US 20110105877 A1
An apparatus and method are disclosed for detecting the disconnection of a vascular access device such as a needle, cannula or catheter from a blood vessel or vascular graft segment. A pair of electrodes is placed in direct contact with fluid or blood in fluid communication with the vascular segment. In one embodiment, the electrodes are incorporated into a pair of connectors connecting arterial and venous catheters to arterial and venous tubes leading to and from an extracorporeal blood flow apparatus. Wires leading from the electrodes to a detecting circuit can be incorporated into a pair of double lumen arterial and venous tubes connecting the blood flow apparatus to the blood vessel or vascular graft. The detecting circuit is configured to provide a low-voltage alternating current signal to the electrodes to measure the electrical resistance between the electrodes, minimizing both the duration and amount of current being delivered. Detection of an increase in electrical resistance between the electrodes exceeding a pre-determined threshold value may be used to indicate a possible disconnection of the vascular access device.
1. A system for detecting the disconnection of a vascular access device from a blood vessel or vascular graft, comprising:
a fluid delivery device for providing fluid through a first conduit into a first site of the blood vessel or graft;
a first electrode in contact with the lumen of the first conduit;
a second electrode in fluid communication with a second site of the blood vessel or graft;
an electronic circuit connected to the first and second electrodes, and configured to deliver a control signal to the first and second electrodes in order to measure the electrical resistance of a fluid between the first and second electrodes, wherein
at least one of the electrodes is located closer to the blood vessel or graft than to the fluid delivery device.
2. The system of
3. The system of
4. The system of
5. The system of
6. The system of
7. The system of
8. The system of
9. The system of
10. The system of
11. An apparatus for monitoring the continuity between a vascular access device and a blood vessel or vascular graft segment, comprising:
a first and second vascular connector, the first connector being attached on a proximal end to a distal end of a fluid-carrying lumen of a first double-lumen tube, and the second connector being attached on a proximal end to a distal end of a fluid-carrying lumen of a second double-lumen tube,
the first connector comprising a first electrode in contact with a lumen of the first connector and electrically connected to a wire within a wire-carrying lumen of the first double-lumen tube, and the second connector comprising a second electrode in contact with a lumen of the second connector and electrically connected to a wire within a wire-carrying lumen of the second double-lumen tube, wherein,
the wire within the first double-lumen tube and the wire within the second double-lumen tube are each connected to an electrical connector at a proximal end of the double-lumen tubes.
12. The apparatus of
13. The apparatus of
14. The apparatus of
15. A vascular connector comprising a proximal fluid connection end, a distal fluid connection end, and an electrode configured to electrically connect a fluid-carrying lumen of the connector with a wire external to the vascular connector.
16. The vascular connector of
17. The vascular connector of
18. The vascular connector of
19. The vascular connector of
20. An electrical circuit for measuring the resistance of a liquid between a first and second electrode, the first electrode connected to a first terminal of the electrical circuit, and the second electrode connected to a second terminal of the electrical circuit, comprising:
a capacitor C1 connected on a first end to the first terminal and a capacitor C2 connected on a first end to the second terminal;
a known reference resistance Rref connected on a first end to a second end of capacitor C1;
switching means for connecting either;
a) a first reference voltage V+ to a second end of Rref, and a lower second reference voltage V− to a second end of C2 to form a first switch configuration or;
b) the first reference voltage V+ to the second end of C2 and the lower second reference voltage V− to the second end of Rref to form a second switch configuration; and measuring means for measuring a voltage Vsense at the connection between C1 and Rref; wherein
the electrical circuit is configured to determine the value of the resistance of the liquid based on the known reference resistance Rref and the observed voltage Vsense for each of the first and second switch configurations.
21. The electrical circuit of
22. The electrical circuit of
23. The electrical circuit of
The present application is a Non-provisional Application which claims priority from U.S. Provisional Patent Application Ser. No. 61/256,735, filed Oct. 30, 2009 and entitled Device and Method for Detecting Disconnection of an Intravascular Access Device, which is incorporated herein by reference in its entirety.
