Implantable sensors for vascular monitoring

Abstract

An implantable sensor for implantation in a vessel, comprising a plurality of electrodes for placement on, in or adjacent a vessel wall, means for providing a drive signal to the electrodes, means for measuring at least one of impedance and capacitance between at least two of the plurality of electrodes, and means for wirelessly communicating data from the sensor and a blood vessel monitoring system comprising same.

Claims

1. A sensor system for monitoring parameters in a vessel, comprising: an implantable support structure configured to move with natural movement of the vessel wall; a plurality of pairs of electrodes coupled to the support structure and configured to be positioned circumferentially spaced around the vessel interior on, in or adjacent a wall of the vessel so as to move with natural movement of the vessel wall when the support structure moves therewith; a drive circuit configured to provide a drive signal to the electrodes, measurement circuitry configured to measure at least one of impedance and capacitance between at least two of the plurality of pairs of electrodes; and a communications circuit configured to wirelessly communicate date from the sensor; at least one reference electrode maintained at a fixed distance from one of the electrodes, wherein the measurement circuitry is configured to measure at least one of impedance or capacitance between said one of the electrodes and said reference electrode; and a signal processing circuit in at least one of the implantable sensor and an external console, wherein the signal processing circuit is configured to calculate distance between the electrode pairs based on the measured impedance or the measured capacitance, and wherein the signal processing circuit comprises a processor configured to execute instructions stored in a memory configured to perform one or more steps of: data correction with parallelogram edge and diagonal correction, by averaging opposed parallelogram sides; ellipse reconstruction to model a vessel shape, based on chordal lengths using parallelogram side calculations; and apply a correction to compensate for change from a round to elliptical cross-sectional shape of the vessel.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) The disclosure will be more clearly understood from the following description of some embodiments thereof, given by way of example only with reference to the accompanying drawings in which:

(2) FIG. 1 is a schematic diagram showing a system of the disclosure incorporating an implantable device;

(3) FIG. 2 is a block diagram showing a circuit of the implantable device;

(4) FIG. 3 is a perspective view of the implantable device;

(5) FIG. 4 is a perspective view of an alternative implantable device, without longitudinal struts;

(6) FIG. 5 is a diagrammatic end view showing how the electrodes are arranged circumferentially and how they can be driven and signals processed for different permutations of pairs;

(7) FIG. 6 is a diagrammatic side view of an alternative device, in which the sensing electrodes are distributed longitudinally along the vessel wall, for impedance planimetry measurements;

(8) FIG. 7 is a circuit diagram of a switching array for the sensing electrodes of the devices of any embodiment;

(9) FIG. 8 is a plot of impedance vs. time for a test using the device of FIGS. 1 to 3;

(10) FIG. 9 is a plot of the conductivity of blood as it changes with velocity;

(11) FIG. 10 is a diagram showing the velocity profile across the vessel;

(12) FIG. 11 is a flow diagram showing operation of a signal processor for processing data from the sensing electrodes;

(13) FIGS. 12 to 16 are sets of diagrams and equations for data processing with computation and correction;

(14) FIG. 17 is a diagrammatic side view of a device having capacitance sensing;

(15) FIG. 18 is a diagram illustrating an alternative system of the disclosure for monitoring IVC diameter and collapsibility, in this case involving electromagnetic devices;

(16) FIG. 19 is a diagram showing operating principle of the FIG. 18 system, using low frequency magnetic techniques, in this case wireless;

(17) FIG. 20 is a diagram showing a further device also using low frequency magnetic techniques, in this case wired;

(18) FIG. 21 is a pair of diagrams illustrating some operating parameters; and

(19) FIG. 22 is a diagram showing antennas for RFID type sensing; and

(20) FIG. 23 is a plot of phase difference vs. time.

DETAILED DISCLOSURE

(21) In various embodiments blood vessel monitoring systems are described which include implantable devices with a number of electrodes, a data processing subsystem, a communications subsystem, and a battery power source. The implantable device has a stent-like support structure for both anchoring and positioning the device within a vessel such as the IVC, and supporting the electrodes and some internal electronics for driving the electrodes and routing data externally. The support structure is flexible and elastic, preferably having little influence on the normal movement and shape of the IVC. In most cases the implantable device is deployed in a manner similar to a stent, within a catheter, and it expands radially to engage the blood vessel upon withdrawal of a sheath.

