The subject matter disclosed herein relates to X-ray tube radiation sources and more particularly to X-ray tube radiation sources having one or several electron beam control electrodes (e.g. gridding electrodes).
In imaging systems, X-ray tubes are used as a source of X-ray radiation in, among others, projection X-ray systems, fluoroscopy systems, tomosynthesis systems, and computer tomography (CT) systems. Typically, the X-ray tube includes a cathode and an anode. The cathode emits a stream of electrons in response to heat resulting from an applied electrical current via the thermionic effect and to an electric field due to a high voltage applied between the cathode and the anode. The anode includes a target that is impacted by the stream of electrons. The target, as a result, produces X-ray radiation and heat. Such systems are useful in medical contexts, but also for parcel and package screening, part inspection, various research contexts, and so forth.
The radiation traverses a subject of interest, such as a human patient, and a portion of the radiation impacts a detector or photographic plate where the image data is collected. In some X-ray systems, the photographic plate is then developed to produce an image which may be used by a radiologist or attending physician for diagnostic purposes. In digital X-ray systems, a photo detector produces signals representative of the amount or intensity of radiation impacting discrete pixel regions of a detector surface. The signals may then be processed to generate an image that may be displayed for review.
Interventional radiology (IR) refers to a subspecialty within radiology that affords minimally (or at least limited) invasive diagnosis and treatment of disease. Various equipment is provided to afford image guidance in connection with diagnosis and treatment of disease. Non-limiting examples of minimally invasive disease treatment include angioplasty and catheter delivered stents. A wide range of imaging modalities may be used to afford image guidance, such as X-ray equipment, ultrasound, MRI and other imaging modalities. Interventional radiologists may utilize imaging equipment during a procedure to obtain images that are used in connection with directing interventional instruments through the body. For example, interventional instruments may utilize needles, catheters and the like.
A voltage supplied to electrodes of the cathode of an interventional imaging system may be controlled to block the X-rays or to adjust the intensity of X-rays that are generated. With respect to controlling this electrode voltage, it is desirable to be able to produce fast transitions from low to high levels (e.g., grid to bias levels), as well as to control electrode voltage waveforms after transition (e.g., stabilization time, accuracy, ripple, etc.) to correctly control the electron beam. Various factors may influence transition times.
In an example, a method for an interventional imaging system comprises applying a voltage to a gridding electrode of a cathode of the interventional imaging system via a multi-stage switching unit including a first control circuit and a second, different control circuit; during a first transition of the voltage from a first, gridding voltage of the interventional imaging system generated by the first control circuit to a second, bias voltage of the interventional imaging system generated by the second control circuit, selectively bypassing a plurality of stages of the first control circuit sequentially in a first non-consecutive order to decrease the voltage from the first, gridding voltage to a common voltage of the interventional imaging system; and during a second transition of the voltage from the second, bias voltage generated by the second control circuit to the first, gridding voltage generated by the first control circuit, selectively engaging the plurality of stages of the first control circuit sequentially in a second non-consecutive order to increase the voltage from the common voltage to the first, gridding voltage.
The above advantages and other advantages, and features of the present description will be readily apparent from the following Detailed Description when taken alone or in connection with the accompanying drawings. It should be understood that the summary above is provided to introduce in simplified form a selection of concepts that are further described in the detailed description. It is not meant to identify key or essential features of the claimed subject matter, the scope of which is defined uniquely by the claims that follow the detailed description. Furthermore, the claimed subject matter is not limited to implementations that solve any disadvantages noted above or in any part of this disclosure.
Various aspects of this disclosure may be better understood upon reading the following detailed description and upon reference to the drawings in which:
Methods and systems are described herein for generating voltage profiles that may be used to control an electron beam (e.g., control of intensity and/or energy) generated by an X-ray tube assembly of an interventional imaging system. It should be noted that although various embodiments may be described in connection with an X-ray tube assembly having a particular configuration, other configurations, geometries and arrangements are contemplated.
The X-ray tube includes a cathode that emits a stream of electrons in response to heat resulting from an applied voltage, and an anode including a target that is impacted by the stream of electrons to generate X-rays (e.g., to perform one or more X-ray exposures on a patient of the interventional imaging system). The voltage is applied at a gridding electrode of the cathode to switch the cathode on (e.g., a bias voltage to generate the X-rays) or off (e.g., a grid voltage to stop generation of the X-rays).
Voltage changes for switching the cathode on and off may be generated by driving electronics of the cathode that are connected through a cable. The cable may vary in length, from around 0.5 m to around 40 m. However, an approach for controlling the cathode through a shorter cable may be less effective when applied to a cathode controlled through a longer cable. Compounding factors may include a polarity of the cathode. The cathode may be bipolar, where the gridding voltage is of a first polarity (e.g., negative) and the bias voltage is of an opposite polarity (e.g., positive), or the cathode may be unipolar, where both the gridding voltage and the bias voltage are of a single polarity (e.g., negative). An approach for controlling a bipolar cathode may be less effective when applied to a unipolar cathode. As a result, current electronics topologies may not be suitable to drive a bipolar cathode via a long cable, due to a degree of voltage precision relied on when a bias voltage is applied.
In particular, some approaches for driving a bipolar cathode through a longer cable may be unnecessarily complex and expensive, and less compact when applied to unipolar cathodes. Other, less complex approaches for driving a bipolar cathode through a shorter cable may lead to slower transitions, higher losses, and potential inaccuracies when applied to cathodes driven through longer cables. One common problem is a temporary drop of cathode voltage when switched from a first voltage to a second voltage. The temporary voltage drop is related to the length of the cable (e.g., due to parasitic capacitance associated with the cable). The temporary voltage drop may be irrelevant (e.g., very small in amplitude and short in duration) when the cable is short (e.g., 0.5 m) but may become unmanageable for longer cables. Thus, current approaches to driving the cathode may not be feasible with newer, top-of-the-line interventional imaging systems with unipolar cathodes, which may rely on cables with lengths of 40 m or more.
To address this issue, a switching unit for controlling a unipolar cathode via a longer cable may be used, where the switching unit has a multi-stage topology including a first control circuit for generating the gridding voltage, and a second control circuit for generating the bias voltage. By separating the two functions, a duration of a transition from the gridding voltage to the bias voltage and vice-versa may be decreased by performing the transition in two steps: a larger step that may be performed rapidly with low precision using the first control circuit, and a smaller step that may be performed with higher precision using the second control circuit. Each of the gridding voltage and the bias voltage may be generated starting from a common voltage (considered herein to be 0V for simplicity). That is, during a first transition from the gridding voltage to the bias voltage (e.g., switching on the cathode), the electrode voltage applied to the cathode is adjusted first to the common voltage (the larger step) and then to the bias voltage (the smaller step with higher precision). During a second transition from the bias voltage to the gridding voltage (e.g., switching off the cathode), the electrode voltage applied to the cathode is adjusted first to the common voltage (the smaller step) and then to the gridding voltage (the larger step). By performing the first transition and the second transition in this manner, the duration may be less than a threshold duration for driving the unipolar cathode via the longer cable.
