APPARATUS FOR TOPICAL APPLICATION OF MATERIAL

20170239454 · 2017-08-24

    Inventors

    Cpc classification

    International classification

    Abstract

    The present invention relates to apparatus for topical application of material for cosmetic purposes (10). The apparatus for topical application of material (10) comprises measurement apparatus configured to measure a property of skin of a human or animal subject and actuating apparatus configured to change a permeability of the skin of the human or animal subject in dependence on the measured property of the skin. The apparatus for topical application of material (10) further comprises application apparatus configured to apply material for cosmetic purposes to the skin whilst substantially no iontophoretic current flows through the skin and after the permeability of the skin has been changed.

    Claims

    1. Apparatus for topical application of material for cosmetic or medical purposes, the apparatus comprising: measurement apparatus configured to measure a property of skin of a human or animal subject; actuating apparatus configured to change a permeability of the skin of the human or animal subject in dependence on the measured property of the skin; and application apparatus configured to apply material for cosmetic or medical purposes to the skin whilst substantially no iontophoretic current flows through the skin and after the permeability of the skin has been changed.

    2. Apparatus according to claim 1 in which the actuating apparatus is configured to change a permeability of the skin by application of an electric signal to the skin.

    3. Apparatus according to claim 2 in which the electric signal is varying.

    4. Apparatus according to claim 2 in which the electric signal comprises at least one of: an electric potential signal; and an electric current signal.

    5. Apparatus according to claim 4 in which the actuating apparatus is configured to apply the electric potential signal and the electric current signal to the skin at different times.

    6. Apparatus according to claim 5 in which the actuating apparatus is configured to apply the electric potential signal and then to apply the electric current signal.

    7. Apparatus according to claim 4 in which the electric potential signal and the electric current signal are applied to the skin at substantially a same time.

    8. Apparatus according to claim 1 in which the actuating apparatus comprises spaced apart members which are susceptible of carrying current and which are operative to develop an electric potential therebetween.

    9. Apparatus according to claim 8 in which the spaced apart members are disposed in substantially the same plane whereby the electrodes present a substantially planar surface that can abut against the skin.

    10. Apparatus according to claim 8 in which the actuating apparatus is configured such that the spaced apart members are electrically isolated from the skin when the actuating apparatus bears against the skin.

    11. Apparatus according to claim 1 in which the actuating apparatus is configured to generate an electric potential signal in the form of a pulse, the actuating apparatus being configured such that the pulse decays progressively from a peak value.

    12. Apparatus according to claim 1 in which the actuating apparatus comprises spaced apart current applying members which carry current and which are operative to pass current therebetween by way of the skin when the spaced apart current applying members are in contact with the skin.

    13. Apparatus according to claim 12 in which the actuating apparatus is configured such that the electric current is substantially constant while it is being applied to the skin.

    14. Apparatus according to claim 12 in which the current applying electrodes are disposed in substantially the same plane whereby the current applying electrodes present a substantially planar surface that can abut against the skin.

    15. Apparatus according to claim 1 in which the measurement apparatus is configured to measure an electrical property of skin of a human or animal subject.

    16. Apparatus according to claim 15 in which the measurement apparatus is configured to measure an impedance of the skin.

    17. Apparatus according to claim 16 operative to make a determination in respect of permeability of the measured skin in dependence on a real part of measured impedance.

    18. Apparatus according to claim 17 operative to make the determination in dependence on a model which relates measured impedance and permeability to each other.

    19. Apparatus according to claim 15 in which the measurement apparatus comprises spaced apart measurement members and a signal generator, the signal generator being operative to apply a varying signal to the spaced apart measurement members.

    20. Apparatus according to claim 1 in which the application apparatus comprises a material actuator which is operative to dispense material for cosmetic purposes from the apparatus for topical application of material and a reservoir which is configured to hold material for cosmetic purposes, the material actuator being operative to dispense material for cosmetic purposes from the reservoir.