(22) Implantable Devices

(23) Referring to FIGS. 1 to 3, a system of the disclosure is shown. The system comprises an implantable device 1 having sensing electrodes 2 coupled to a stent-like support or anchor structure 3. One of the struts 5 also has a reference electrode 9, for use in correcting for variations in blood conductivity. There are electrical connections to an electronic circuit in a housing 4, containing power 4(a), microcontroller 4(b) and communications 4(c) components as shown in FIG. 2, all mounted on the anchor structure 3. The implantable device 1 communicates wirelessly to an external console 7, which includes data processing circuitry as well as circuits for communication to cloud servers 8. Remote interfaces are provided for use by care providers, nurses, physicians, and the patient which can receive and/or transmit data from the external console 7 via a cloud server 8.

(24) Referring especially to FIG. 3, in the implantable device 1 the multiple electrodes 2 and 9 are mounted on the cantilevered longitudinal struts 5 extending from the support structure 3. There are active and reference electrodes 2 and 9 mounted a short distance apart on one strut 5 in a manner whereby their separation is fixed. This allows calibration to detect changes in conductivity between the electrodes, so that impedance measurements between electrodes having a variable separation can be corrected.

(25) However, in another embodiment shown in FIGS. 1 and 4 there may be electrodes 2 and 9 mounted directly on a structure 21. The anchor structure 21 has a sinusoidal wave-like pattern for radial expansion and collapse. In this case the structure 21 has a low radial force to avoid ‘stenting’ the vessel and preventing the vessel from moving (and thus negating the sensing). Where particularly low radial force is required, then additional means of anchoring are preferably incorporated to prevent the device from migrating, such as one or more of the following: Anchor spikes such as sharp spikes to interact with the vessel wall. Anchor features to anchor or hang the device from the renal vein or veins. High friction surfaces to interact with the wall. Ingrowth-promoting material, such as a polyester, to accelerate tissue ingrowth. Oversizing—low radial force could be maintained while still setting the natural uncompressed diameter of the device to much greater than the maximum diameter of the vessel.

(26) An implantable device may have an arrangement of electrodes mounted directly to the support structure 21 as shown in FIG. 4 in addition to electrodes mounted on longitudinal struts as shown in FIG. 3, the two sets being used at the same time or in an alternating manner for redundancy, calibration, comparison or averaging for higher accuracy, or other purposes.

(27) Because the electrodes 2 of the implantable device 1 are insulated from or arranged outside of the support structure 3, any potential electrical interference from the structure and electronics is minimized, thereby allowing measurements to be taken in a portion of the vessel not affected by the support structure 3. Advantageously, there is physical separation of the electrodes from the support structure so that any distortion of vessel shape/collapsibility by the support does not influence the vessel shape where electrodes are located.

(28) In various examples, the electrodes 2 are disposed at the tips of elongated flexible struts (numbering between two and eight) which are biased outwardly in a cantilevered manner into contact with the vessel wall and are sufficiently flexible to allow the electrodes 2 to move inwardly and outwardly with the natural collapse and expansion of the vessel. The struts preferably have a length selected such that the electrodes 2 are positioned far enough from the support structure 3 that in the region engaged by the electrodes 2 the vessel undergoes its natural collapse and expansion without being constrained or distorted by the support structure 3, which is preferably at least about 30 mm in length.

(29) The support structure 3 is preferably stent-like and may take any suitable stent or anchor type form, as is well known in the art, providing support for the electrodes in a secure manner within the blood vessel. The support structure properties may be of the type known for supporting IVC filters for example. The structure 3 supports the electronics unit 4 containing the circuit which provides electrode drive signals, and performs signal processing from them and wireless delivery of data to the external console 7. If the support does influence vessel shape, it preferably has a known and predictable amount that can be characterised empirically in testing and corrected for in the calculation of vessel diameter, and the system is preferably programmed to compensate for it. The stent may be either super flexible/compliant so that it does not influence vessel shape significantly, or the amount of distortion should be predictable and included in the calculation.

(30) Some or all electrodes may be mounted to the inside of the support structure (closer to the centre of the lumen) in which case the thickness of the support structure would be corrected for. Alternatively, at least some may be mounted to lie alongside the members, at the same radial position. In a further example, at least some may be radially outside the members and hence in contact with the vessel wall in use.