However, one problem with this approach is that a capacitor voltage imbalance between stages of the multi-stage switching unit may occur specifically during the larger step of the transitions from the low gridding voltage (e.g., −8 kV) to the common voltage (e.g., 0V) and vice-versa, which may damage components of the first control circuit. While the physics of the transition apply to the smaller step as well, the effect is minimal due to a relatively small voltage change entailed by switching from the common voltage to the bias voltage (e.g., −1.2 kV) and vice-versa. As described in greater detail below, the first control circuit includes a plurality of stages, each with a capacitance pre-charged to 1 kV. The plurality of stages are engaged when the desired cathode voltage is −8 kV (cathode gridded off), and the plurality of stages are disengaged (e.g., bypassed) when the cathode desired voltage is the common voltage (e.g., 0V). Each time that a stage of the plurality of stages is engaged/disengaged, there is an energy transfer to/from the cable and cathode capacitance, as well as energy losses due to switching.
A straightforward way to control the first control circuit is to engage/disengage the plurality of stages at the same time. However, this operation may generate high energy losses, a mainly, unacceptable current and voltage constraints on the electric components of the switching unit. Alternatively, the stages can be engaged/disengaged sequentially, leading to an almost 10× decrease in the current and voltage constraints. However, taking full advantage of the energy saving may rely on timing the engaging/disengaging of each stage such that each stage reaches a steady state, to recover the capacitor charge/discharge. The timing-to-steady-state may be dependent on a stage capacitance value and a load capacitance value (which includes a cable capacitance), which may be negligible in a computed tomography (CT) system, but may be unmanageably long in an interventional imaging system due to the longer cable length. Suboptimal energy saving can still be achieved even if the timing between engaging two consecutives stages is not reached, therefore is still advantageous operating them sequentially.
The capacitor voltage imbalance between stages may temporarily arise when stages are operated sequentially with a short time between two consecutives stages. Indeed, as stages are engaged/disengaged progressively to the output and as engaged stages' capacitors are charged/discharged at each step, there will be a unbalance between stages, leading to higher voltage constraints and higher timing-to-steady-state for stages that are connected to the output for the longest duration during transitions. While this issue may clear itself after a relevant stage reaches the steady state, it adds stresses to parts of the circuit that may lead to premature aging and, in the worst cases, immediate parts failure. The aging and potentially sudden parts failure can be avoided by choosing larger rated components, but the larger rated components may use more space and may be more expensive. Since space is quite limited, this approach may not be desirable.
To address the problem of the aging and potentially sudden parts failure due to the capacitor voltage imbalance without relying on the larger rated components, a control strategy is proposed herein for controlling the engagement/disengagement of the stages of the first control circuit in such a way that the unbalance is kept at a minimum even before steady state is reached at each step, via alternative stage switching during the transitions, which allows most or all of the stages to be connected to the output during transitions for a same duration.
The cathode 62 is configured to receive electrical signals via a series of electrical leads 68 (e.g., coupled to a high voltage source) that cause emission of an electron beam 70. The anode 66 is configured to receive the electron beam 70 on a target surface 72 and to emit X-rays, as indicated by dashed lines 74, when impacted by the electron beam 70 as depicted in
The gridding electrode 58 is configured to receive electrical signals via a series of electrical leads 76 that cause the gridding electrode 58 to grid the electron beam 70. The electrical signals may be timing/control signals (via the X-ray controller/power supply 38) that cause the gridding electrode 58, when energized or powered to a specific level (e.g., less than +6000 V to −5000 V), to grid the electron beam 70. The gridding electrode 58 is disposed about a path 78 of the electron beam 70 between the electron beam source 60 (e.g., cathode 62) and the anode assembly 64 (e.g., anode 66). The gridding electrode 58 may be annularly shaped. As depicted in
Various combinations of bias voltages and currents may be employed to control the electron beam. In particular, different circuits that may be used to form a multi-stage control arrangement will now be described, which may be implemented as a multi-stage architecture or topology having voltage supplies generated at the X-ray controller/power supply 38. The stages may be configured to change the voltage fast, such as sub-micron seconds, control the maximum voltage and/or control the shape of the waveforms used to apply the voltage to the gridding electrode 58. The stages may each be configured differently to allow switching at different speeds.
For example,
The switching unit 300 includes a pair of switches 302 and 304 (connected in series) that are each independently controllable to provide voltage switching from a reference voltage, illustrated as a voltage source 306. In this embodiment, the switch 302 is labeled switch A and the switch 304 is labeled switch B with the voltage output (Vout) 308 between the switches 302 and 304. The switching unit 300 includes a capacitor 321, which is connected to the switches 302 and 304 in parallel with the voltage source 306. Voltage source 306 generates a charge at capacitor 321, which may be discharged depending on a configuration of the switches 302 and 304.
