENSOR FOR MEASURING pH", filed March 4, 2013, the disclosure of which is incorporated by reference herein in its entirety.

Field of the Invention

[0002] Embodiments described herein relate to methods for measuring analytes, such as with an optical absorbance-based sensor for the detection of pH.

Background

[0003] The precision and robustness of a sensor is closely associated with the quality and robustness of its calibration. Known sensing methods to detect, for example, biologically relevant analytes such as pH require the use of a single- or multi-point calibration by the user before use. This can require a dedicated device for calibration and can take up to 30 minutes. Additionally, once a sensor is calibrated, measurement errors can be introduced by changes in the measured light levels, changes in optical component configurations, and other causes. For example, changes in the light source intensity, bending of optical fibers, and detector temperature changes can be detected incorrectly as pH changes. Furthermore, manufacturing variability between sensors can lead to inconsistent and unreliable measurements between sensors.

[0004] Some known sensors need calibration at many data points and at frequent intervals. Other known sensors may need calibration at only one data point and one time. Known methods of manufacturing a sensor with robust calibration, typically, involve a highly reproducible manufacturing process for both the instrumentation and the sensing material, and implementation of functionalities that can eliminate or reduce the possibility of changes in the sensing material and instrumentation over time. Such known manufacturing methods can also add to the cost and the complexity of the sensor. [0005] Accordingly, a need exits for an analyte sensor that is calibration-free, e.g. that can reliably and accurately measure analytes regardless of manufacturing variability, changes in ambient conditions or operating parameters.

Summary

[0006] Disclosed embodiments relate to relationships between the absorbance of a pH-sensitive sensor molecule and the pH of the solution to which the sensor molecule is exposed. The absorbance of a given molecule(s) at any wavelength is the ratio of the intensity of light transmitted through the molecule(s) at that wavelength to the intensity of light transmitted with no molecule(s) present in the optical path at that wavelength. Disclosed embodiments relate to methods for accurately determining the absorbance at any wavelength of a sensor molecule situated in a sensor where the sensor molecule(s) is fixed in the optical path and cannot be removed from the optical path.

Brief Description Of The Drawings

[0007] FIG. 1 shows the optical path of a fiber-optic based pH sensor with the sensor molecule present in the optical path, according to an embodiment.

[0008] FIG. 2 shows the optical path of a fiber-optic based pH sensor with no sensor molecule present in the optical path, according to an embodiment.

[0009] FIG. 3 shows the optical path of a fiber-optic based pH sensor with three optical fibers, according to an embodiment.

[0010] FIG. 4 shows the optical path of a fiber-optic based pH sensor with three optical fibers, according to another embodiment.

[0011] FIG. 5 is a graph illustrating the pH determination accuracy for a first pH sensor using Phenol Red indicator over a range of pH values.

[0012] FIG. 6 is a graph illustrating the pH determination accuracy for a second pH sensor using Phenol Red indicator over a range of pH values. [0013] FIG. 7 is a graph illustrating the pH determination accuracy for the second pH using calibration constants from the first pH sensor over a range of pH values.

Detailed Description

[0014] The following detailed description is organized into the following three sections:

(i) Section 1 addresses the derivation of mathematical expressions for pH measurement;

(ii) Section 2 addresses the different methods for determining Ro; and (iii) Section 3 describes the results of experiments conducted to evaluate the accuracy of the proposed methods to measure pH.

SECTION 1 - Derivation of mathematical expressions for pH measurement

[0015] The pH of a solution is a measure of the activity of the (solvated) hydrogen ion [H ] in the solution. Hence, the pH of a solution is a measure of the hydrogen ion concentration in the solution. Pure water has a pH of approximately 7 at 25°C. Solutions with a pH less than 7 are said to be acidic and solutions with a pH greater than 7 are basic or alkaline.

[0016] In living organisms, pH affects many essential metabolic and homeostatic functions. For example, pH affects how enzymes function, as they can only work at specific pH depending upon the enzyme. If the pH is not correct then the enzyme's active site can be altered permanently, i.e. the enzyme is denatured. This can prevent key chemical reactions from occurring within the body.