(31) The support structure may have one, two, or more rings or hoops and interconnecting longitudinal members.

(32) Each longitudinal strut 5 has a Nitinol spine, coupled to which are insulated leads for the electrodes 2.

(33) In some embodiments, the electrodes 2 and/or the longitudinal strut 5 may be configured to be fixed to the vessel wall to ensure that the electrode moves with it. For example, the electrode 2 and/or the longitudinal strut 5 may have barbs, hooks, or other features on its outer side that penetrate or engage the wall tissue. The electrode 2 and/or longitudinal strut 5 may alternatively or additionally be coated with a material that adheres to tissue or encourages tissue growth around or into these components. In other embodiments the longitudinal strut 5 may have a tip extending beyond the electrode 2 and configured to penetrate into the vessel wall.

(34) The structure 3 diameter is preferably in the range of 5 mm to 40 mm, and the length is preferably in the range of 10 mm to 40 mm.

(35) In various embodiments, the support structure 2 may have one, two, or more rings or hoops and interconnecting longitudinal members or struts between the hoops, the hoops being resiliently biased radially outwardly in a stent-like manner to engage the vessel wall and securely anchor the device 1 in the vessel. The rings or hoops may have a sinusoidal, zig-zag, or other radially collapsible configuration to facilitate delivery through the vessel to the desired location of placement and to impart a relatively consistent radial fixation force against the vessel wall over a wide range of diameters.

(36) The support structure may also have other anchoring features such as those which are known for IVC filters and commonly known in the art.

(37) The microcontroller, measurement circuitry, the communication sub-system, and the battery are located within the electronics enclosure 4, which is hermetically sealed. An alternating current is sequentially applied between pairs of electrodes 2 and the measurement circuitry determines an impedance measurement between at least two of the electrodes 2. If it is assumed that the blood conductivity is constant, the impedance measurement between the active electrodes is related to distance between them. It is therefore possible to obtain information on the relative distances between electrodes, allowing IVC diameter and possibly also other data such as cross-sectional area and shape to be determined. The inclusion of a reference electrode 9 enables the system to accommodate changes in the conductance of blood as the reference electrode 9 is at a known distance from a sensing electrode 2 and internal calibration is performed automatically. The reference electrode 9 also facilitates some calculations to reject or correct for any changes with endothelialisation and the resulting changes in conductance.

(38) Measurement of IVC diameter or collapsibility has certain unique considerations and challenges not present in the measurement of other blood vessels. One such challenge is the asymmetrical shape and dynamics of the vessel as it collapses and expands. The IVC tends to collapse in the anterior-posterior direction, moving from a more circular cross-section at higher blood volumes to a flattened, oval cross-section at lower blood volumes. Thus the direction of measurement is an important factor. The device 1 may be specially configured to enable the determination of the vessel dimensions and/or collapsibility in a desired direction (e.g. anterior-posterior). For example, the support structure 3 may have radiopaque or ultrasonic markers to guide the user during placement so that it may be oriented with electrodes 2 along the desired axis. Alternatively, the support structure 3 may be configured to self-orient by means of varying circumferential radial force, into a desired rotational position in the IVC upon deployment such that a pair of the electrodes 2 are disposed along the anterior-posterior axis.

(39) In various embodiments, the implantable device has a circumferential array of electrodes disposed at a predetermined circumferential spacing from each other as shown in FIGS. 3 and 4. For example, three, four, five, six or more electrodes may be arranged around the circumference of the device 1. The system may be configured to allow selection of various pairs of electrodes between which impedance or other parameters may be measured. The maximum and minimum distances between various electrode pairs may thus be determined so that the pair most closely aligned with the anterior-posterior axis may be selected. Such selection may be performed manually by the user, or the system may be configured to automatically sample various electrode pairs and determine through software which pair is oriented closest to the desired axis of measurement, and/or between which pair the diameter variation or collapsibility is greatest or lowest. This embodiment could also be utilized to estimate irregular shapes of IVC cross section which may be useful in understanding particular blood volume patient states.

(40) Sensing and Blood Conductivity Correction

(41) The presence of multiple electrodes facilitates numerous pairs to be selected and impedance measurements taken and subsequently converted into distances and then derived parameter values. As can be seen in FIG. 5, with six electrodes 2, there are multiple ways to calculate the position of any one electrode. All or a portion of the distances between an electrode and each other electrode on the implant may be calculated. This over-constrained problem provides redundancy in the system and allows for errors or drift to be corrected for in the algorithms.