In operation, in various embodiments, one of the switches 302 and 304 is closed (ruining a short in a closed state) and the other switch is open (in an open state). For example, if the switch 304 is closed and the switch 302 is open, Vout=Vcommon, which in various embodiments is zero volts (illustrated as ground 310 in
The switching units 300 may be combined or cascaded, for example, to form a multi-stage switching unit 400 shown in
In operation, if the switches 304a and 304b are closed (in which case the switches 302a and 302b are open), voltage sources 306a and 306b and capacitors 321a and 321b are not connected to the output and Vout=Vcommon. If the switch 304b is open and the switch 304a is closed (in which case the switch 302b is closed and the switch 302a is open), voltage source 306a and capacitor 321a are not connected to the output, voltage source 306b and capacitor 321b are connected to the output and Vout=Vcommon+V. Similarly, if the switch 304b is closed and the switch 304a is open (in which case the switch 302b is open and the switch 302a is closed), voltage source 306a and capacitor 321a are connected to the output, voltage source 306b and capacitor 321b are not connected to the output and Vout=Vcommon+V. If both switches 304a and 304b are open (in which case both switches 302a and 302b are closed), voltage sources 306a and 306b and capacitors 321a and 321b are connected to the output and Vout=Vcommon+V+V. Thus, in this operating state, the reference voltages from the two stages are summed. Accordingly, as more stages are added, incremental increases in output voltage are possible (e.g., discrete changes) by opening and closing the various switches in one or more of the stages. For example, if an output voltage (Vout) of 6 kV is desired, six switching units 300, each with a 1 kV reference voltage source 306, may be connected similar to the arrangement shown in
First control circuit 502 includes eight switching units (also referred to herein as stages): a first stage 510, a second stage 511, a third stage 512, a fourth stage 513, a fifth stage 514, a sixth stage 515, a seventh stage 516, and an eighth stage 517. In other embodiments, first control circuit 502 may include a different number of switching units, depending on a demand for an amount of voltage. Each stage may be a non-limiting example of a switching unit 300 of
In various embodiments, each voltage source 520 of each stage of first control circuit 502 may supply a voltage of up to 1 kV via a respective capacitor 521 (e.g., capacitor 321 of
During bias to grid transitions, all capacitors 521 of stages 510-517 will be slightly discharged due to a discharge current used to offset the parasitic capacitance generated by cable used to control the unipolar cathode. Thus, immediately after a bias to grid transition (for instance, after 50 μs), the total electrode voltage supplied by the respective capacitors 521 of stages 510-517 will be less than an expected nominal voltage (e.g. the number of stages multiplied by the reference voltage), but still greater than a threshold voltage (e.g., −5.5 kV) to not generate an X-ray. After a longer time (for instance, 5 ms), capacitors 521 of stages 510-517 will achieve the nominal voltage value with voltage sources 520 of the stages 510-517. This temporary voltage drop is described in greater detail below in reference to
Referring briefly to
In contrast,
Returning to
In the illustrated embodiment, the X-ray unit 610 includes an electrode 612. A voltage above the gridding voltage threshold provided to electrode 612 de-activates the X-ray unit 610 by stopping the electron beam. A secondary voltage (bias voltage) well below the gridding voltage provided to electrode 612 focuses or controls the dimension of the produced electron beam.
The controller 620 is configured to control various aspects of the system 100, including the provision of voltage to control the X-ray unit 610, for example by controlling the voltage control modules 640 of the circuit assembly 630. For example, based on a sensed voltage in the cable 650 measured with sensor 653, the controller 620 may adjust a voltage provided to the X-ray unit 610 by controlling switches of one or more fine tuning circuit portions of the voltage control modules 640 (e.g., the switches 522 and 524 of the stages 510-517). The controller 620 may include processing circuitry configured to perform one or more tasks, functions, or steps discussed herein. It may be noted that “controller” as used herein is not intended to necessarily be limited to a single processor or computer. For example, the controller 620 may include multiple processors and/or computers, which may be integrated in a common housing or unit, or which may distributed among various units or housings. The circuit assembly 630 may be generally similar in various respects to the multi-stage switching unit 500 discussed herein.
In the illustrated embodiment, the controller 620 includes a memory 622 which includes a tangible and non-transitory computer readable medium. It may be noted that the memory 622 may have stored thereon instructions for directing the controller 620 to perform one or more aspects of the methods, steps, or processes discussed herein. In various embodiments, the controller 620 may control individual voltage control modules and/or a group or groups of voltage control modules simultaneously to control the total delivered voltage. For example, the controller 620 may actuate switching portions of all or most of the modules to provide a large voltage change to turn an electrode on and off, and may control one or more of the modules for fine tuning of voltage to focus an electron beam.
The cable 650 operably connects the circuit assembly 630 and the X-ray unit 610. For example, a conductor 652 of the cable 650 may be operably coupled to a group of voltage control modules and to the electrode 612. Voltage provided via the conductor 652 may be utilized to turn the X-ray unit 610 on and off and/or to control focus of the electron beam. The provided voltage may include a gridding voltage and/or a bias voltage applied to electrode 612 (e.g., the electrode 550 in
In various embodiments, redundancy may be provided for improved reliability. For example, in some embodiments, a plurality of low voltage circuit portions may be utilized, with each low voltage circuit portion coupled to a group of voltage control modules and configured to control a voltage provided to the corresponding group of voltage control modules from a given low voltage circuit portion. Alternatively or additionally, a plurality of transformers may be utilized, with each transformer operably coupled to at least one corresponding voltage control module. In some embodiments, a given transformer and a corresponding low voltage circuit portion may be coupled to a corresponding low voltage circuit portion.
Such systems may include constraints for a maximum transition time from on-to-off and vice-versa of less than 50 μs, which may not be met by other alternative circuit control architectures. Method 700 may be executed by a controller or processor of the interventional imaging system, based on instructions stored in a memory of the interventional imaging system.
In contrast to the alternative circuit control architectures, the multi-stage circuit of method 700 separates a first grid function and a second bias function, as described above in reference to
Method 700 begins at 702, where method 700 includes receiving a first instruction to switch the unipolar cathode of the interventional imaging system on. In various embodiments, the first instruction may be an instruction to initiate an X-ray pulse generated by a protocol selected by an operator of the interventional imaging system.