    21. (canceled)

    22. Apparatus according to claim 1 comprising a housing which contains and supports components of the apparatus, the housing being configured to be gripped in one hand.

    23. Apparatus according to claim 1 configured to measure a property of the skin by way of the measurement apparatus before and after the actuating apparatus is operative.

    24. Apparatus according to claim 1 configured to at least one of measure a property of the skin and change a permeability of the skin after operation of the application apparatus.

    25. Apparatus according to claim 1 comprising data storage, data stored therein being from previous operation of the apparatus for application of material in respect of at least one of: previous measurement by the measuring apparatus; previous characteristics of operation of the actuating apparatus; previous characteristics of operation of the application apparatus.

    26. (canceled)

    27. A method of topically applying material for cosmetic or medical purposes, the method comprising: measuring a property of skin of a human or animal subject with measurement apparatus; changing a permeability of the skin of the human or animal subject with actuating apparatus in dependence on the measured property of the skin; and applying material for cosmetic or medical purposes to the skin with application apparatus whilst substantially no iontophoretic current flows through the skin and after the permeability of the skin has been changed.

    Description

    BRIEF DESCRIPTION OF DRAWINGS

    [0049] Further features and advantages of the present invention will become apparent from the following specific description, which is given by way of example only and with reference to the accompanying drawings, in which:

    [0050] FIG. 1 is a schematic of apparatus for topical application of material according to the present invention;

    [0051] FIG. 2 is a block diagram of the main operative components of the apparatus of FIG. 1;

    [0052] FIG. 3 shows an electrode assembly comprised in the apparatus of FIG. 1;

    [0053] FIG. 4A is a flow chart showing the main steps during operation of the apparatus of FIG. 1;

    [0054] FIG. 4B is a graph of skin impedance against rate of transepidermal water loss;

    [0055] FIG. 5A is an example of an electrical equivalent model of the stratum corneum; and

    [0056] FIG. 5B is a representative Cole-Cole plot for skin tissue.

    DESCRIPTION OF EMBODIMENTS

    [0057] A schematic of apparatus for topical application of material 10 is shown in FIG. 1. The apparatus comprises a housing 12 which supports and contains components of the apparatus and defines an external surface of the apparatus. The housing comprises two parts: a main body 14; and an operative body 16. The housing is of a shape and size that the main body may be gripped in the hand of a user. The main body 14 contains and supports a reservoir (not shown) which contains a cosmetic agent such as skin-care lotion (which constitutes material for cosmetic purposes). The main body 14 also contains and supports six rechargeable AA NiMH battery cells which provide electrical power for the apparatus 10. The battery cells are rechargeable by way of an external battery charger in accordance with conventional practice. The operative body 16 comprises electronic and electro-mechanical components of the apparatus 10. The electronic and electro-mechanical components are described below with reference to FIG. 2. The distal end of the operative body 16 defines a substantially planar surface on which an electrode assembly 18 is mounted. The electrode assembly 18 is described below in with reference to FIG. 2 and subsequently in more detail with reference to FIG. 3.

    [0058] A block diagram of the main operative components of the apparatus of FIG. 1 is shown in FIG. 2. The main operative components comprise an ARM Cortex M3 embedded processor 32, electrical power supply circuitry 34, a USB communication port 36, communication port driver circuitry 38, a loudspeaker 40, LED indicators 42 and an on-off switch 44. The ARM Cortex M3 embedded processor 32 is operative to control operation of the apparatus 10 of FIG. 1 in respect of measurement, actuation and application of cosmetic agent as is described further below. The ARM Cortex M3 embedded processor 32 is therefore operative to store in integral memory firmware to control such operation and to provide for control and operation as otherwise described herein. The provision of such firmware is within the ordinary design capabilities of the notionally skilled person. The ARM Cortex M3 embedded processor 32 comprises integral components such as timers, an analogue-to-digital converter, and a digital-to-analogue converter and plural digital input/output lines. The analogue-to-digital converter is operative to provide for analogue-to-digital conversion of acquired analogue signals for processing within the ARM Cortex M3 embedded processor 32. The digital-to-analogue converter is operative to convert digital data to analogue signals for the actuating apparatus described below. The digital input/output lines are operative to control components of the apparatus 10, such as in respect of putting electronic components into a tri-state condition or into or out of a power conserving mode, and provide for control of whatever further external apparatus may be provided, such as skin abrading apparatus.