(42) However, blood conductivity is reliant on a number of blood properties which may vary over the course of the day/year: Glucose may vary over the day by 50-100%. It has a direct effect on conductivity, different ranges for normal/diabetes patients. Orientation of Erythrocyte cells affects conductivity and dielectric properties. Environmental factors, such as exposure to pollutants (e.g. Benzene), can cause 40% variation. Blood Type: Dielectric properties can vary by up to 50% depending on A, B, AB and O Blood type. Haematocrit may vary annually by approximately 15% due to blood loss. Support structure material may also affect electrical conductivity.

(43) Given blood conductivity variability, it is preferred that the measurements have an empirical correction factor accounting for blood conductivity. This is achieved by use of the reference electrodes 9 within the structure or on a linked structure which maintains them at a fixed separation from an adjacent sensing electrode 2.

(44) The correction factor is preferably obtained by fixing two electrodes a set distance apart, measuring blood impedance and using this as a correction. Such reference electrodes are preferably spaced-apart in the longitudinal direction because it is simpler to maintain a fixed separation in this direction. However, they may alternatively be radially spaced-apart.

(45) The IVC contracts and expands with each respiration (and to a lesser extent with each heart beat). Regular IVC diameter measurements are thus taken over multiple respiratory cycles allowing for the recording of maximum and minimum diameters, with which a measure of collapsibility can be determined.

(46) The recorded data may be stored in a memory device within electronics enclosure 4, and transmitted via Radio Frequency (RF) communication to the external console for processing and display. Alternatively raw measured signals may be transmitted upon measurement directly to the external console where they are stored and processed.

(47) Impedance Planimetry Approach

(48) In other embodiments, at least some of electrodes 2 are arranged longitudinally and in-line, at fixed distances apart. FIG. 6 shows a device 30 having a stent-like support 31, a substrate 32, power electrodes 33, and sensor electrodes 34. The IVC cross-sectional area measurement technique is based on impedance planimetry. An alternating current (AC) is applied across the outer powered pair of electrodes 33 while AC voltage measurements are made between the inner pair of sensor electrodes 34 positioned mid-way between the powered electrodes. The AC voltage measurement is inversely related to the cross-sectional area of the IVC, assuming a constant AC power source and a medium of constant conductivity.

(49) This embodiment is advantageous because it uses impedance planimetry without the use of a balloon filled with media within which to set up the electric field. In the present disclosure, the existing blood flow within the vessel is used to do this. A constant current source is applied at the power electrodes shown and the sensing is done between them using the sensor electrodes shown. An advantage of this system is that it gives an actual area of the lumen (irrespective of shape), it could also be deployed over a larger/longer area, and it may require less processing power and post processing.

(50) The AC voltage measurements allow estimation of the extent of the diameter of the vessel at the mid-point between the power electrodes 33. It is important that the voltage drop across the medium is generated from a constant AC current source. The fact that the conductivity of the blood is not constant may give rise for a need to apply a correction factor (and potentially using the electrode array as a set of reference electrodes) as described above.

(51) Switching Array

(52) FIG. 7 shows a switching array 40 for driving electrodes of any embodiment. In the switching array 40 the switching controller runs through the combinations of source detector pairs by using a series of programmable solid state switches to create an electrical path between the source and an electrode and also creating an electrical path from the opposite paired electrode current detection path to ground to close the circuit.

(53) The switching array 40 is connected to impedance measurement circuitry, which preferably includes an impedance analyser chip, and a SoC (System on chip) for the main data processing within the electronics enclosure 4, and from there data is communicated wirelessly to the external console.

(54) In exemplary embodiments the microcontroller 4(b) (FIG. 2) delivers a 100 kHz sinusoidal waveform that consumes 2 mW for the contact electrodes, and 2 μW for capacitive electrodes. The algorithm cycles through each electrode 2 pair taking impedance measurements.

(55) The drive frequency is preferably at least 100 kHz.