At 704, method 700 includes decreasing an electrode voltage supplied to the gridding electrode 550 by one or more −1 kV first voltage sources of the interventional imaging system to the common voltage. It should be appreciated that as the voltages supplied to the gridding electrode 550 are negative voltages, for the purposes of this disclosure, decreasing the electrode voltage refers to decreasing an absolute value of the electrode voltage (e.g., decreasing the electrode voltage in a negative direction), and increasing the electrode voltage refers to increasing the absolute value of the electrode voltage (e.g., increasing the electrode voltage in the negative direction). The first voltage sources may be non-limiting examples of the voltage sources 520 of the stages 510-517 of the first control circuit 502 of the multi-stage switching unit 500 of
Decreasing the electrode voltage supplied to the gridding electrode 550 by one or more voltage sources to the common voltage may include switching each of the first voltage sources off in a series of steps, thereby reducing the electrode voltage by 1 kV at each step as a corresponding stage is bypassed, until all of the voltage sources are switched off and the voltage supplied to the gridding electrode 550 is the common voltage. Each of the voltage sources may be switched off by either opening or closing switches 522 and 524 of each of the stages 510-517, as described above in reference to
In one approach, the first voltage sources may be switched off and the stages bypassed by following a basic protocol where the stages are bypassed sequentially in a consecutive fashion, from stage 510-517. For example, a first voltage source 520 of the first stage 510 may be switched off first; a second voltage source 520 of the second stage 511 may be switched off second; a third voltage source 520 of the third stage 511 may be switched off third; and so on until an eighth voltage source 520 of the eighth stage 517 is switched off. However, if the stages are bypassed sequentially in the consecutive fashion, a voltage imbalance may occur between capacitors 521 of the stages 510-517, due to a higher capacitance of the longer cable described in reference to
To reduce the voltage imbalance, the stages 510-517 may be bypassed in accordance with an alternative control strategy that specifies a first non-consecutive order for switching off the first voltage sources. The first non-consecutive order may be specified in a first optimized protocol that establishes an sequence for disengaging the stages 510-517 such that the voltage imbalance is minimized. At each step of the sequence, one or more stages may be selectively bypassed or engaged. For example, at a first step of the optimized protocol, the first stage 510 may be bypassed (e.g., the voltage source 520 of the first stage 510 may be switched off); at a second step, the fourth stage 513 may be bypassed; at a third step, the fifth and sixth stages 514 and 515 may be bypassed and the fourth stage 513 may be engaged; at a fourth step, the seventh and eighth stages 516 and 517 may be bypassed and the fifth stage 514 may be engaged; and so on, until all of the stages 510-517 are bypassed. By selectively disengaging and engaging the stages in the non-consecutive order, the voltages generated at the capacitors 521 of the stages 510-517 may be partially or totally equalized, such that the voltage imbalance is prevented. As a result, the potential damage to the components may be prevented or avoided. The alternative control strategy is described in greater detail below in relation to
At 706, method 700 includes increasing the electrode voltage supplied to the gridding electrode 550 from the common voltage to the bias voltage (e.g., −1.2 kV with a precision of +/−50V). Increasing the electrode voltage supplied to the gridding electrode 550 from the common voltage to the bias voltage may include maintaining the voltage sources of stages 510-517 off. Concurrently, the bias voltage may be generated by the second control circuit 504, which may be connected to the gridding electrode 550 by opening switch 563 and closing switch 562. When the bias voltage is achieved, the cathode may be switched on, whereby X-rays may be generated by the cathode and the X-ray may be performed.
At 708, method 700 includes receiving a second instruction to switch the unipolar cathode off (e.g., to stop the X-ray). The second instruction may be generated by the X-ray exposure protocol, or in a different manner.
At 710, method 700 includes decreasing the electrode voltage from the bias voltage to the common voltage. Decreasing the electrode voltage to the common voltage may be accomplished by opening switch 562 and closing switch 563 of the second control circuit, so that no bias voltage generated by the second voltage source is applied to the cathode (e.g., to the gridding electrode 550). Decreasing the electrode voltage to the common voltage from the bias voltage via the second control circuit can be performed quickly and without precision.
At 712, method 700 includes increasing the electrode voltage from the common voltage to the gridding voltage, to switch the unipolar cathode off, thereby ending the X-ray. Increasing the electrode voltage to the common voltage may be accomplished as described above in reference to steps 704 and/or 706, but where individual voltage sources of various stages of the multi-stage circuit are sequentially switched on. In particular, a second optimized protocol may be used to sequentially engage the stages 510-517 in a second, non-consecutive order similar to the first non-consecutive order described above at step 704, to avoid a voltage imbalance generated by the cable capacitance. In various embodiments, the second non-consecutive order may be a reverse order of the first non-consecutive order. For example, at a first step of the optimized protocol, the eighth stage 517 may be engaged (e.g., the voltage source 520 of the eighth stage 517 may be switched on); at a second step, the sixth stage 515 and seventh stage 516 may be engaged, and the eighth stage 517 may be bypassed; at a third step, the seventh stage 516 may be bypassed and the fourth stage 513 and the fifth stage 514 may be engaged; and so on, until all of the stages 510-517 are engaged. By selectively disengaging and engaging the stages in the non-consecutive order, the voltages generated at the capacitors 521 of the stages 510-517 may be partially or totally equalized, such that the voltage imbalance is prevented. As a result, the potential damage to the components may be prevented or avoided.
In some embodiments, the second non-consecutive order may be established in a matrix used by a controller of the interventional imaging system to execute the second optimized protocol, such as the stage engagement matrix described below in reference to FIG. 16. Similarly, the first non-consecutive order may be established in a matrix used by a controller of the interventional imaging system to execute the first optimized protocol.
Thus, the electrode voltage applied to the gridding electrode 550 to start the X-ray exposure may be generated by the second control circuit, and the electrode voltage applied to the gridding electrode 550 to end the X-ray exposure may be generated by the first control circuit. The split of these two functions allows for a decrease in voltage when precision is not required (grid), while allowing suitable voltage precision in a short period of time when the bias voltage is applied to the gridding electrode 550. One advantage of splitting the two functions is that the bias voltage generated by the second voltage source 570 of second control circuit 504 may be unaffected by a temporary decrease in voltage at the gridding electrode 550 of the cathode due to parasitic capacitance associated with long cables (e.g., cable 650 of
During this last step switching from the common voltage to −8 kV, the temporary voltage decrease may be evident when the electrode voltage achieves-7.1 kV, after which the electrode voltage may increase more slowly to −8 kV, as shown in
Referring now to
Timing diagram 800 shows a plot 802, which illustrates an amount of electrode voltage generated by the circuit over time as the circuit transitions from a first voltage at which a unipolar cathode of an interventional imaging system is switched off (e.g., does not generate X-rays and does not expose a patient of the interventional imaging system to radiation), to a second, bias voltage at which the cathode is switched on (e.g., generating X-rays and exposing the patient to the radiation). Time points of interest during the transition are illustrated by vertical dotted lines. In the depicted embodiment, the second, bias voltage at which the cathode is switched on is −1.2 kV with a precision of +/−50V, indicated by a dashed line 804. A dashed line 806 indicates a threshold voltage of −5.5 kV at which an electron beam may not be generated by the cathode. Newer interventional imaging systems may be gridded off with a voltage of −8 kV or less, as indicated by a dashed line 808. In the depicted embodiment, the first voltage at which the cathode is gridded off is −8 kV, as indicated by a dashed line 810.
At a time t0, the cathode is gridded off. At a time t1, a X-ray exposure may be initiated via the interventional imaging system. For example, the X-ray exposure may be initiated in accordance with a protocol executed by the interventional imaging system based on input from an operator of the interventional imaging system. When the X-ray exposure is initiated, between the time t1 and a time t2, instructions are supplied to a controller of the interventional imaging system, that when executed, actuate one or more switches of the multi-stage circuit to decrease the electrode voltage (in a negative direction) to a common voltage of the interventional imaging system, as indicated by plot 802. In the depicted embodiment, the common voltage is considered to be 0V.