    [0059] The electrical power supply circuitry 34 comprises the electric batteries described above with reference to FIG. 1, and is otherwise configured by way of bandgap reference circuitry and voltage generation and regulation circuitry to provide electrical power rails for the electronic circuitry and required reference voltages. The electric batteries are recharged when recharging current is provided by way of gold plated copper terminals 35 provided on the exterior of the housing 12. The design of electrical power supply circuitry 34 is within the ordinary design capabilities of the notionally skilled person. The loudspeaker 40 is operative under control of the ARM Cortex M3 embedded processor 32 to provide audible notification as to when components of the apparatus 10 of FIG. 1, such as the measurement apparatus and the actuating apparatus, are operating. The LED indicators 42 are operative under control of the ARM Cortex M3 embedded processor 32 to provide visible notification as to when the apparatus 10 of FIG. 1 is switched on and otherwise, such as by use of different colours, to provide visible notification as to when different parts of the apparatus 10 of FIG. 1 are operating, such as when each of the measurement apparatus and the actuating apparatus is operating. The communication port driver circuitry 38, which is under control of the ARM Cortex M3 embedded processor 32, drives the USB communication port 36 to provide for reception of data by and transmission of data from the apparatus 10 of FIG. 1 as is described in more detail below. In alternative forms, the communication port driver circuitry 38 is operative to drive a WiFi transceiver to provide for wireless communication of data to and from the apparatus. Design of the apparatus to provide for WiFi communication will be a matter of ordinary design for the skilled reader. The apparatus 10 of FIG. 1 is brought into data communication with a computer, such as a laptop, by way of a USB cable which is connected to the USB communication port 36.

    [0060] The main operative components of FIG. 2 further comprise a signal generator 46, actuation signal conversion and conditioning circuitry 48, measurement signal conversion and conditioning circuitry 50 and the electrode assembly 18, 52. The signal generator 46 is under control of and receives data from the ARM Cortex M3 embedded processor 32 and is operative to drive each of the actuation signal conversion and conditioning circuitry 48 and measurement signal conversion and conditioning circuitry 50 at different times. The signal generator 46 is operative to determine voltage and current amplitude, frequency, duty cycle and duration of signals generated. The actuation signal conversion and conditioning circuitry 48 comprises a 12-bit digital-to-analogue converter from Analog Devices, namely an AD5339, and other circuitry to provide for current limit control and voltage compliance control depending on the mode of operation and to interface with the electrode arrangement 52. The measurement signal conversion and conditioning circuitry 50 comprises a digital sinewave generator, namely an AD9832 from Analog Devices, a 25 MHz master clock generator, namely a SG8002DCOHB from Epson, and other circuitry to interface with the electrode arrangement 52.