The present invention relates generally to systems and methods to detect disconnection of an indwelling vascular line, such as a catheter or needle, or its attached tubing. If not quickly detected, a disconnection can lead to rapid exsanguination, particularly when the blood in the catheter or tubing is under positive pressure. Examples of circumstances involving positive intravascular pressure include the positive pressure associated with an artery or arterio-venous fistula, or the positive pressure associated with an extracorporeal blood pump circuit. In hemodialysis, for example, a blood pump can generate blood flow rates of 400-500 ml/min, making rapid, reliable disconnect detection particularly desirable. Indeed any medical treatment involving relatively high flow or high pressure extracorporeal circulation (such as, for example, hemoperfusion or cardiopulmonary bypass) can be made safer by having an effective system to monitor the integrity of the arterial (withdrawal) and venous (return) blood lines.
In hemodialysis, for example, extracorporeal blood circulation can be accomplished with vascular access using either a single indwelling catheter, or two separate indwelling catheters. In a single catheter system, blood is alternately withdrawn from and returned to the body via the same cannula. A disconnection in this system can be quickly detected by placing an air monitor in the line at or near the pump inlet, because air will be drawn into the line from the disconnection site during the blood withdrawal phase of the pumping. On the other hand, in a two-catheter system, blood is typically continuously withdrawn from the body via one catheter inserted in a blood vessel or fistula, and returned to the body via the second catheter inserted in the same vessel some distance from the first catheter, or in a separate blood vessel altogether. In the two-catheter system, it is also possible to monitor for catheter or tubing dislodgement in the blood withdrawal or ‘arterial’ segment by using a sensor to detect the presence of air being entrained into the arterial tubing as blood is withdrawn from the blood vessel under negative pump pressure and/or positive fistula pressure. However, air-in-line detection cannot reliably detect a disconnection of the venous (return) segment of the extracorporeal circuit. In this case, if the blood-withdrawal path remains intact, air will not be introduced into the line. Thus it is particularly important to be able to detect a disruption in the continuity of the return line from the extracorporeal pump to the vascular access site.
Attempts have been made to develop systems to detect dislodgment based on the electrical, mechanical or acoustical properties of blood in the extracorporeal circuit. These systems have not been very effective because of the relatively high impedance of a blood circuit that includes long stretches of tubing, one or more blood pumps, valves, air traps and the like. Furthermore, the electrical interference generated by various devices along the blood path may obscure the signal that one is attempting to monitor.
An electrical signal can be introduced into the blood circuit through induction using a field coil surrounding a section of the blood tubing. It may also be introduced through capacitive coupling. For reasons of patient safety, the strength of an electrical signal introduced into the blood circuit necessarily must be small. However, the dielectric properties of the wall of the blood tubing can cause excessive noise or interference when attempting to detect conductivity changes in the blood from an electrical signal introduced through inductive or capacitive coupling. Therefore, it may be more desirable to introduce a brief, small electrical signal through direct contact with the blood path, to limit the length (and therefore impedance) of the blood path being monitored, and to perform the monitoring function at a suitable distance from any interference-producing components.
In one aspect, the invention comprises a system for detecting whether a vascular access device, such as a needle, cannula, catheter, etc. becomes disconnected or dislodged from a blood vessel or vascular graft. The system includes a fluid delivery device that provides for the flow of a liquid through a tube or conduit into the blood vessel via an indwelling needle or catheter at a first site on the blood vessel or graft. The fluid may be an electrolyte solution or other solution suitable for intravenous infusion, or it may be blood or blood components. An electrode is disposed to be in contact or fluid communication with the lumen of the conduit, and a second electrode is disposed to be in fluid communication with blood within the blood vessel or graft via a second on the blood vessel or graft. An electronic circuit is connected to the first and second electrodes, and configured to deliver a control signal to the first and second electrodes in order to measure the electrical resistance of the fluid between the first and second electrodes, such that at least one of the electrodes is located closer to the blood vessel or graft than to the fluid delivery device. In some embodiments the electrode is located at about 50-70% of the distance from the fluid delivery device to the blood vessel or graft. In other embodiments, the electrode is located at about 70-90% or more of the distance from the fluid delivery device to the blood vessel or graft. The fluid delivery device can include a pump, either for blood or for other therapeutic or diagnostic fluid. The fluid delivery device can be part of a hemodialysis blood flow circuit, which may or may not include a blood pump, a dialyzer cartridge, or an air trap and associated tubing. The second electrode may be placed in contact with the lumen of a second conduit or tube that is in fluid communication with the blood vessel or graft at the second site. The second conduit may form part of a fluid flow path from the blood vessel or graft to the fluid delivery device. The fluid in the second conduit may be blood being delivered to an extracorporeal blood flow circuit.