Between the time t2 and a time t3, the electrode voltage remains at the common voltage (e.g., 0V). For example, the time between time t2 and time t3 may be less than 2.5 μs. In general, a time of 3.0 μs may be a threshold duration imposed by the interventional imaging system for stabilizing the electrode voltage delivered to the gridding electrode 550 at each step of a transition between voltages. A set of exemplary steps of a transition are described below in reference to
At the time t4, the cathode is supplied with the bias voltage, and the cathode is switched on, whereby X-rays are generated by the interventional imaging system and the X-ray exposure is performed. The X-ray exposure is performed from the time t4 to a time t5. At the time t5, the X-ray exposure stops, for example, in accordance with the protocol. When the X-ray exposure stops, instructions are supplied to the controller, that when executed, actuate the one or more switches of the multi-stage circuit to decrease the electrode voltage (in the negative direction) back to the common voltage. At a time t6, the electrode voltage reaches the common voltage, where it remains from the time t6 until a time t7.
At the time t7, instructions are supplied to the controller, that when executed, actuate the one or more switches of the multi-stage circuit to increase the electrode voltage (in the negative direction) back to first voltage. Between the time t7 and a time t8, the electrode voltage increases (in the negative direction).
At the time t8, the electrode voltage has increased to −7.1 kV, achieving the threshold voltage relied on by the newer interventional imaging systems for gridding off. As a result, by time t8, the interventional imaging system is no longer generating X-rays, having past the threshold for generating the electron beam indicated by dashed line 806, and the patient is not exposed to the radiation. Between the time t8 and a time t9, due to the temporary voltage decrease due to the cable length described above, the electrode voltage slowly increases (in the negative direction) to achieve the first voltage, at which in this embodiment the cathode is gridded off.
Thus, under the proposed method for controlling the voltage transition between the first gridding voltage to the second bias voltage (and vice-versa), using the multi-stage circuit architecture described in reference to
When switching the cathode on, in a first step, the electrode voltage is decreased to the common voltage (e.g., between the time t1 and the time t2) in a first transition, and in a second step, the electrode voltage is increased to the bias voltage (e.g., between the time t3 and t4) in a second transition. The first step and the second step can be performed more rapidly than decreasing the electrode voltage directly to a precise, different (e.g., non-zero) voltage, because the first transition generated by the second control circuit 504 (e.g., a bias circuit) is independent from the second transition generated by the first control circuit 502 (e.g., a gridding circuit). As a result, the high precision voltage source 570 of the second control circuit 504 may be less perturbed, and may recover the bias voltage rapidly and with a desired precision (e.g., less of 100 μs).
Similarly, when the unipolar cathode is switched off, a second transition from the second bias voltage to the first gridding voltage (e.g., time t5 to t9) may be performed in two steps, a first step where the electrode voltage is decreased to the common voltage (by connecting to the common voltage, where precise control of the voltage transition is not an issue), and a second step where the electrode voltage is increased to the first gridding voltage. During the second step, the voltage transition from the common voltage to the threshold voltage for gridding off the cathode (e.g., time t7 to t8) may be performed quickly (e.g., in less than 50 μs) and with less precision, since once the cathode is no longer generating X-rays, achieving the first gridding voltage may be accomplished over a longer period of time, as indicated by plot 802 between time t8 and t9. For example, the longer period of time may be as much as 5 ms.
Then, at the time t4, the bias voltage shown by line 906 may be generated by the second control circuit 504 of multi-stage switching unit 500. For example, switches 562-563 of multi-stage switching unit 500 may be actuated to generate the bias voltage via the second high precision voltage source 570. In this way, the transition from the first gridding voltage to the bias voltage is advantageously performed in two steps by two different circuits of the multi-stage circuit. A first total time 920 taken by the multi-stage circuit to achieve the bias voltage is the time between time t1 and time t4.
In contrast, a second, dashed line 908 shows an alternative transition from the first gridding voltage directly to the bias voltage using the multi-stage circuit with the architecture disclosed herein. This alternative transition, even if it has some advantages, is less repeatable (more dependent on circuit (components tolerance) and environment (cable length) variability) and includes simultaneous transitions of the flyback stage and of the 1 kV stages (involving additional perturbation on bias voltage and needing more complex control). A second alternative transition from the first gridding voltage directly to the bias voltage (without transitioning through the common voltage) may be performed using an alternative circuit with a different architecture and without using the multi-stage circuit with the architecture disclosed herein, but with higher constraints on the electronic components.
Referring now to
A first portion 1202 shows a change in a combined voltage generated by the voltage sources (e.g., voltages sources 520 and/or voltage source 570) of the switching unit 500 over the transition. First portion 1202 includes a first plot 1210 indicating a ladder output voltage, meaning, a commanded voltage generated by switching unit 500 at different points in time, and a second plot 1212, indicating a circuit output voltage, meaning, an actual voltage generated at a cathode of the interventional imaging system (e.g., at bias/grid electrode 550) at the different points in time as a result of the commanded voltage. A vertical axis of first portion 1202 shows voltage.
A second portion 1204 shows a change in voltage generated at a capacitor (e.g., capacitor 521) of each stage of the first control circuit 502 over time during the first transition. A first plot 1220 shows a first charge generated at a first capacitor 521 of the first stage 510; a second plot 1221 shows a second charge generated at a second capacitor 521 of the second stage 511; a third plot 1222 shows a third charge generated at a third capacitor 521 of the third stage 512; and so on until an eighth plot 1227 shows an eighth charge generated at an eighth capacitor 521 of the eighth stage 517. A vertical axis of second portion 1204 shows voltage. A voltage contribution of the second control circuit 504 is not shown in second portion 1204.
A third portion 1206 indicates an engagement of each stage of switching unit 500 (including the high precision voltage source stage of the second control circuit 504 generating the bias voltage) during the transition towards the bias voltage. Each stage may be ENGAGED or BYPASSED. For example, a stage may be ENGAGED when a first configuration of switches of the stage (e.g., switches 522 and 524) connects the voltage source 520 of the stage to a circuit including the bias/grid electrode 550, whereby the voltage contribution to the electrode voltage is the (negative) output voltage of voltage source 520. The stage may be BYPASSED when a second configuration of the switches bypasses the voltage source, whereby the voltage contribution to electrode voltage is 0V.