    [0061] The main operative components of FIG. 2 yet further comprise a signal measurement arrangement 54, a first measurement interface arrangement 56, and a second measurement interface arrangement 58. The signal measurement arrangement 54 comprises an 18-bit analogue-to-digital converter, namely an MCP3421 from Microchip, and is under control of and provides digital data to the ARM Cortex M3 embedded processor 32 in dependence on analogue signals received from the first measurement interface arrangement 56 and the second measurement interface arrangement 58 at different times. The signal measurement arrangement 54 is operative to determine voltage amplitude and phase angle and current amplitude and phase angle. The first measurement interface arrangement 56, comprises circuitry to interface with the electrode arrangement 52. The second measurement interface arrangement 58 comprises circuitry to interface with the electrode assembly 52. In addition the main operative components of FIG. 2 comprise an electrode assembly switching control 60 and a pump arrangement 62. The electrode assembly switching control 60 is under the control of the ARM Cortex M3 embedded processor 32 and is operative to determine the mode of operation of the electrode assembly 52 as is described further below. The pump arrangement 62 is under the control of the ARM Cortex M3 embedded processor 32 and is operative to pump cosmetic agent contained in the reservoir of the apparatus 10 of FIG. 1. A conduit from the reservoir is operative to convey pumped cosmetic agent to an aperture beside the electrode assembly 52 whereby cosmetic agent is dispensed from the apparatus 10 of FIG. 1.

    [0062] The electrode assembly 18, 52 of FIGS. 1 and 2 is shown in more detail in FIG. 3. The electrode assembly 80 of FIG. 3 comprises a first electrode arrangement 82 and a second electrode arrangement 84. The first electrode arrangement 82 comprises two first electrodes 86 which are spaced apart from each other such that the second electrode arrangement 84 is disposed therebetween. The two first electrodes 86 lie in substantially the same plane, each define a semicircle in area and are disposed such that the linear bases of the semicircles face each other. The two first electrodes 86 are formed of gold plated copper and are not covered by an insulating material. The second electrode arrangement 84 comprises two second electrodes 88 which each define serpentine paths and are disposed relative to each other such that they define an interdigitated structure. The two second electrodes 88 lie in substantially the same plane and in the same plane as the two first electrodes 86. The two second electrodes 88 are formed of gold plated copper. A layer of an insulating material, such as polyurethane, covers the two second electrodes 88. The width of each of the two second electrodes 88 is 0.1 mm and the separation between the two second electrodes 88 is 0.06 mm. Different electrode spacings are used depending on the thickness of the skin to which the cosmetic is to be applied. An electrode spacing of 0.06 mm is appropriate where the stratum corneum is thin, such as around the eye. An electrode spacing nearer to 0.1 mm is appropriate where the stratum corneum is thicker, such as the heel. The total area of the electrode assembly 80 is 2 cm.sup.2 (2 cm long by 1 cm wide).

    [0063] Operation of the apparatus described above with reference to FIGS. 1 to 3 will now be described with reference to the flow chart 100 shown in FIG. 4A. After the apparatus 10 of FIG. 1 is switched on by way of the on/off switch 44 the apparatus is programmed 102. Programming the apparatus comprises configuring the apparatus to carry out a skin preparation and cosmetic agent application regime. The apparatus is configured by downloading configuration data from a computer which stores the configuration data by way of a USB cable to the USB communication port 36 and thereafter to the ARM Cortex M3 embedded processor 32 for storage therein. The configuration data comprises phenotype data such as gender, age and ethnic origin and also skin type data such as normal, dry, oily and combination. The user makes an appropriate selection on the computer before the configuration data is downloaded. The configuration data also comprises historic data which has been uploaded from previous use of the apparatus 10 of FIG. 1, with such historic data being operative to provide for refining of the skin preparation and cosmetic agent application regime. According to one approach, frequency of use of the apparatus and the amount of cosmetic agent dispensed on each occasion is stored. The processor 32 is operative in dependence on the stored data to restrict the amount of cosmetic agent dispensed during further use of the apparatus. For example a maximum weekly dose for a particular cosmetic agent may be 2 ml based on previous use. The processor 32 is therefore operative to provide that no more than this amount is dispensed in a seven day period or to reduce the amount dispensed during the latter part of the seven day period. If a user does not use the apparatus for one or more days during a seven day period the processor is operative to increase the amount dispensed during the remaining days of the seven day period. According to another approach, historic data provides for distinguishing between trends and isolated events. The historic data comprises environmental factors such as temperature and humidity. Such factors affect skin characteristics such as a skin moisture content and permeability. Historic temperature and humidity data allows the present skin measurements to be applied in the context of presently measured temperature and humidity. For example, if presently measured temperature and humidity are very low this indicates that skin impedance measurements are higher than they would be otherwise whereby high impedance measurements are a consequence of current environment rather than poor skin health. The processor 32 is therefore operative to adjust present skin impedance measurements to take account of presently measured temperature and humidity whereby an appropriately lower amount of cosmetic product is dispensed.

