`
`Precision Control of Eluted Activity from a Sr/Rb Generator
`for Cardiac Positron Emission Tomography
`
`R. Klein1, A. Adler2, R. S. Beanlands1, R. A. deKemp1
`1National Cardiac PET Centre, University of Ottawa Heart Institute, Ottawa, Ontario, Canada
`2School of Information Technology and Engineering, University of Ottawa, Ontario, Canada
`
`Abstract(cid:151) A rubidium-82 (82Rb) elution system is described
`for use with clinical positron emission tomography. The system
`is self-calibrating with 1.4% repeatability, independent of
`generator activity and elution flow rate. Saline flow is switched
`between a 82Sr/82Rb generator and a bypass line to achieve a
`constant activity elution of 82Rb. In the present study, pulse
`width modulation (PWM) of a solenoid valve is compared to
`simple threshold control as a means to simulate a proportional
`valve. A predictive-corrective control algorithm is developed
`which produces a constant activity elution within the
`constraints of long feedback delay and short elution time.
`Accurate constant-activity elutions of 10-70% of the total
`generator activity were demonstrated using the threshold
`comparison control. The adaptive-corrective control of the
`PWM valve provided a substantial improvement in precision of
`the steady-state output.
`
`Keywords(cid:151)Strontium-82 Rubidium-82 generator, elution
`system control, cardiac PET imaging
`
`
`I. INTRODUCTION
`
`Eluting the generator at a constant flow rate results in a
`
`repeatable and characteristic curve of activity vs. volume
`over a wide range of flows [2], whereas the eluted activity
`vs. time is dependent on the saline flow rate [5]. The scale
`of the characteristic curve depends on the amount of 82Sr in
`the column, and the shape is characterized by an initial peak
`of high activity as the volume of the generator column is
`flushed (bolus stage) followed by an asymptotic decrease to
`an equilibrium of 82Rb production, flushing, and decay
`(continuous stage). The purpose of this study was to
`investigate the use of feedback control to obtain constant-
`activity elutions from the 82Rb generator.
`
`
`II. DESIGN
`
`
`A. System Description
`
`A bypass line of the generator is used with a single two-
`
`way solenoid pinch valve to direct flow through the
`generator or to bypass it (Fig.1). The lines are merged
`immediately upstream from an activity (positron) counter.
`The line volume between the generator and the activity
`counter is kept to a minimum, while ensuring significant
`shielding to reduce background counts from the generator.
`Downstream from the counter an additional two way pinch
`valve routes the elution to the patient outlet or to a shielded
`waste container.
`A constant flow rate F is set with a peristaltic pump.
`This allows for prediction of the activity at the patient outlet,
`Apat, after a transmission delay of D seconds, based on
`counts measured at the activity counter, Cdet using
`
`
`D
`−λ
`
`⋅
`
`e
`
`⋅
`
`K
`
`
`
`(1)
`
`
` Myocardial perfusion imaging with the radiotracer
`
`rubidium-82 (82Rb) and positron emission tomography
`(PET) is used commonly to diagnose coronary artery
`disease. Absolute measurements of perfusion can also be
`made from the rate of tracer uptake using dynamic PET
`imaging [1]. To facilitate reproducible measurements, the
`tracer should be introduced at a constant rate over a short
`period of time (30 s). 82Rb is produced from a 82Sr/82Rb
`generator and has a very short half-life (76 s). Therefore it
`requires direct intravenous infusion to the patient with an
`automated generator elution system [2].
`82Sr/82Rb generators have been described by our group
`
`and others for the production of 82Rb [3,4]. The generator is
`an ion-exchange column of tin-oxide that binds the parent
`isotope 82Sr (25 day half-life) but not the daughter 82Rb
`resulting from 82Sr decay. Therefore 82Rb is eluted from the
`generator simply by flushing with 0.9% saline. In the
`generator column, 82Rb exists at equilibrium levels with 82Sr
`and regenerates within 10 minutes after elution, making this
`tracer convenient for rapid serial perfusion studies.