Specifically, a first stage plot 1230 indicates whether the first stage 510 is ENGAGED; a second stage plot 1231 indicates whether the second stage 511 is ENGAGED; a third stage plot 1232 indicates whether the third stage 512 is ENGAGED; a fourth stage plot 1233 indicates whether the fourth stage 513 is ENGAGED; a fifth stage plot 1234 indicates whether the fifth stage 514 is ENGAGED; a sixth stage plot 1235 indicates whether the second stage 515 is ENGAGED; a seventh stage plot 1236 indicates whether the seventh stage 516 is ENGAGED; and an eighth stage plot 1237 indicates whether the eighth stage 517 is ENGAGED. A ninth stage plot 1238 indicates whether the high precision voltage source stage of second control circuit 504 is ENGAGED.
At a time t0, the cathode is gridded, and a maximum voltage of the interventional imaging system is applied (e.g., −8 kV), as indicated by plots 1210 and 1212 of first portion 1202. All stages are ENGAGED, as indicated by the third portion 1206. Between times t1 and t8, the stages of the first control circuit 502 are bypassed in a consecutive sequence, as indicated by plots 1230-1237 of third portion 1206. At time t1, the first stage indicated by plot 1220 is BYPASSED; at time t2, the second stage indicated by plot 1221 is BYPASSED; at time t3, the third stage indicated by plot 1222 is BYPASSED; and so on, until time t8 when all of the stages 510-517 of the first control circuit are BYPASSED. At the time t9, the high precision voltage source stage of the second control circuit 504 is ENGAGED, as indicated by plot 1238 of the third portion 1206. When the high precision voltage source stage is ENGAGED, the voltage generated by the switching unit 500 increases to the second, bias voltage, as shown by the plots 1210 and 1212 of the first portion 1202.
However, as is shown in second portion 1204, the sequential switching off of the stages generates an increasing voltage imbalance between the stages. If the operating sequence is consecutive (stage 510, then stage 511, then stage 512, up to stage 517), the first stage that is bypassed will remain at its initial voltage value whenever another stage is bypassed, and a last stage that is bypassed will suffer a voltage rise whenever another stage is bypassed, potentially leading to the failure of the board. As indicated in the second portion 1204, as the voltage sources of plots 1220-1227 are switched off in the consecutive sequence, a voltage at the capacitor 521 of each subsequent stage increases. As a result, a voltage generated at the eighth capacitor indicated by eighth plot 1227 may exceed a threshold voltage, where the eighth stage and/or other components of the switching unit 500 may be damaged.
Specifically, at time t1, the first stage 510 is BYPASSED, and plot 1220 shows that the voltage generated at the capacitor 521 of the first stage (but not applied to the cathode) remains at 1.00 kV. At time t2, the second stage 511 is BYPASSED, and plot 1221 shows that the voltage generated at the capacitor 521 of the second stage increases to 1.03 kV, due to the cable capacitance. At time t3, the third stage 512 is BYPASSED, and plot 1222 shows that the voltage generated at the capacitor 521 of the third stage increases to 1.07 kV. In this way, the voltage generated at each capacitor 521 of each of the stages 510-517 of the first control circuit increases incrementally as each stage is bypassed, until time t8, when plot 1227 shows that the voltage generated at the capacitor 521 of the last stage 517 increases above 1.15 kV, which may exceed a threshold voltage for the stage and cause damage to the stage. For example, one or both of switches 522 and 524 of the last stage 517 may be damaged.
A similar situation occurs during a second transition, when the cathode is switched off (e.g., after performing an X-ray exposure), as described in method 700 of
A first portion 1302 shows a change in a combined voltage generated by the voltage sources (e.g., voltages sources 520 and/or voltage source 570) of the switching unit 500 over the second transition. First portion 1302 includes a first plot 1310 indicating a ladder output voltage, meaning, a commanded voltage generated by switching unit 500 at different points in time, and a second plot 1312, indicating a circuit output voltage, meaning, an actual voltage generated at the bias/grid electrode 550 at the different points in time as a result of the commanded voltage. A vertical axis of first portion 1302 shows voltage.
A second portion 1304 shows a change in voltage generated by the capacitor 521 of each stage of the first control circuit 502 over time during the second transition. A first plot 1320 shows a voltage generated at a first capacitor 521 of the first stage 510; a second plot 1321 shows a second voltage generated at a second capacitor 521 of the second stage 511; and so on up to an eighth plot 1327 showing an eighth voltage generated at an eighth capacitor 521 of the eighth stage 517. A vertical axis of second portion 1304 shows voltage. A voltage contribution of the second control circuit 504 is not shown in second portion 1304.
A third portion 1306 indicates an engagement of each stage of switching unit 500 (including the bias voltage generated by the high precision voltage source stage of the second control circuit 504) during the second transition. Each stage may be ENGAGED or BYPASSED. A first stage plot 1330 indicates whether the first stage 510 is ENGAGED; a second stage plot 1331 indicates whether the second stage 511 is ENGAGED; a third stage plot 1332 indicates whether the third stage 512 is ENGAGED; and so on until an eighth stage plot 1337 indicates whether the eighth stage 517 is ENGAGED. A ninth stage plot 1338 indicates whether the high precision voltage source stage of second control circuit 504 is ENGAGED.