[0017] For a pH-sensitive sensor molecule, the relationship between the pH of a solution with which the sensor molecule is in contact and its optical absorbance at two different wavelengths can be represented as:

where CI = K

[0018] Additionally, K is the sensor molecule's equilibrium constant and the other terms are the sensor molecule's absorption coefficients. The terms ABS and ABS are the absorbance of the sensor molecule measured at wavelength λ ² and λ ¹ , where λ ¹ is a wavelength at which only one of the sensor molecule's forms (acid form or base form) absorbs light. The ABS terms in Equation 1 are the only measured parameters, and can be defined by the following equation:

Where:

ABS* = the absorption of species x at wavelength λ

I = the intensity of light transmitted through the species x at wavelength λ

I ₀ =the intensity of light transmitted with no species x present at wavelength λ.

[0019] To use Equation 1 , I ₀ and I must be measured at both λ ¹ and λ ² . In some instances that involve a typical spectrometer, it is possible to change the measurement conditions from one in which the sensor molecule (or indicator) is in the optical path (I) to another in which the sensor molecule (or indicator) is not in the optical path (I ₀ ), so that it is possible to measure I ₀ and I separately and calculate a value for ABS* using Equation 2. However, in other instances that involve a sensor in which the sensing chemistry is fixedly located in the optical path, measuring I ₀ is non-trivial and non-obvious.

[0020] The disclosed embodiments present a practical way to measure I ₀ at any wavelength λ, in an optical system where the sensor molecule (or indicator) is fixedly located in, i.e. cannot be removed from, the optical path. Typically, for most sensor molecules (absorbance indicators) there are wavelengths at which the sensor molecule exhibits no absorbance. In this specification, a wavelength at which a sensor molecule exhibits no absorbance is referred to as k ^re ^, and the intensity of light measured at such wavelength is referred to as f ^re ^. Additionally, a wavelength at which the sensor molecule does have absorbance is referred to as X ^abs , and the intensity of light measured at such wavelengths is referred to as† ^abs .

[0021] In instances in which there is no sensor molecule in the optical path of the sensor, the ratio of the light at these two wavelengths can be represented as: where the "o" denotes the absence of the sensor molecule (or indicator) in the optical path.

[0022] In instances in which the sensor molecule is present in the optical path of the sensor, ratio of the measured light intensity of these two wavelengths can be represented as:

^abs

= R _D

, ^re f , Eq. 4

'D where the "D" denotes the presence of the sensor molecule in the optical path of the sensor.

[0023] Since the sensor molecule has no absorbance at ^re f , the following representation can be made:

pfef _X ref

I ₀ = I _D . Eq. 5

[0024] Assuming that both the light source and optical path are spectrally stable, then R ₀ is a

constant and thus, Equations 3 and 5 can be combined to express I ₀ as a function of

1 _D ^A and R ₀ :

l ^bS = ( l ₀ ^Xref * R ₀ ) = ( ^Aref * Ro)■ Eq. 6

[0025] Using Equation 6, I ₀ can be determined at any time by measuring I _D and R ₀ .

Pi ^re f

Since I _D is measured with the sensor molecule present in the optical path, it is possible to measure Ι ₀ ^{λ f} at any time by applying light at A ^re f to the optical path of the sensor and measuring the intensity of the transmitted light. However, a need still exits to determine R ₀ . Six methods to accurately determine R ₀ are described in the following sections.

SECTION 2 - Methods and devices for determinine Rn

Embodiment 1:

[0026] If the optical path of the sensor does not spectrally alter light transmitted through it, R ₀ can be measured using a suitable detector system placed such that the detector system is directly exposed to the light source. This can be accomplished using a number of detector systems such as, for example, a beam splitter combined with band pass filters and photodiodes, or a micro spectrometer. In this embodiment, R ₀ can be measured as often as necessary to compensate for changes in the light source intensity or changes in the light source spectral composition. In some instances, where the light source is unstable, determination of R ₀ can be required as part of each measurement. In other instances, where the light source is stable (e.g., where the light source is a light emitting diode (LED)), determination of R ₀ may be required only once for the lifetime of the sensor.