`
`Computer (with data-acquisition card)
`
`A
`
`pat
`
`
`
`tCDt )( )(
`
`
`=
`+
`det
`
`
`
`
`
`where λ=ln(2)/76 is the 82Rb decay constant. The calibration
`constant K, accounting for the intrinsic and geometric
`efficiency of the activity counter is used to convert counter
`readings to 82Rb activity in Bq/ml.
`
`
`Saline
`Supply
`
`Peristaltic
`Pump
`
`Activity Counter
`
`Dose Calibrator
`or Patient Outlet
`
`Generator
`Valve
`
`82Rb/82Sr
`Generator
`
`Patient
`Valve
`
`Waste
`Container
`
`Patient
`Outlet
`
`Fig. 1 (cid:150) 82Rb elution
`system diagram showing
`saline line (thick lines),
`control signals, sensor
`signals,
`and
`major
`components.
`
`
`
`1 of 4
`
`JUBILANT EXHIBIT 1013
`Jubilant v. Bracco, IPR2018-01449
`
`

`

`Integral Activity at Patient Outlet (vial) - No Aperture Correction
`
`Detector: Convolved
`Calibrator: Delayed
`
`150
`100
`50
`Integral Activity at Patient Outlet (vial) - With Aperture Correction
`
`200
`
`Detector: Convolved
`Calibrator: Delayed
`
`15
`
`10
`
`05
`
`0
`
`15
`
`10
`
`150
`
`200
`
`
`
`50
`
`05
`
`0
`
`Integral Activity (MBq)
`
`Integral Activity (MBq)
`
`100
`Time (s)
`Fig. 2 (cid:150) Integral activity at the vial as measured by the dose calibrator (thin
`line) and estimated from the activity counter (thick line). The lower graph
`demonstrates the improvement in the estimate due to compensation for the
`aperture of the dose calibrator (γ=0.01). Flow rate is 5ml/min.
`
`Start pump
`All lines flushed and primed
`Constant elution through generator
`Threshold reached
`Start control of generator valve
`Constant activity reached
`Switch flow from waste to patient
`Desired total activity reached
`Switch generator valve to bypass
`All activity flushed to patient
`Stop pump
`Fig. 3 - Constant activity elution sequence diagram.
`
`
`
` A
`
` second, approach involved the simulation of a
`variable pinch valve by pulse-width-modulation (PWM) of
`the saline flow [6]. The valve was vibrated at 5Hz and the
`duty cycle was controlled. A minimum (cid:145)on(cid:146) time, Tmin, is
`required to overcome the valve spring and cause it to move
`which limits the vibration frequency. The PWM was
`implemented in a single software block, and allowed us to
`develop the remaining control algorithms as if controlling a
`variable pinch valve (Fig. 4).
`(PID)
`The
`traditional Proportional-Integral-Differential
`controller has some inherent shortcomings which make it
`inadequate for this application. These include a varying
`feedback delay due to different saline flow rates. In addition,
`a PID loop will always lag in response to the error as a result
`of feedback delay. Finally, the short elution time and low
`sampling frequency do not allow for long stabilization
`times.
`
`
`Fig. 4 - Pulse-width-modulation control of a solenoid valve to simulate a
`variable pinch valve. Flow through the generator increases as the duty cycle
`is increased.
`
`
`
`=
`
`pat
`
`∑∑
`
`K
`
`=
`
`
`
`(3)
`
`Ft
`
` )(tG
`ce
`
`=
`The parameter γ was adjusted emperically based on a
`
`series of calibration runs at 5-25 ml/min. The resulting plots
`corresponded more closely in shape, especially at low flow
`rates of 5-10 ml/min.
`
`C. Constant Activity Elution and Control Algorithms
`
`The readings from the activity counter are used as
`
`feedback to a real-time control system, which controls the
`pinch valve to achieve a constant activity rate. Initially, the
`patient valve routes the elution to the waste until the
`threshold activity is reached (Fig. 3). It is switched by the
`control system to the patient outlet after the flow delay from
`the activity counter to the patient valve. This removes the
`initial transient rise of activity to produce a step response at
`the patient outlet. The elution continues until the desired
`total activity has been produced. At the end of the elution
`the generator valve is closed creating a step drop in output.