The system may comprise a first and second connector connecting a pair of vascular access catheters accessing a blood vessel segment or vascular graft segment at two different sites. The first and second connectors may each connect to a flexible tube leading to the fluid delivery device. Each connector may include an electrode that is exposed to the lumen of the connector. A wire may be attached to each connector, the wire being connectable on its other end to the electronic circuit. The flexible tubes may be double lumen tubes having a first lumen for carrying fluid and a second lumen for carrying a wire. The wires of each tube may be connected on the other end of the tube to a connector for connection to the electronic circuit.
The electronic circuit or an associated microprocessor may be configured to convert the voltages measured across terminals connected to the electrodes by the electronic circuit into resistance values. The system may comprise a controller configured to receive a signal from the electronic circuit or microprocessor, the signal representing the electrical resistance between the electrodes, the controller being programmed to trigger an alert signal when the electrical resistance value exceeds a pre-determined threshold. The alert signal may be an audible or visual signal to the person whose blood vessel is being accessed, and optionally an alert signal may include an electrical command to a tubing occluder apparatus. The tubing occluder apparatus may be actuated to mechanically occlude one or more of the tubes leading from the vascular access sites. The tubing occluder may operate in a number of ways, such as, for example electromechanically, hydraulically, or pneumatically.
In another aspect, the invention comprises an apparatus for monitoring the continuity between a vascular access device and a blood vessel or vascular graft segment, comprising, a first and second vascular connector, the first connector being attached on a proximal end to a distal end of a fluid-carrying lumen of a first double-lumen tube, and the second connector being attached on a proximal end to a distal end of a fluid-carrying lumen of a second double-lumen tube. The first connector comprises a first electrode in contact with a lumen of the first connector and electrically connected to a wire within a wire-carrying lumen of the first double-lumen tube, and the second connector comprises a second electrode in contact with a lumen of the second connector and electrically connected to a wire within a wire-carrying lumen of the second double-lumen tube. The wire within the first double-lumen tube and the wire within the second double-lumen tube are each connected to an electrical connector at a proximal end of the double-lumen tubes. The distal end of each connector may be configured with a locking feature to provide a reversible, air-tight connection between the connector and a mating connector of a vascular catheter. The proximal end of the double-lumen tubes can be connected to a blood pump on an arterial side, and an air trap on a venous side; and in a hemodialysis system, the blood pump and air trap may each be reversibly connectable to a dialyzer cartridge.
In another aspect, the invention comprises a vascular connector comprising a proximal fluid connection end, a distal fluid connection end, and an electrode configured to electrically connect a fluid-carrying lumen of the connector with a wire external to the vascular connector. The proximal end of the connector may be configured to connect with a flexible tube, and the distal end of the connector may be configured to connect with a mating connector of a vascular catheter. The electrode may be installed in a conduit on the connector that connects the lumen of the connector to the exterior of the connector. The electrode may be lodged into the conduit in a manner to provide an air-tight seal between the lumen and the exterior of the connector. An elastomeric member such as an O-ring may be installed between the electrode and the conduit to contribute to the air-tight seal.
In another aspect, the invention comprises an electrical circuit for measuring the resistance of a liquid between a first and second electrode, the first electrode connected to a first terminal of the electrical circuit, and the second electrode connected to a second terminal of the electrical circuit, comprising a capacitor C1 connected on a first end to the first terminal and a capacitor C2 connected on a first end to the second terminal; a known reference resistance Rref connected on a first end to a second end of capacitor C1; switching means for connecting either (a) a first reference voltage V+ to a second end of Rref, and a lower second reference voltage V− to a second end of C2 to form a first switch configuration or; (b) the first reference voltage V+ to the second end of C2 and the lower second reference voltage V− to the second end of Rref to form a second switch configuration; and measuring means for measuring a voltage Vsense at the connection between C1 and Rref; such that the electrical circuit is configured to determine the value of the resistance of the liquid based on the known reference resistance Rref and the observed voltage Vsense for each of the first and second switch configurations. The resistance Rref may be chosen to be a value that permits conductivity measurement of an electrolyte solution or other solution suitable for intravenous infusion. The electrolyte solution may include dialysate solution. The resistance Rref may also be chosen to permit measurement of the resistance of a volume of blood between the first and second electrodes.