At a time t0, the second, bias voltage is applied to the cathode by the second control circuit 504, and no voltage is applied by the first control circuit 502, as indicated by plots 1310 and 1312 of first portion 1302. All stages of the first control circuit 502 are BYPASSED, as indicated by plots 1330-1337, and the second control circuit 504 is ENGAGED, as indicated by the plot 1338. At time t1, the high precision voltage source 570 of the second control circuit 504 is switched off, and the voltage decreases to the common voltage (e.g., 0V) by time t2, as shown by plots 1310 and 1312. Between times t2 and t9, the stages 510 to 517 of the first control circuit 502 are ENGAGED in a consecutive sequence from stage 517 to stage 510, as indicated by plots 1330-1337 of third portion 1306. At the time t9, the voltage generated by the switching unit 500 approaches the first, gridding voltage, as shown by the plots 1310 and 1312 of the first portion 1302. A threshold voltage (e.g., indicated by dashed line 806 of
However, as is shown in second portion 1304 and as seen in second portion 1204 of
To reduce the risk of damage entailed by the sequential engaging and disengaging of the stages of the first control circuit 502 of the multi-stage switching unit 500 described in relation to
A second portion 1404 shows change in voltage generated by the capacitor (e.g., capacitor 521) of each stage of the first control circuit 502 over time during the first transition. A third portion 1406 indicates an engagement of each stage of switching unit 500 (including the bias voltage generated by the high precision voltage source stage of the second control circuit 504) during the first transition. Each stage may be ENGAGED or BYPASSED (e.g., disengaged). A set of stage plots 1430-1438 correspond to the stages described in relation to stage plots 1230-1238 of
At a time t0, the cathode is gridded, and a voltage of −8.0 kV is applied, as indicated by plots 1410 and 1412 of first portion 1402. All stages are ENGAGED except the high precision voltage source stage of the second control circuit 504, which is bypassed, as indicated by the third portion 1406. As in
As can be seen in the second portion 1404, as a result of applying the alternative control strategy for disengaging the stages 510-517, the voltage imbalance of
A second portion 1504 shows change in the voltage generated by the capacitor 521 of each stage of the first control circuit 502 over time during the second transition. A third portion 1506 indicates an engagement of each stage of switching unit 500 (including the bias voltage generated by the high precision voltage source stage of the second control circuit 504) during the second transition. Each stage may be ENGAGED or BYPASSED. A set of stage plots 1530-1538 correspond to the stages described in relation to stage plots 1330-1338 of
At a time t0, the bias voltage of approximately −1.2 kV is applied, as indicated by plots 1510 and 1512 of first portion 1502. All stages are BYPASSED except for the high precision voltage source stage of the second control circuit 504 generating the bias voltage, as indicated by the third portion 1506. At time t1, the high precision voltage source stage 504 is BYPASSED. The voltage applied to the cathode is 0V, as shown by plots 1510 and 1512. As in
As can be seen in the second portion 1504, as a result of applying the alternative control strategy for engaging the stages 510-517, the voltage imbalance of
It should be appreciated that
In various embodiments, the steps may be performed by software of the interventional imaging system, in accordance with a protocol for the alternative switching strategy that specifies which stages of stages 510-517 are to be engaged at different times during the first and the second transitions. For example, the protocol may engaged programmatically using a stage engagement matrix, as shown in
Referring to
For example, a first row 1610 includes all zeros, indicating that all eight stages are disengaged and no stages of the first control circuit 502 are engaged during a first step. A second row 1612 includes a one in a first column 1620, and zeros in all other columns, indicating that during the second step, only one stage (e.g., the eighth stage) of the eight stages is engaged (e.g., switched from BYPASSED to ENGAGED). A third row 1614 includes a zero in the first column 1620, a one in a second column 1622, a one in a third column 1624, and zeros in all other columns, indicating that during the third step, the eighth stage is disengaged (e.g., switched from ENGAGED to BYPASSED), and the seventh and sixth stages are engaged. A fourth row 1616 includes a zero in the first column 1620, indicating that the eighth stage is maintained disengaged (e.g., maintained BYPASSED); a zero in the second column 1622, indicating that the seventh stage is disengaged; a one in the third column 1624, indicating that the sixth stage is maintained engaged (e.g., maintained ENGAGED); a one in a fourth column 1626, indicating that a fifth stage is engaged; a one in a fifth column 1628, indicating that a fourth stage is engaged; and zeros in all other columns. The remaining cells of stage engagement matrix 1600 are similarly filled in, such that stage engagement matrix 1600 provides an efficient binary (e.g., machine readable) representation that may be consulted, for example, as a lookup table, by a software routine of the interventional imaging system. The software routine may be performed by a processor of the interventional imaging system.
The technical effect of using a non-consecutive control strategy for engaging and disengaging stages of a control circuit for controlling an electrode voltage of a interventional imaging system during transitioning between a gridding voltage of the interventional imaging system and a bias voltage of the interventional imaging system is that a voltage imbalance between the stages may be reduced, decreasing a risk of damage to components of the control circuit.
The disclosure also provides support for a method for an interventional imaging system, the method comprising: applying a voltage to a gridding electrode of a cathode of the interventional imaging system via a multi-stage switching unit including a first control circuit and a second, different control circuit, during a first transition of the voltage from a first, gridding voltage of the interventional imaging system generated by the first control circuit to a second, bias voltage of the interventional imaging system generated by the second control circuit, selectively bypassing a plurality of stages of the first control circuit sequentially in a first non-consecutive order to decrease the voltage from the first, gridding voltage to a common voltage of the interventional imaging system, and during a second transition of the voltage from the second, bias voltage generated by the second control circuit to the first, gridding voltage generated by the first control circuit, selectively engaging the plurality of stages of the first control circuit sequentially in a second non-consecutive order to increase the voltage from the common voltage to the first, gridding voltage. In a first example of the method, the cathode is a unipolar cathode, and both of the first, gridding voltage and the second, bias voltage are negative voltages. In a second example of the method, optionally including the first example, driving electronics of the unipolar cathode are connected through a cable with a length greater than 40 meters. In a third example of the method, optionally including one or both of the first and second examples: each stage of the plurality of stages of the first control circuit includes a −1 kV voltage source, a capacitor, and at least two switches to bypass or negatively connect the −1 kV voltage source to the cathode, and the second control circuit includes a high precision voltage source capable of generating up to 1.2 kV with a precision of +/−50V, a capacitor, and at least two switches to bypass or negatively connect the high precision voltage source to the cathode. In a fourth example of the method, optionally including one or more or each of the first through third examples: the first, gridding voltage is −8 kV with respect to the common voltage, and the second, bias voltage is between 0 and −1.2 kV with respect to the common voltage. In a fifth example of the method, optionally including one or more or each of the first through fourth examples, the second non-consecutive order is the reverse of the first non-consecutive order. In a sixth example of the method, optionally including one or more or each of the first through fifth examples: selectively bypassing the plurality of stages of the first control circuit sequentially in the first non-consecutive order comprises performing a first sequence of steps, where during each step of the first sequence of steps at least one stage of the plurality of stages is bypassed, and during at least one step of the first sequence of steps, a previously bypassed stage is engaged, and selectively engaging the plurality of stages of the first control circuit sequentially in the second non-consecutive order comprises performing a second sequence of steps, where during each step of the second sequence of steps at least one stage of the plurality of stages is engaged, and during at least one step of the second sequence of steps, a previously engaged stage is bypassed. In a seventh example of the method, optionally including one or more or each of the first through sixth examples, the method further comprises: selectively bypassing the plurality of stages of the first control circuit sequentially in the first non-consecutive order based on a first protocol generated based on a first stage engagement matrix stored in a memory of the interventional imaging system, and selectively engaging the plurality of stages of the first control circuit sequentially in the second non-consecutive order based on a second protocol generated based on a second stage engagement matrix stored in the memory, wherein the first stage engagement matrix and the second stage engagement matrix indicate when each stage of the plurality of stages is to be engaged and when each stage of the plurality of stages is to be bypassed. In a eighth example of the method, optionally including one or more or each of the first through seventh examples, the first stage engagement matrix and the second stage engagement matrix indicate when each stage of the plurality of stages is to be engaged and when each stage of the plurality of stages is to be bypassed via a binary coding where a one indicates that the stage is to be engaged, and a zero indicates that the stage is to be bypassed. In a ninth example of the method, optionally including one or more or each of the first through eighth examples, the first protocol and the second protocol are optimized to reduce a voltage imbalance between stages of the plurality of stages.