(56) Data Processing

(57) In executing an algorithm to determine collapsibility the following factors and considerations are applied by the data processor: expected respiration and cardiac cycle periods; expected maximum and minimum IVC diameters; corrections for blood conductivity and conductivity changes due to gradual endothelialisation using reference electrode measurements; any calibrations that may be required at implantation; and corrections facilitated due to the over constrained nature of the solution set and multiple measurements for each dimension.

(58) The recorded data is stored and transmitted via Radio Frequency (RF) communication to the external console 7. Some data processing may be done with a processor or processing circuitry in the implant prior to transmission externally. Optionally the data may be stored in a memory device on the implant. Alternatively, only raw electrode signals correlated with measured electric parameters such as impedance or capacitance are transmitted wirelessly, and the required data processing is performed by processing circuitry in the console 7, which may be a computer, or a smartphone, or any other computing device.

(59) It will be understood that in any of the embodiments described herein, the terms “signal processing circuit”, “processing circuitry,” and the like may refer to circuitry and/or processors within the electronics housing 4 on the implant, in the external console 7, or combinations thereof, and the data processing and calculations performed by the processing circuitry may be performed entirely within the implant, entirely in the external console, or partially in each. Further, in some embodiments, the external console may communicate with remote computer systems via Bluetooth, wireless or wired communication, and some or all of the data processing referred to herein may be performed on such remote systems.

(60) The impedance to distance calibration is based on the initial resting dimensions of the electrodes. If the impedance of the blood changes with respect to time, all of the impedance measurements are scaled with respect to the reference electrode set. A geometric reconstruction may be performed based on the assumption that the IVC has an elliptical shape. Fouling detection and compensation may be performed with either of two methods, geometric or time-dependent, as described more fully below.

(61) FIG. 8 is a plot of impedance vs. time for an animal study using the device shown in FIG. 4, showing the impedance between the pairs of electrodes 2 varying in synchronism with the IVC distension. It may be seen that the impedance between pairs of electrodes varies as the wall of the IVC moves. The frequency of the variation in the wall of the IVC and therefore the signal, is determined by the rate set on the mechanical ventilator (11 breaths per minute in this case). When the ventilator is stopped (simulating breath hold) the variation in the impedance stops and recommences when respiration is restarted, again demonstrating that the signal seen is a direct result of the IVC wall motion induced by the ventilator.

(62) In diagnosing and monitoring heart failure, it may be valuable to determine other parameters such as blood flow velocity and/or pressure gradient, or ΔP/Δx. FIG. 9 shows the relationship of blood conductivity as a function of flow velocity. It may be seen that conductivity increases with flow velocity. This relationship presents the opportunity to determine blood flow velocity based upon the determination of impedance between electrodes. From blood flow velocity and vessel radius, pressure gradient may be calculated.

(63) FIG. 10 shows several of the key parameters for the data processing performed by the system when calculating the blood flow from the individual velocities inferred between pairs of electrodes. It will be seen that the radius “R” at any point in time is a parameter in calculation of the velocity for any radial position “r”, which in turn is related to the pressure gradient ΔP/Δx. In more detail:

(64) $v_m=\frac{1}{4_n}\frac{\Delta P}{\Delta x}{R}^2\mathrm{where}\frac{\Delta P}{\Delta x}=\mathrm{pressure}\mathrm{gradient},\mathrm{and}n=\mathrm{viscosity}\mathrm{and},v\left(r\right)=v_{m\left[1-\frac{r^2}{R^2}\right]}$
gives the velocity profile.

(65) This information may be used in combination to compute the blood flow rate. Vessel diameter may be determined using the impedance and, using different chords as shown in FIG. 5 through the cross section and the variation of conductance with velocity, each chord could be assigned a velocity. These velocity profiles could then be combined to compute a blood flow rate, or pressure gradient, or flow velocity.

(66) The switching array sequentially connects each pair of electrodes to the impedance analyser chip within the electronics enclosure 4, which determines the impedance measurement for that pair of electrodes. Each of these results is then recorded on the SoC (which is part of the communications block 4(c)) which also performs the communications function to transmit the stream of data to the external console 7.

(67) One approach for this device is to allow the electrodes to endothelialize and therefore reduce the risk of thrombus or embolization. This does however bring the challenge of managing the potential changes in impedance due to the varying media and tissue thickness between the electrodes. A reference electrode may be utilized as a solution to this issue as described above. An alternative option is to prevent the electrodes from being incorporated into the vessel wall. In this situation the electrodes are exposed to blood and may be subject to fouling due to thrombus formation. Anti-fouling coatings may be used for the implanted electrode surfaces. The coatings may comprise one or some of carbon nanotubes, conductive polymers, hydrogels, conductive hydrogels, bioactive coatings, and a tissue engineered neural interface.