An exemplary electrical circuit shown in
The circuit shown in
The switching network 2 can be driven by a pair of alternating binary control signals 13, 14 that connect VA to V+ and VB to V− during one half-cycle, and V11 to V+ and VA to V− during the other half-cycle. This results in a waveform at the Vsense node 5 that is similar to the waveform 20 shown in
A change in voltage ΔVsense before and after each square wave edge, can be shown to depend only on the reference resistance Rref 4, the unknown resistance Rx of subject media 1, and any series resistance (including, e.g., Rs 7), and is generally independent of series capacitance C1 or C2 6, since during this short time period the capacitor acts as an incremental short circuit. In particular,
where Ry=Rx+2Rs+Rth, where Rth=source series resistance from multiplexer 2 and voltage divider 8, and ρ=Ry/(RRef+Rth). (Source series resistance Rth, can be derived as the sum of the resistance of multiplexer 2 and the Thevenin equivalent resistance of the voltage divider 8. For example, for R1=10 ohms, R2=2K ohms, then Rth=R1∥(R1+R2)=9.95 ohms). Thus, if Ry is a short circuit, then ρ=0 and Δα=−1. The sense node's change in voltage ΔVsense is then equal to the voltage change at VB which has an amplitude opposite to the drive node at VA. If Ry is an open circuit, then ρ=∞ and Δα=1. The sense node's change in voltage ΔVsense is then equal to the voltage change at the drive node VA. Accordingly, if this change in voltage is measured, the preceding equations can be solved for the unknown resistance Rx:
As shown in
The reference voltages V+ and V− may be advantageously derived from a voltage divider 8 so that V+ is close to the reference voltage VRef of the ADC 11, and V− is close to the ground reference voltage of the ADC 11. For example, for R1=10Ω, R2=2 kΩ, and Vref=4.0V, then V+=3.980V, and V−=0.020V. This places both voltages within but near the edges of the active sensing region of the ADC 11, where they can be used for calibration (discussed below). Switch SW1 12 may be used to help calibrate the load resistance sensing.
Several improvements may decrease errors related to variations of component values. First, a calibration step can be introduced where VA is switched to V+ for a relatively long period of time, until settles and is approximately equal to V+, at which point ADC 11 can take a measurement of Vsense. A second calibration step can involve switching VA to V− for a relatively long period of time, until Vsense settles and is approximately equal to V−, at which point ADC 11 can take another measurement of Vsense. This allows the ADC 11 to measure both V+ and V−.
Secondly, as shown in
As a result, both edges of the waveform can be used to measure ΔVSense=[(V2−V1)+(V3−V4)]/2, so that asymmetric responses to the circuit are likely to be canceled out. Alternatively, an average voltage at about the midpoint of the waveform may be used; so that, for example, Δα=ΔVSense/(V+−V−)=[(V7−V6)+(V7−V8)]/2(V+−V−), and ΔVSense=[(V7−V6)+(V7−V8)]/2. In addition, only differential measurements of the input signal Vin of the ADC 11 can be used. Thus, any offset errors of the buffer amplifier 10 and ADC 11 can be canceled out. Also, Δα is a ratiometric quantity based on measurements using the same signal path. Thus, any gain errors of the ADC 11 can also be canceled out.
The reference resistor RRef 4 may be optimally chosen to be equal to the geometric mean of the endpoints of the desired range of unknown resistances, taking series resistances Rs 7 into account. For example, if Rs=100Ω and Rx varies from 100Ω to 3000Ω, then Ry=Rx+2R, varies from 300Ω to 3200 Ω, and Rref should be approximately the square root of (300Ω·3200Ω)=980Ω. To measure an unknown resistance in the range of 100 k-300 k ohms (as in, for example, a column of blood extending from one electrode to another via an arterio-venous fistula), the reference resistor Rref 4 can be changed to approximately 200 k ohms and the filter capacitor RF of low pass filter 9 at the input to the buffering amplifier 10 can be removed completely.
Because a voltage divider's output is a nonlinear function of its resistance ratio, errors or noise in readings from the ADC 11 produce their lowest fractional error (sensitivity) in the resultant calculation of Ry when it is equal to Rref, and the sensitivity increases the more Ry diverges from the reference resistance Rref. Specifically, it can be shown that the sensitivity in resistance ratio is as follows:
When Ry=Rref, ρ=1, Δα=0 and Sρ=2. Thus, for a change in Δα of 0.001 (0.1% of the ADC full-scale) around this point, the calculated resistance Ry changes by 0.002 or 0.2%. The sensitivity increases as ρ diverges from 1, as shown in Table 1.