Embodiment 2:

[0027] In many instances, the assumption in Embodiment #1 described above is not valid, as the optical path of a sensor alters the spectral characteristic of the light transmitted through it. For example, most optical fibers attenuate the shorter visible wavelengths (blue light) more than longer visible wavelengths (green light and red light). In such instances, if the light source is spectrally stable and the spectral changes to the light passing through the optical path of the sensor are reproducible, the following technique for determining R ₀ can be used. In this embodiment, an optical path for a sensor can be implemented that does not have any sensor molecule in the optical path. The measurement can be repeated with the sensor molecule in the optical path of the sensor, thus allowing R ₀ to be determined.

[0028] In this embodiment, the determination of R ₀ is a system calibration and may need to be done only once. This technique for determining R ₀ can apply, for example, for the case of a fiber optic based pH sensor. The method involves building two sensors that are identical for all relevant parameters (e.g., fiber length, fiber diameter, fiber material, etc.), except that the first sensor has the sensor molecule in its optical path (see FIG. 1) and the second sensor does not have the sensor molecule in its optical path (see FIG. 2). In this embodiment, the sensor without the sensor molecule can be connected to the measurement system (e.g., an optical detector) to determine R ₀ . The sensor that includes the sensor molecule can then be used to make another

-t abs

measurement, so that the I _D values can be determined. Equations 1 , 3 and 6 can then be

p, abs

used to calculate pH using I _D and R ₀ .

[0029] This embodiment is appropriate for systems in which the spectral properties of the light source and the optical fiber do not change. A white LED can provide the required stable light source if the LED is not driven with high voltage for an extended period of time. If such an LED is turned on only when a measurement is needed (e.g., if the LED is pulsed) and additional measures are implemented, such as using a current limiting resister when driving the LED, then the spectral properties of the LED can be stable for long periods of time (days or weeks).

Embodiment 3:

[0030] Even the most stable light sources eventually undergo changes in their spectral properties (e.g., due to prolonged use or as a result of changes in ambient or room temperature). Additionally, most optical paths implemented in sensors also change their spectral properties with time and usage. Hence, for determining R ₀ that is not compromised by such changes is desirable. A system and method for determining R ₀ for a fiber optic based sensor is illustrated in FIG. 3.

[0031] In this embodiment the light source is optically coupled to a first, or proximal, end of optical fiber 2. Light from the light source exits the second, or distal, end of optical fiber 2 and is reflected from the mirror and into the second, or distal, end of each of optical fibers 1 and 3. The light returning through optical fiber 1 to the first, or proximal, end of the fiber does not pass through any sensor molecules before it reaches the optical detector (not shown in FIG. 3) at the first end of the fiber and thus can be used to determine R ₀ . In contrast, the light returning through optical fiber 3 to the first, or proximal, end of the fiber passes through a gap in the fiber in which the sensor molecule (or indicator) is disposed before it reaches the optical detector. This light is

T abs

used to measure all the necessary I _D values. In this embodiment, a detector system capable of measuring all the required wavelengths can be selectively optically coupled to the first, or proximal, end of each of optical fiber 1 and optical fiber 2 to detect the light conducted through the fibers from their second ends. In one example, the detector system can be selectively optically coupled to the fibers by, for example, moving a fiber connected to the detector between a position in which it receives light from the first end of optical fiber 1 and a position in which it receives light from the first end of optical fiber 2. The receiving fiber can be moved between the two positions by using a piezoelectric motor (e.g., the M3-L motor from New Scale Technologies). Such piezoelectric motors can have sub-micron resolution and can operate in a translational mode, thus enabling accurate positioning of two fibers (applicable for small core fibers as well). [0032] The frequency at which fiber 1 would need to be connected to measure R ₀ would depend on the rate at which the spectral properties of the light source and the optical path are changing. In some instances where the light source and the optical path are stable, R ₀ can be measured only once during the sensor lifetime. In other instances where the light source and/or the optical path are not stable, R ₀ can be determined before each measurement from fiber 3. Hence, with this method, spectral changes in the light source can be corrected or compensated for at any time. Since the optical paths of fiber 1 and fiber 3 are the same, spectral changes in the fibers (due to bending or ageing) will be the same in both optical paths and thus corrected for each time R ₀ is measured.