The disclosure also provides support for an interventional imaging system, comprising: an X-ray source including a unipolar cathode, a multi-stage switching unit including a first control circuit configured to generate a first, gridding voltage at a gridding electrode of the unipolar cathode via a plurality of stages of the multi-stage switching unit, and a second control circuit configured to generate a second, bias voltage at the gridding electrode, and a controller operably connected to the X-ray source and configured to: when transitioning from the gridding voltage to the bias voltage, selectively bypass the plurality of stages of the first control circuit sequentially in a first non-consecutive order to decrease a voltage applied to the gridding electrode, and when transitioning from the bias voltage to the gridding voltage, selectively engage the plurality of stages of the first control circuit sequentially in a second non-consecutive order to increase the voltage applied to the gridding electrode, the second non-consecutive order the reverse of the first non-consecutive order. In a first example of the system, both of the first, gridding voltage and the second, bias voltage are negative voltages with respect to a common voltage of the interventional imaging system, and driving electronics of the unipolar cathode are connected through a cable with a length greater than 40 meters. In a second example of the system, optionally including the first example: each of the plurality of stages of the first control circuit includes a −1 kV voltage source, a capacitor, and at least two switches to bypass or negatively connect the −1 kV voltage source to the unipolar cathode, and the second control circuit includes a high precision voltage source capable of generating up to 1.2 kV with a precision of +/−50V, a capacitor, and at least two switches to bypass or negatively connect the high precision voltage source to the unipolar cathode. In a third example of the system, optionally including one or both of the first and second examples, the controller is further configured to: selectively bypass the plurality of stages of the first control circuit sequentially in the first non-consecutive order by bypassing at least one stage of the plurality of stages at each step of a first sequence of steps, and engaging a previously bypassed stage during at least one step of the first sequence of steps, and selectively engage the plurality of stages of the first control circuit sequentially in the second non-consecutive order by engaging at least one stage of the plurality of stages at each step of a second sequence of steps, and bypassing a previously engaged stage during at least one step of the second sequence of steps. In a fourth example of the system, optionally including one or more or each of the first through third examples, the controller is further configured to: selectively bypass the plurality of stages of the first control circuit sequentially in the first non-consecutive order based on a first protocol generated from a first stage engagement matrix stored in a memory of the interventional imaging system, and selectively engage the plurality of stages of the first control circuit sequentially in the second non-consecutive order based on a second protocol generated from a second stage engagement matrix stored in the memory, wherein the first stage engagement matrix and the second stage engagement matrix indicate when each stage of the plurality of stages is to be engaged and when each stage of the plurality of stages is to be bypassed. In a fifth example of the system, optionally including one or more or each of the first through fourth examples, the first stage engagement matrix and the second stage engagement matrix indicate when each stage of the plurality of stages is to be engaged and when each stage of the plurality of stages is to be bypassed via a binary coding where a one indicates engaging a relevant stage, and a zero indicates bypassing the stage. In a sixth example of the system, optionally including one or more or each of the first through fifth examples, the first protocol and the second protocol are optimized to reduce a voltage imbalance between stages of the plurality of stages. In a seventh example of the system, optionally including one or more or each of the first through sixth examples: in a first condition where the plurality of stages of the first control circuit are sequentially bypassed in a consecutive order and not in the first non-consecutive order, the voltage imbalance between the stages causes a voltage at a stage to exceed a threshold voltage, the threshold voltage a voltage at which damage may be caused to at least one component of the stage, in a second condition where the plurality of stages of the first control circuit are sequentially bypassed in the first non-consecutive order, the voltage imbalance does not cause the voltage at the stage to exceed the threshold voltage.
The disclosure also provides support for a method for an interventional imaging system, the method comprising: in response to receiving an instruction to switch on a cathode of the interventional imaging system: retrieving a first stage engagement matrix from a memory of the interventional imaging system, the first stage engagement matrix including a binary encoding indicating a first non-consecutive order for bypassing and/or engaging a plurality of stages of a first control circuit of a multi-stage switching unit of the interventional imaging system, generating a first protocol for controlling the first control circuit based on the first stage engagement matrix, decreasing a voltage supplied to a gridding electrode of the cathode from a first, gridding voltage of the interventional imaging system to a common voltage of the interventional imaging system in accordance with the first protocol, and increasing the voltage from the common voltage to a second, bias voltage of the interventional imaging system via a second control circuit of the multi-stage switching unit, and in response to receiving an instruction to switch the cathode off: generating a second protocol for controlling the first control circuit based on a second non-consecutive order, the second non-consecutive order the reverse of the first non-consecutive order, decreasing the voltage from the second, bias voltage to the common voltage via the second control circuit, and increasing the voltage from the common voltage to the first, gridding voltage in accordance with the second protocol. In a first example of the method, the second non-consecutive order is indicated by a binary encoding of a second stage engagement matrix stored in the memory.
When introducing elements of various embodiments of the present disclosure, the articles “a,” “an,” and “the” are intended to mean that there are one or more of the elements. The terms “first,” “second,” and the like, do not denote any order, quantity, or importance, but rather are used to distinguish one element from another. The terms “comprising,” “including,” and “having” are intended to be inclusive and mean that there may be additional elements other than the listed elements. As the terms “connected to,” “coupled to,” etc. are used herein, one object (e.g., a material, element, structure, member, etc.) can be connected to or coupled to another object regardless of whether the one object is directly connected or coupled to the other object or whether there are one or more intervening objects between the one object and the other object. In addition, it should be understood that references to “one embodiment” or “an embodiment” of the present disclosure are not intended to be interpreted as excluding the existence of additional embodiments that also incorporate the recited features.
In addition to any previously indicated modification, numerous other variations and alternative arrangements may be devised by those skilled in the art without departing from the spirit and scope of this description, and appended claims are intended to cover such modifications and arrangements. Thus, while the information has been described above with particularity and detail in connection with what is presently deemed to be the most practical and preferred aspects, it will be apparent to those of ordinary skill in the art that numerous modifications, including, but not limited to, form, function, manner of operation and use may be made without departing from the principles and concepts set forth herein. Also, as used herein, the examples and embodiments, in all respects, are meant to be illustrative and should not be construed to be limiting in any manner.