    [0064] The second stage comprises measurement of the permeability of the skin 104 during which the electrode assembly 18 is brought into contact with the skin. Two forms of measurement are made: skin impedance measurement; and skin capacitance measurement. Each form of measurement will now be described in turn although the two forms of measurement are both used to provide enhanced characterisation of skin permeability.

    [0065] Considering skin impedance measurement first, the signal generator 46, the measurement signal conversion and conditioning circuitry 50 and the first electrode arrangement 82 are operative together under control of the ARM Cortex M3 embedded processor 32 to apply an alternating current signal of swept frequency between 100 Hz and 1 MHz or an alternating current signal comprising frequencies between 100 Hz and 1 MHz. The signal measurement arrangement 54, the second measurement interface arrangement 58 and the first electrode arrangement 82 are operative together under control of the ARM Cortex M3 embedded processor 32 to measure the current signal between the electrodes of the first electrode arrangement 82 at different frequencies. The ARM Cortex M3 embedded processor 32 is operative to determine the impedance on the basis of the current measurements and the applied voltage and then to determine the real and imaginary parts of the impedance. The thus determined real part of the impedance is then correlated with skin permeability by the ARM Cortex M3 embedded processor 32 in dependence on a model stored in the processor 32. A graph which relates skin impedance to transepidermal water loss is shown in FIG. 4B. The graph of FIG. 4B forms the basis for a model that relates impedance to skin permeability. The graph of FIG. 4B and the model based thereon are described further below. The ARM Cortex M3 embedded processor 32 is further operative to determine a capacitance of the skin in dependence on the imaginary part of the impedance, the frequency of the applied signal and a resistance value representing resistance of an outermost layer of the stratum corneum in accordance with the model of the skin described below with reference to FIGS. 5A and 5B.

    [0066] Turning now to consider skin capacitance measurement, the signal generator 46, measurement signal conversion and conditioning circuitry 50 and the second electrode arrangement 84 are operative together under control of the ARM Cortex M3 embedded processor 32 to apply an electric field to the skin. More specifically the electrodes of the second electrode arrangement 84 are operative as plate of a capacitor with the skin constituting the dielectric between the plates of the capacitor. The signal generator 46 is operative to provide for application of a signal of alternating current form to the electrodes of the second electrode arrangement 84. The signal measurement arrangement 54 and the second measurement interface arrangement 58 are operative together under control of the ARM Cortex M3 embedded processor 32 to provide for measurement of the current and voltage between the electrodes of the second electrode arrangement 84. The ARM Cortex M3 embedded processor 32 is operative to determine the capacitive reactance and then relative permittivity in dependence thereon. The ARM Cortex M3 embedded processor 32 is also operative to provide for determination the thickness of the skin. Determination of relative permittivity and of skin thickness will now be described further below.

    [0067] The reactance of the capacitor defined by the electrode plates of the second electrode arrangement 84 and the skin is given by:

    [00001] X C = 1 2 .Math. π .Math. .Math. fC

    [0068] Re-arranging we obtain:

    [00002] C = 1 2 .Math. π .Math. .Math. fX c

    [0069] The capacitance is related to the permittivity of the material between the plates by:

    [00003] C = .Math. .Math. A d

    [0070] Combining the two immediately preceding equations and making c, the relative permittivity, the subject of the combined equation we obtain:

    [00004] .Math. = d 2 .Math. π .Math. .Math. fX c .Math. A

    [0071] A, the area of the plates and f, the frequency, are known. As mentioned above, the capacitive reactance, X.sub.c, is measured and thus known. The distance separating the plates, d, is estimated based on the typical thickness of the part of the skin being measured. The relative permittivity, c, is therefore calculated.