For calibration purposes, a switch SW1 12 can be used to make resistance measurements to calibrate out a point at Rx=0. Preferably this switch 12 should be placed across the terminals VTA and VTB 3, or as close to the terminals as feasible, which would give a true zero-point calibration. In practice, however, locating the switch 12 close to the terminals VTA and VTB 3 may make the switch 12 prone to external noise and surge voltages, and may introduce DC leakage current into the subject media 1.
The series capacitances C1 and C2 6, and the use of square waves are important for unknown resistances that include an electrolytic conductive path. There are at least two reasons for this. First, it may be important in many applications to prevent DC current from flowing through an electrolyte solution or a bodily fluid having similar properties; otherwise electroplating and/or electrolysis of electrodes at the terminals VTA and VTB 3 can occur. In this circuit, the capacitors C1 and C2 6 block DC currents. Furthermore, because the capacitors may allow very small currents to flow (microamps or less), using an alternating square wave voltage may help to limit the average current further.
Secondly, in the event that a small electrochemical DC voltage is induced in the subject media 1 (for example, the electrodes in a fluid path may oxidize over time at different rates), this DC voltage can be blocked by the capacitors C1 and C2 6. Because the method for calculating resistance takes differential measurements, any residual DC voltage may be canceled out through the process of calculating the unknown resistance Rx of subject media 1.
With the appropriate modifications of a conductivity measurement circuit such as the one described above, it is possible to detect the conductivity and changes in the conductivity of blood. More specifically, it is possible to detect the change that occurs in the conductivity of a volume of blood when air enters the volume. This situation can occur, for example, when an intravascular access site becomes dislodged in an extracorporeal blood circuit.
The circuit shown in
The advantages of using this circuit to monitor the continuity of a column of a bodily fluid such as blood or plasma include the following:
With the lower reference resistor RRef 4 value (e.g. 680 ohms), this circuit is appropriately configured for dialysate conductivity measurements. With a much higher reference resistor Rref 4 value (e.g. 200 k ohms) this circuit is appropriately configured for measuring the resistance between an arterial needle and a venous needle to detect vascular needle dislodgement from an arterio-venous fistula.
The continuity of a fluid column leading from a fluid delivery apparatus to a patient's blood vessel or vascular graft can be monitored using the electronic circuit described above. The fluid being delivered may include blood or any electrolyte solution, including dialysate fluid. Although the following discussion will involve a hemodialysis system, the same principles of operation of the invention can apply to any device that is configured to deliver a fluid to a patient via a vascular access. In an embodiment illustrated by
The continuity of any segment of the fluid flow circuit 100 can be monitored by positioning two electrodes in contact with the fluid on either side of the fluid and blood-containing segment of interest. In order to monitor for a disconnection of the arterial access needle 102, or the arterial catheter tubing 104, or the venous access needle 132 or venous catheter tubing 130, one electrode can be placed in continuity with the lumen of the venous side of the blood flow circuit, while a second electrode is placed in continuity with the lumen of the arterial side of the blood flow circuit. In one embodiment, the two electrodes can be positioned on or near the dialysis machine 200, with an electrode in contact with blood upstream of blood pump 110, and a second electrode in contact with blood downstream of the dialyzer 118 and/or air trap 122. For example, the electrodes can be incorporated into transition locations 110 and 124.
In another embodiment, one of the electrodes can be positioned to be in contact with the fluid in the fluid flow circuit 100 at a point that is closer to the vascular access site 134 than it is to the equipment (e.g. a dialysis machine) used to deliver fluid flow to the accessed blood vessel or vascular graft. In a preferred embodiment, both electrodes can be positioned to be nearer to the patient's blood vessel or vascular graft than the equipment associated with the dialysis machine 200. This may further reduce electrical interference associated with the dialysis machine 200. An electrode A can be conveniently placed at or near the arterial catheter tubing connector 106 and a second electrode B can be conveniently placed at or near the venous catheter tubing connector 128. In this arrangement, the electrical continuity pathway from the first electrode through the patient's vascular access to the second electrode is much shorter—and the electrical resistance lower—than the pathway extending back toward the dialysis machine 200. In some cases, the access catheters 104 and 130 can be as short as about a foot, whereas the arterial and venous tubings 108 and 126 can be about six feet long. Because of the electrical conductive properties of the fluid in the circuit, the electrical resistance associated with the pathway incorporating tubing 108 and 126, and components of the dialysis machine 200, can be many times greater than the electrical resistance associated with the pathway through the patient's blood vessel or fistula 134.