`The elution of saline is continued through the bypass line to
`flush the activity from the counter to the patient outlet.
`Two approaches to control the generator/bypass valve
`were explored. The threshold comparison approach controls
`the valve through comparison of the instantaneous activity
`rate to the set point. This results in activity fluctuations
`around the desired set point. The set point was compensated
`for hysteresis using a single factor that was empirically
`determined and verified to be 1.2 and is independent of flow
`rate.
`
`B. Calibration
`
`An external dose calibrator (Capintec CRC-15R) is used
`as the gold standard for comparison of the accumulated
`counter readings both for calibration and testing. Calculation
`of the calibration constant was modified from that described
`in [2] using
`
`
`
`
`−λτ
`
`
`
`D
`
`−λ
`
`(2)
`
`(cid:136)
`∑
`
`tA )(
`e
`
`tA (
`)
`τ
`−
`⋅
`cal
`cal
`∑
`
`A
`t)(
`eF
`e
`
` tC )((
`
`t
`)
`
`−λ
`⊗
`⋅
`det
`The effective delay from the activity counter to the dose
`calibrator, τ, was determined through minimization of the
`mean square error between the calibrator readings, ´cal, and
`the predicted accumulated activity in the vial, Apat.
`
`Calibration runs were carried out at a flow rate of
`15ml/min over 60 seconds. Over the entire elution and the
`following 120 seconds, readings from the activity counter
`and the dose calibrator were recorded simultaneously at 1
`second intervals. Plotting of ´cal and Apat reveals slightly
`different shapes of the calibrator vs. detector curves (Fig.2).
`This was determined to be due to detection of activity in the
`patient line upstream from the patient outlet. An additional
`convolution kernel was created to describe this geometric
`aperture. The kernel was estimated to have the shape of a
`normalized Gaussian over the interval |-∞,0] with the width
`adjusted for the geometry of the dose calibrator.
`
`
`(
`)2
`γ−
`
`2 of 4
`
`

`

`
`
`To overcome the shortcoming of the PID controller, a
`predictive-corrective controller was developed. The activity
`from the generator is predicted based on the activity-volume
`curves measured during the same day(cid:146)s calibration run. A
`ratio of the desired activity and the predicted instantaneous
`activity is used as an estimate of the position of the variable
`valve. A PID feedback loop uses the measured count errors
`to correct the valve position.
`
`D. PWM Controlled Valve Calibration
`
`
`At the end of an elution the discrepancy in elution time
`is used to adjust Tmin. This iterative process adapts the
`estimation of Tmin over time. Tmin is expected to change due
`to material fatigue, change of tubing and other system
`variations. In our system Tmin converged to 162ms within
`less than 20 elutions and has not changed significantly since.
`Since the long Tmin corresponds to a minimum duty
`cycle of 80.1% a relatively small active range of the PWM
`is left for control. Since the implementation is in discrete
`time, this results in a reduced resolution of the control
`signal. The number of quantized steps, Q, is given by (4)
`where M (Hz) is the software model refresh rate and V (Hz)
`is the vibration frequency. In our case the model is run at
`2000Hz resulting in 78 quantized steps.
`
`
`
`(4)
`
`(
`1
`
`−
`
`VT
`min
`
`
`
`
`
`)
`
`VM
`
`
`
`
`Q
`
`=
`
`
`
`
`III. EXPERIMENTAL METHODS
`
`
`A. Calibration
`
`Daily calibration runs were conducted as described
`above to test for repeatability of the calibration and test for
`variation over time. Additional calibration runs were carried
`out at flow rates ranging from 5 to 25ml/min to test the
`accuracy of the physical model with changing flows.