    [0072] As described above, measurement using the first electrode arrangement 82 also provides for determination of the capacitance C. In view of capacitance being related to relative permittivity by:

    [00005] C = .Math. .Math. A d

    [0073] We re-arrange to obtain:

    [00006] d = .Math. .Math. A C

    [0074] The capacitance, C, is provided by measurement with the first electrode arrangement 82, the relative permittivity, c, is provided by measurement with the second electrode arrangement 84 and the area, A, of the second electrode arrangement is known. Hence d, the plate separation or more specifically the depth of the stratum corneum, is calculated to thereby provide a more accurate value for d.

    [0075] Returning now to FIG. 4A now that the permeability of the skin has been determined, the ARM Cortex M3 embedded processor 32 is operative to determine whether or not the permeability meets the requirements stored at the first stage 102 of the process. If not, the process progresses to a step in which the permeability of the skin is increased 106. The permeability of the skin is increased by two approaches: application of an electric potential signal; and application of an electric current signal. Each approach will now be described in turn although the two approaches are both used to provide for an enhanced increase in permeability of the skin.

    [0076] Considering application of an electric potential signal first, the signal generator 46, the actuation signal conversion and conditioning circuitry 48 and the second electrode arrangement 84 are operative together under control of the ARM Cortex M3 embedded processor 32 to apply an electric potential in the range of 20 volts to 140 volts in the form of a pulse of duration of 10 μs to 10 ms. The pulse is operative to reversibly form plural pathways through the stratum corneum to thereby increase permeability. During application of the electric potential, the signal measurement arrangement 54 and the first measurement interface arrangement 56 are operative to measure the electric potential at the second electrode arrangement 84 to monitor the applied electric potential and provide feedback control.

    [0077] Turning now to consider the application of an electric current signal, the signal generator 46, the actuation signal conversion and conditioning circuitry 48 and the first electrode arrangement 82 are operative together under control of the ARM Cortex M3 embedded processor 32 to apply a substantially constant current to the skin by way of the electrodes of the first electrode arrangement 82. A potential of no more than 50 Volts and a current of up to 500 μA/cm.sup.2 are applied to the skin. During application of the current, the signal measurement arrangement 54 and the first measurement interface arrangement 56 are operative to measure the current at the first electrode arrangement 82 to monitor the applied current and provide feedback control. Application of the current is operative to maintain the pathways formed by the pulsed electric potential in the absence of the latter.

    [0078] After step 106 of FIG. 4A, the apparatus 10 of FIG. 1 is operative to measure the permeability as described above with reference to step 104 of FIG. 4A. Steps 106 and 104 are repeated until a desired permeability is achieved.

    [0079] When a desired permeability is achieved, operation of the apparatus 10 of FIG. 1 progresses to application of the cosmetic agent to the skin 108. More specifically the pump arrangement 62 is operative under control of the ARM Cortex M3 embedded processor 32 to pump cosmetic agent from the reservoir through the aperture provided adjacent the electrode assembly 18 onto the skin. The amount and rate of application of cosmetic agent to the skin is determined in accordance with data stored in the ARM Cortex M3 embedded processor 32 at step 102 in FIG. 4A to meet a desired cosmetic application regime. In certain forms, application of cosmetic agent takes place in plural stages with measurement performed in accordance with step 104 and actuation in accordance with step 106 performed between stages of application of cosmetic agent.

    [0080] When application of cosmetic agent is complete 110, data relating to the just completed skin preparation and cosmetic agent application process is stored by the ARM Cortex M3 embedded processor 32 for later transmission to the user's computer. As described above such historic data is used in subsequent treatments.