(68) One or more of the following approaches may be used to compensate or correct for the effects of fouling. Impedance to distance calibration based on resting dimensions Salinity recalibration—scales impedance measurements with reference change Geometric reconstruction with elliptical assumption Fouling detection and rejection Geometric Requires data from 3 electrodes to reconstruct ellipse, and compensation data used to detect and reject fouling Time-Dependent Uses varying time scales to detect fouling

(69) FIG. 11 is a flow diagram for the overall data processing. Initially, the current signals are read from between each successive pair of electrodes in a drive scheme set by the microcontroller and the switching array. As shown in FIG. 5 there may be trans-vessel flow chords 27, mid-vessel flow chords 26, and/or wall flow chords 25. As a known voltage is applied between the electrodes of each pair and the current is detected, the resistance and hence distance can be determined by comparing the reference impedance to the impedances calculated from each electrode pair adjusted for any fouling correction.

(70) The system processes derived data to recognize the asymmetrical shape change in the IVC, specifically the use of multiple electrodes to get dimensional measurement in multiple axes and reconstructs an ellipse from these dimensions.

(71) There are preferably a sufficient number of electrodes to minimize the error of being oriented off-axis (i.e. not aligned with anterior-posterior axis of the vessel). There is preferably a minimum of four electrodes, but preferably at least six, arranged circumferentially around the implant, and the sampling is preferably of all possible electrode combinations in order to model the ellipse. The fouling detection and correction in software is very advantageous, and eliminates outliers in the detected data.

(72) Also, advantageously in some embodiments the data processor is programmed to determine flow rate and/or pressure gradient in addition to vessel dimension, as described above.

(73) The length of the structure helps it to conform to IVC or other blood vessel, and this is preferably in the range of 10 mm to 50 mm. For optimum performance, there is preferably one structure peak per electrode.

(74) The processor is programmed to sweep through frequencies for fouling elimination/correction, as fouling will be detected more for some frequencies than others.

(75) In the next step there is a fouling check, in which any outliers are eliminated. There is then edge and diagonal correction, followed by ellipse reconstruction.

(76) FIG. 12 shows the construction of a parallelogram from chordal lengths l.sub.12, l.sub.34, l.sub.14, and l.sub.23 as determined by the impedance between two pairs of electrodes. A correction is then applied to both parallelogram edges and diagonals, in which opposed lengths are added and the sum divided by two. The parallelogram edge correction is thus based on the fact that the opposing parallelogram edges are equal to each other. Basic geometrical expressions as illustrated are used to determine the diagonals of the parallelogram. The subsequent diagonal correction is based on the minimal correction needed such that the intrinsic geometric relationship between parallelogram edges and diagonals can be satisfied.

(77) FIG. 13 shows ellipse reconstruction from the parallelogram, in which there is correction applied to compensate for change from a round (top left diagram) to elliptical (top right) shape of the support structure in end view. Two criteria for reconstructing the ellipse are: The reconstructed ellipse must encompass the parallelogram (the ellipse outline needs to pass through the four corners of the parallelogram). There is a stretch in an “X” direction, the longer diagonal or major axis of the parallelogram. When the reconstructed ellipse is transformed to its un-deformed circular shape, the diagonals of the corresponding parallelogram need to form an angle of 90°.

(78) With the two criteria above, the reconstructed ellipse is uniquely defined.

(79) The ellipse reconstruction algorithm is as follows, in which: a and b are the parallelogram long and short side lengths, and c and d are the major and minor axes; the electrodes are referred to as electrodes 1, electrode 2, electrode 3, and electrode 4 in sequence circumferentially around the vessel.

(80) Define the included angle of the diagonals as:

(81) $\Phi =\frac{\mathrm{acos}\left(d^2+c^2-4a^2\right)}{2dc}$

(82) Define the point 1 position and point 2 position as

(83) $\left[\begin{array}{c}{x}_1\\ y_1\end{array}\right]=\left[\begin{array}{c}\frac{c}{2}\\ 0\end{array}\right],\left[\begin{array}{c}{x}_2\\ y_2\end{array}\right]=\left[\begin{array}{cc}\frac{d}{2}\cos & \left(\Phi \right)\\ \frac{d}{2}\sin & \left(\Phi \right)\end{array}\right],$
respectively.