Embodiment 4:

[0033] In another embodiment, the mirror shown in FIG. 3 can be replaced by a luminescent material capable of emitting the desired wavelengths of light for any application, as shown in FIG. 4. Note that the desired wavelengths of light would be determined by the specific sensor molecule (or indicator) being used. In this method, excitation light capable of exciting the luminescent material on the end of the fibers would be transmitted from through fiber 2 from the first, proximal end to the second, distal end of the fiber. The resulting luminescent light emitted from the luminescent material would be, at least in part, collected by the second, or distal, end of each of fiber 1 and fiber 3 and returned through the fibers to the optical detector in a manner similar to that described in Embodiment #3. A suitable luminescent material can be, for example, the compounds used to make white LED's (e.g., InGaN-Yitterbium Aluminum Garnet(YAG), ZnSe, etc.). Such compounds can emit white light when excited by a excitation light source such as a blue LED. Typically the blue LED emits excitation light in the range of 450 nm to 480 nm, but some devices also use luminescent material designed to be excited by excitation light at 400nm. In all cases white light is produced by such compounds with most visible wavelengths being part of the emission spectrum.

[0034] One advantage of this embodiment is the ease of manufacturing. In Embodiment #3, the mirror's position relative to the end of the fibers will need to be precisely maintained to assure light is efficiently coupled into fibers 1 and 3. In Embodiment #4, the luminescent material can be, for example, a silicone matrix in which the luminescent molecules are evenly dispersed. In this embodiment, the application of the silicone will only require that enough of the silicone is present to cover the fiber ends. The silicone provides the additional benefit of bonding the ends of the three fibers together.

Embodiment 5:

[0035] This method is similar to Embodiment #4 in that it uses a luminescent material on the ends of the fibers. However Embodiment #5 only requires two optical fibers (instead of the three optical fibers used in Embodiment #4). In this embodiment, optical fiber 1 shown in FIG. 4 is eliminated. The embodiment works by first applying the excitation light to the first, or proximal, end of optical fiber 3 and measuring the luminescent light returned through optical fiber 2. If an excitation light wavelength is chosen that is not strongly absorbed by the sensor molecule (e.g., λ = 400nm when using Phenol Red as the sensor molecule), then the excitation light will cause the luminescent material (lumiphore) to emit luminescent light. The light returned through optical fiber 2 to the optical detector will not have passed through the sensor molecule (or indicator). Thus, this light will be suitable for determining R ₀ . If the excitation light source is then optically coupled to optical fiber 2 and the optical detector is optically coupled to fiber 3 (e.g., using a

y. abs

piezoelectric motor) all the necessary I _D measurements can be made to allow Equations 1 -3 to be used. This method has the advantage of using fewer fibers. In applications in which space is limited (e.g., intravascular blood measurements) this can be a useful advantage.

Embodiment 6:

[0036] This embodiment is different from the preceding methods discussed above in that it does not rely on using the equations described above. In this embodiment, a reference library of absorbance curves for a sensor molecule (or indicator) is created. The reference library can include multiple features or properties of the absorbance curves for the sensor molecule. Examples of such features can include, but are not limited to, absorbance curves of the sensor molecule at different target analyte concentrations, absorbance curves having absorbance information collected at equally spaced wavelengths or at specifically chosen wavelengths that are the same for all curves in the library, absorbance curves that cover the entire analyte concentration range of interest, the difference in the analyte concentrations where absorbance curves are obtained is equally spaced, the differences (i.e., "steps") between target analyte concentrations is equal to the desired measurement resolution or, if greater, can be used with an interpolation method to achieve a higher resolution, normalization of each absorbance curve in the library, etc. The features of the absorbance curves for the sensor molecule to include in the library discussed above are not exclusive and other features can also be added to the library.

[0037] The absorbance curves described above can become a reference library for comparing to a measured sample curve to determine the measured sample's analyte concentration. A sample absorbance curve can be obtained by measuring the absorbance at each wavelength used in the reference library absorbance curves. The absorbance measurement is performed by measuring abs jaijs

I _D and R ₀ (using one of the methods, above) and then calculating I ₀ using Equation 6.

The absorbance at each wavelength

Normalizing the data, as the data in the reference library, can complete the measurement of the sample curve.