Electrical interference associated with the dialysis machine 200 is thus reduced, and a change in electrical resistance due to an access-related disconnection can more easily be detected. Preferably, the electrodes A and B are positioned to be more than 50% of the distance from the dialysis machine to the patient. More preferably (and more conveniently), the electrodes A and B are located near the last disengageable fluid connection before reaching the patient. In one embodiment of a hemodialysis system, the blood tubing 108 and 126 is approximately 6 feet in length, and the arterial and venous catheter tubes 104, 130 are about two feet or less in length. A convenient location for electrodes A and B would then be at the arterial line and venous line connectors 106, 128 (which can be, e.g. Luer type connectors or modifications thereof) that connect the arterial and venous blood circuit tubes 108, 126 with the arterial and venous catheter tubes 104, 130.
As shown in
An elastomeric O-ring may be particularly useful in hemodialysis or other extracorporeal systems in which the blood-carrying components are subjected to disinfection or sterilization using heated liquids. The thermal coefficients of expansion of the plastic components of a connector may be sufficiently different from that of an incorporated metal electrode that a permanent seal may not be preserved after one or more sterilization or disinfection procedures. Adding an elastomeric component such as an O-ring at the junction between an electrode and the connector seat on which it is positioned may preserve the seal by accommodating the different rates of expansion and contraction between the electrode and the connector.
As shown in
To ensure a more secure seal to prevent blood leakage between the connector and electrode, and to limit the area under the electrode where blood elements may migrate and become lodged, an O-ring 316 can be incorporated into the inner surface of electrode 310 near the electrode internal ledge 320. This is seen in enlarged detail in
A wire 326 can be soldered, welded or otherwise secured onto the outer surface of electrode 310, and can travel under the overlying stretched tubing 318 until exiting more distally along the connector 300. The wire can thus conduct electrical signals to and from the electrode 310 as the internal surface 312 makes contact with the intraluminal fluid (e.g. blood). In the example shown, wire 326 is soldered to a distal portion of electrode 310 and travels under tubing 318, to emerge at the abutment of tubing 318 with a corresponding stop 326 of connector 300.
In another embodiment as shown in
In yet another embodiment, the mid-portion 406 of connector 400 may have two access ports, as shown in the cross-sectional view of
In any of the above electrode embodiments, the electrodes may be replaced by a suitably sized thermistor, or combination of a thermistor and electrical conductor, for the additional purpose of monitoring the temperature of the fluid passing through connector 300, 400 or variants thereof.
In one embodiment, the wires carrying electrical signals to or from a pair of electrodes on connectors 106, 128 (one on the arterial side and one on the venous side of the blood flow circuit) can travel separate and apart from the blood tubing 108, 126 back toward dialysis machine 200, where they ultimately terminate and connect to, a conductivity detecting circuit, such as the conductivity circuit shown in
Wires that extend together or separately between the dialysis machine and the patient are at risk of getting tangled, broken or becoming disconnected. Therefore, preferably, each wire 326 or 426 can be attached, fused, or otherwise incorporated into its associated tubing 108, 128. Incorporating a wire into its associated tubing provides a convenient way of protecting the wires and connections, and simplifying the interface between the patient and the dialysis apparatus. Exemplary methods of achieving this are shown in
In some of the above methods, the resulting tube-wire combination may have a tendency to curl because of the difference in thermal coefficients of expansion between the wire and the silicone material of the tubing. As the material cools after extrusion, the silicone may capture the embedded wire tightly, causing the cooled tube-wire bundle to curl. In a preferred embodiment, the wire lumen of the extrusion die is constructed to be large enough to accommodate a cross-sectional area significantly larger than the cross-sectional area of the wire to be embedded. Then as the silicone cools, the passageway surrounding the wire does not shrink to the point of tightly encasing the wire. A co-extrusion process incorporating an insulated wire can generate a tube-wire bundle as shown in