(84) Define an unknown θ to be solved later.

(85) Two virtual positions which used to help reconstruct the ellipse are:

(86) $\left[\begin{array}{c}{x}_1^{\prime }\\ y_1^{\prime }\end{array}\right]=\left[\begin{array}{cc}\cos \left(\theta \right)& \sin \left(\theta \right)\\ -\sin \left(\theta \right)& \cos \left(\theta \right)\end{array}\right]\left[\begin{array}{c}{x}_1\\ y_1\end{array}\right]\left[\begin{array}{c}{x}_2^{\prime }\\ y_2^{\prime }\end{array}\right]=\left[\begin{array}{cc}\cos \left(\theta \right)& \sin \left(\theta \right)\\ -\sin \left(\theta \right)& \cos \left(\theta \right)\end{array}\right]\left[\begin{array}{c}{x}_2\\ y_2\end{array}\right]$

(87) Based on the position relationship of electrode 1 and electrode 2 at unreformed position, the following relationship needs to be satisfied:
x.sub.1′y.sub.1′+x.sub.2′y.sub.2′=0
θ can be solved by the equation above.

(88) The corresponding major and minor axis of the ellipse are solved by
Major axis=max(√{square root over (x.sub.1′.sup.2+x.sub.2′.sup.2)},√{square root over (y.sub.1′.sup.2+y.sub.2′.sup.2)})
Minor axis=min(√{square root over (x.sub.1′.sup.2+x.sub.2′.sup.2)},√{square root over (y.sub.1′.sup.2+y.sub.2′.sup.2)})

(89) FIG. 14 shows the effects of noise and fouling on the ellipse.

(90) Referring to FIGS. 15 and 16, if the two edges associated with Electrode i (l.sub.i i−1 and l.sub.i i+1) are significantly larger than their corresponding opposite edges, the processor assumes that there is fouling on electrode. This may be corrected using the parallelogram edge and diagonal correction procedure described with reference to FIG. 12.

(91) FIG. 17 shows a further embodiment in which the implantable device 100 has capacitance electrodes or pads. The device 100 consists of conductor pads (electrodes 102), a data processing subsystem, a communications subsystem, and a battery power source contained in a housing 103. The components are housed and incorporated into a stent-like support structure 101 for both anchoring and positioning the device within the IVC, in a manner as described above in any embodiment. The support structure is flexible and elastic, having little influence on the normal movement and shape of the IVC.

(92) The electrodes are positioned such that they lie on the endothelium of the IVC wall on directly opposing interior wall. The electrode is arranged such that it extends outside of the stent support, thus minimising any electrical interference from the structure.

(93) The drive circuitry may apply an alternating voltage across the two conductive electrodes, thus creating an effective capacitor with the blood as a dielectric material. The measurement circuit, e.g. an analyser chip, can then measure the capacitance between the electrodes. If it is assumed that the blood dielectric value is constant, the distance (corresponding to the IVC diameter) between the plates can be estimated accurately by measuring the capacitance. It is expected that the use of a capacitance measure may be less influenced by any intervening material (endothelial/blood/other cells).

(94) Some or all of the features described above for the embodiments with sensing electrodes to measure impedance apply to this embodiment with capacitive electrodes.

(95) Electromagnetic Aspect

(96) In other embodiments, power may be provided to sensing electrodes by electromagnetism, and relative movement of beacon transponders may be tracked.

(97) In these embodiments blood vessel monitoring systems include an implantable device with at least one electrode in the form of an electromagnetic beacon transponder, a data processing subsystem, a communications subsystem, and a battery power source. The electrodes are supported by a stent-like support structure for both anchoring and positioning the device within a vessel such as the IVC. The support structure is flexible and elastic, having little influence on the normal movement and shape of the IVC. Some or all of the features described above for the other embodiments may apply for the embodiments with beacon transponders, the transponders being mounted in a manner akin to the mounting of the sensing electrodes of any embodiment.