    [0081] FIG. 4B shows a graph which relates skin impedance to the rate of transepidermal water loss (TEWL). Transepidermal water loss is a measurement of water lost through the skin by way of the stratum corneum other than by sweating. As per FIG. 4B, the units of water loss are expressed in g/m.sup.2/h (grams per meter squared per hour). As can be seen from FIG. 4B, there is a generally linear relationship between the log of skin impedance and the rate of transepidermal water loss with impedance decreasing as the rate of transepidermal water loss increases. It is known that the rate of transepidermal water loss corresponds to skin permeability. The model used by the ARM Cortex M3 embedded processor 32 in determining skin permeability is based on the relationship of FIG. 4B between skin impedance and the rate of transepidermal water loss.

    [0082] A simple electrical equivalent model of the stratum corneum 120 is shown in FIG. 5A. The model consists of a first resistor R.sub.1 in parallel with a capacitor C with this parallel arrangement being in series with a second resistor R.sub.2. C and R.sub.1 represent the capacitance and resistance of the outermost layer of the stratum corneum and R.sub.2 represents the resistance found in deeper layers of the stratum corneum. Typical values for R.sub.1 range from 100Ω to 5 MΩ cm.sup.2 and R.sub.2 from 0.1Ω to 1 kΩ cm.sup.2. The model reflects the frequency dependence of skin and in particular the decrease in magnitude of the impedance as frequency increases. Based on skin impedance measurements as described above and the theory for biological tissues according to the Cole brothers (Bioelectrical impedance analysis—part I: review of principles and methods, Kyle, U. G., I. Bosaeus, et al. (2004), Clinical Nutrition 23(5): 1226-1243), values for R.sub.1, R.sub.2 and C can be calculated. A typical complex plot obtained when impedance of any biological tissue is analysed is shown in FIG. 5B. According to the Cole brothers' empirical equation the impedance is given by:

    [00007] Z = R + R 0 - R 1 + ( j .Math. .Math. ω .Math. .Math. t ) α Equation .Math. .Math. 1

    [0083] Where R.sub.∞ is the resistance at very high frequencies where the semicircle of FIG. 5B crosses the x axis (i.e. when the reactance is zero), R.sub.0 is the resistance at very low frequencies where the semicircle of FIG. 5B crosses the x axis (i.e. when the reactance is zero), ω is the angular frequency, T is a time constant and φ=α(π/2) is the constant phase angle. The general equation for this circuit can be written as:


    Z=Z.sub.series+Z.sub.parallel  Equation 2

    [0084] Based on a comparison of Equation 1 with Equation 2 the following equations can be obtained:

    [00008] Z series = R = R 2 Equation .Math. .Math. 3 Z parallel = R 0 - R 1 + ( j .Math. .Math. ω .Math. .Math. t ) α = R 1 1 + j .Math. .Math. ω .Math. .Math. R 1 .Math. C Equation .Math. .Math. 4

    [0085] The parallel impedance has real and imaginary parts and can be represented in the Cartesian form as:

    [00009] Z parallel = Z + Z = R 1 1 + ω 2 .Math. R 1 2 .Math. C 2 - j .Math. ω .Math. .Math. R 1 2 .Math. C 1 + ω 2 .Math. R 1 2 .Math. C 2 Equation .Math. .Math. 5

    [0086] In Equation 5 Z″ is the part of interest which provides for calculation of the value of C:

    [00010] Z = j .Math. ω .Math. .Math. R 1 2 .Math. C 1 + ω 2 .Math. R 1 2 .Math. C 2 Equation .Math. .Math. 6

    where Z″ is measured, ω is known and R.sub.1 is R.sub.0 at low frequencies or R.sub.∞ at high frequencies. Equation 6 is solved for C in view of Z″, R.sub.1 and ω being known.