[0038] The sample's absorbance curve can then be compared to the reference library to determine which reference absorbance curve is the closest match to the sample's absorbance curve. The analyte concentration of the best matched reference library absorbance curve can then be reported as the measured sample's analyte concentration. Multiple methods can be employed for making the comparison such as, for example, least squares regression analysis. The number of wavelengths used in each absorbance curve in the reference library will depend on the complexity of the curve's shape. In some instances, only two or three points may be needed. In other instances, more complicated absorbance curves may require a large number of data points. It will be advantageous to use as few points as possible so as to minimize the computational resources needed to perform the comparison.

SECTION 3 - Experimental results validating the disclosed embodiments to measure nil

[0039] To test the disclosed embodiment to measure the pH of a sample, three fiber optic sensors were built, similar to those shown in FIGS. 1 and 2. Two of the sensors used Phenol Red as the pH-sensitive sensor molecule (or indicator) in the optical path (see FIG. 1) and the third sensor had no pH-sensitive sensor molecule (see FIG. 2). The experiment was carried out using Embodiment #2 described above. Measurements from both of the sensors with the pH-sensitive sensor molecule (or indicator) were made in eight phosphate buffer saline (PBS) solutions. The buffers ranged from a pH of approximately 6.95 to 7.65 in nominal 0.1 pH unit increments. Each buffer was also measured using a calibrated pH meter with a calomel pH electrode and temperature probe. After making all the measurements, the data from two buffers with pH values of 6.945 and 7.648, were used to calculate the constants CI and C2 in Equation 1. Using these constants, the rest of the data was converted to calculate pH values using Equation 1. The pH bias (the difference between the calculated pH values and the pH values measured with the pH electrode) was then plotted versus the measured pH in a classic Bland-Altman chart. The charts for the two sensors are shown in FIG. 5 and FIG. 6.

[0040] FIGS. 5 and 6 show that the disclosed method to calculate pH was accurate. It can thus be said that sensors with the same sensor molecule (or indicator) but with different sensor molecule concentrations, optical path lengths and illumination intensities should have the same values for CI and C2 (data not shown). Said in another way, the second sensor should not require any calibration provided Equation 1 is valid and Embodiment #2 works as predicted. To test this hypothesis, the data from second sensor was analyzed using Equation 1 and the constants obtained from the first sensor. The data was plotted in the same way as the previous data and is shown in FIG. 7. FIG. 7 shows that both Equation 1 and Embodiment #2 worked as predicted since the overall bias of the second sensor is essentially the same with both sets of calibration constants.

[0041] The disclosed embodiments to determine pH address the problem of measuring I ₀ in an optical path containing a light absorbing material (sensor molecule). Several embodiments have been described by which pH can be accurately determined. It is anticipated that additional methods will become apparent as specific applications are considered. The general concept, however, provides a link between the theory of measuring pH using the ratio of the absorbance at two different wavelengths and a practical method of implementing the theory. The data generated with two sensors is compelling and it is should be noted that the indicator concentration and path length were not controlled in any way when these sensors were made.

[0042] The equations derived above and the disclosed embodiments provide a practical means for making a sensor or implementing a sensing technique that can measure pH of a solution. Such embodiments meet two of the criteria set forth in the problem that is being addressed, namely, measurements independent of manufacturing variability, for example, sensor molecule concentration and optical path length, and measurements independent of the light source intensity changes caused by any sources, including fiber bending. Although the disclosed embodiments use a pH-sensitive sensor molecule such as Phenol Red to detect the pH of a solution, the embodiments can employ any sensor molecule that exists in two states, in one of which the sensor molecule is reversibly bound to a species or an analyte to be measured and in the other of which it is not bound to the species, and the two sensor molecule states are optically distinct and measurable. These embodiments and equations can enable the development of a sensing technique (or a sensor) that can potentially be applied broadly to measure many different analytes (e.g., sodium, potassium, lactate, etc.) provided that a sensor molecule with the required two forms can be found.

[0043] The various embodiments described herein should not to be construed as limiting this disclosure in scope or spirit. It is to be understood that no limitation to the scope of the disclosure is intended thereby. It is to be further understood that resort may be had to various other embodiments, modifications, and equivalents thereof which may suggest themselves to those skilled in the art without departing from the spirit of the present disclosure and/or scope of the appended claims.

[0044] Those skilled in the art will recognize, or be able to ascertain, using no more than routine experimentation, numerous equivalents to the specific embodiments described specifically herein. Such equivalents are intended to be encompassed in the scope of the following claims.