(98) Referring to FIG. 18 a system 200 is described for providing measurement of IVC lumen diameter and collapsibility. An implantable device 201 comprises a stent-like support structure 202 with peaks 204, and a number of passive beacon transponders arranged 203 around the structure's periphery. There is an external electromagnetic coil and sensor array 205 linked with a data processing console 206. There is a communications subsystem and power source within one of the transponders 203, or alternatively in a separate hermetically sealed capsule mounted to the support structure.

(99) The electromagnetic beacon transponder electrodes 203 are coupled to the stent-like support structure 202 such that they are positioned along the circumference of the IVC endothelium.

(100) Each transponder 203 consists of a miniature electrical circuit contained in a sealed glass capsule, measuring approximately 1.85 mm in diameter and 8.0 mm in length. The transponders are preferably passive having no power source and, thus, are excited externally by the flat panel array 205 on which the patient lies. The flat panel 205 houses both a series of electromagnetic source coils and a sensor array. The transponders 203 are excited via the electromagnetic source coils of the array 205 with each transponder emitting a unique resonant frequency signal. The spatial profile of each resonant signal is detected by the multiple channel sensors, allowing for the position of each transponder to be determined.

(101) Accordingly, the diameter of the IVC may be determined as the distance between opposing transponders 3, the spatial resolution of which is less than 0.25 mm. Alternatively, where multiple beacons are incorporated into the stent support structure 202, it may be possible to infer IVC cross-sectional area.

(102) The data processing functions described above may be applied in any desired combination to this embodiment.

(103) Referring to FIG. 19, coils 250 are within the beacon transponders 203 and the magnetic field between them is monitored at the “B amplitude” location. This is in response to a low frequency stimulus. There may be more than two coils, giving multiple axes for 3 dimensional (3D) positions. In this case the communication is wireless to a host which performs the data processing. The coils may have a 19 kHz resonant frequency, and the external stimulating array may have 32 coils to reconstruct position

(104) Referring to FIG. 20, in another embodiment an implanted device 300 has coils 301 and a sensing coil 303 is connected by a wired link 305 with an amplifier connected to signal processing circuits. In this case it is expected that a stronger external magnetic field may be applied.

(105) Referring to FIG. 20, in another embodiment an implanted device configuration 300 has a pair of coils 301 used for excitation (transmission) and an implanted sensing coil 303. The sensing coil 303 is connected by a wired link 305 to the outside circuit with an amplifier connected to the signal processing circuits. The excitation magnetic field generated by the excitation coils 301 is assumed to vary linearly across the range of possible sensing coil locations and, in order to induce a measureable voltage in the sensing coil, the excitation current in the coils 301 is varied using a known resonance frequency (e.g. 19 kHz). The variation of the excitation magnetic field across space causes spatially-dependent magnitude shifts in the sensing coil 303 and hence the location of the sensing coil 303 within the body can be resolved. Pre-amplification is used to improve the signal-to-noise-ratio of the sensed signal in the sensing coil 303 and in order to reduce the necessary magnetic field strength to be created by the excitation coils 301. The same may be achieved through use of multiple array detectors.

(106) Referring to FIG. 21, in an implantable device 350 transponders 351 are mounted around the periphery of an implantable support structure 352. There is an externally-applied magnetic field, operating at a frequency in the range of 100 MHz to 300 MHz. In one example, a 1 mm difference in separation of two opposing electrodes 351 gives a phase shift of 0.36°. The electrodes 352 are in this case passive, being powered by the external RF field.

(107) A variation on this embodiment is shown in FIGS. 22-23, in which an implantable device has multiple separated antennas 400 and phase difference from the antennas is measured. An external oscillator detects the phases ϕ1, ϕ2, ϕ3 and in one example operates at 300 MHz, giving a 0.36° phase shift for a 1 mm change in position.

(108) The disclosure is not limited to the embodiments described but may be varied in construction and detail. The term “electrode” in this specification is intended to mean in the relevant context an electrode for either impedance or capacitive measurements or a passive electromagnetic transponder. Various embodiments may include one or more of any of the physical, electrode, of electronic features of any embodiment to achieve the desired result of monitoring a vessel dimension. It is also envisaged that the processor operations to perform re-construction or modelling of vessel dimensions based on parallelograms and/or ellipses may be performed based on monitoring chords by sensors other than electrodes, such as for example by way of ultrasonic transducers in which time of flight for echo signals or direct transfers across a vessel are monitored.