`
`
`x 10-4
`
`Variation in calibration constant over time
`
`3
`
`2
`
`1
`
`Calibration constant
`
`5
`
`10
`
`20
`15
`Variation in activity over time
`
`25
`
`30
`
`35
`
`0123
`
`0
`
`Calibration constant
`
`1500
`
`1000
`
`500
`
`Activity
`
`B. Constant Activity Elutions
`
` A
`
` series of 30 s constant-activity elutions was carried
`out for desired output activity in the range of 10-70% of the
`total calibration activity. Output activity was measured
`relative to the calibration activity to accommodate for the Sr
`decay over the course of the study. Both threshold
`comparison control and adaptive-corrective controls were
`assessed for comparison.
`
`
`
`IV. RESULTS
`
`
`A. Calibration
`
`Over the life-span of one generator, 35 calibration runs
`were conducted at 15ml/min flow rate (Fig. 5). The
`calibration constant appears unchanged with a standard
`deviation of 1.4% over time.
`Calibration values were analyzed at flow rates ranging
`from 5-25 ml/min (Fig. 6). The value of the calibration
`constant did not vary over the range 10-25 ml/min, but at 5
`ml/min decreased slightly. The reason for this variation has
`not been determined but is not of much concern as this low
`flow rate is an extreme case and is not typically used in
`clinical application.
`
`B. Constant Activity Elutions
`
`Table 1 shows the mean square error (MSE), elution
`time error, and dose error as a function of the desired
`relative dose. These data show the desired elution time is
`achieved using
`the
`threshold comparison control but
`fluctuations cause a >30% mean squared error. The
`proposed control method improves the MSE at intermediate
`activities but performs less well at the extremes. These
`results are partly artifacts of the initial activity peak after the
`threshold activity is detected (Fig. 7). The source of this
`peak has not yet been confirmed, but is expected to be a
`sudden drop in back pressure as the patient valve is switched
`
`
`x 10-4
`
`Variation in calibration due to flow rate
`
`0
`
`0
`
`5
`
`10
`
`20
`15
`Date (days)
`Fig. 5 (cid:150) Calibration constant over the course of a generator life (top) and
`the dose from the generator during calibration over the same time period
`(bottom)
`
`25
`
`30
`
`35
`
`
`
`
`
`0
`
`0
`
`5
`
`10
`
`20
`
`25
`
`15
`Flow Rate (ml/min)
`Fig. 6 (cid:150) Calculated calibration constant over the range of flow rates.
`
`30
`
`
`
`3 of 4
`
`

`

`and did not detect significant breakthrough activity. Even
`after exceeding this specification by approximately 50%,
`breakthrough activity remained 15 and 13 times below the
`82Sr and
`85Sr
`established breakthrough
`limits
`for
`respectively. This leads us to believe that breakthrough is
`not significantly accelerated by using
`the
`feedback
`controlled elutions, but more experience is required for
`confirmation.
`
`
`V. CONCLUSION
`
`
`
`We have demonstrated a feedback control system for
`82Rb/82Sr generators to achieve constant-activity elutions. In
`addition we have confirmed the understanding of the
`physical model through successful calibration at various
`flow rates and generator activity. Work to date indicates that
`using pulse-width-modulation to simulate a variable position
`valve will enable constant-activity elutions with improved
`precision. In addition a predictive-corrective algorithm is
`able to control the modulation, however, more work is still
`required to reduce the initial transient overshoot.
`
`ACKNOWLEDGMENT
`
`
` We would like to thank May Aung and Kimberly
`Gardner for their collaboration and feedback during the
`initial clinical trials of the system.
`
`
`
`
`REFERENCES
`
`[1]
`
`J. W. Lin, R. R. Sciacca, R. L. Chou, A. F. Laine, S. R.
`Bergmann, (cid:147)Quantification of myocardial perfusion in human
`subjects using 82Rb and wavelet-based noise reduction(cid:148), J. Nucl.
`Med., Vol. 42, No. 2, February 2001.
`[2] N. J. Epstein, A. Benelfassi, R. S. Beanlands, R. A. deKemp, (cid:147)A
`82Rb infusion system for quantitative perfusion imaging in 3D
`PET(cid:148), App. Radiat. Isot, In Press, 2004.
`[3] T. M. Alvarez-Diez, R. A. deKemp, R. S. Beanlands, J. Vincent,
`(cid:147)Manufacture of strontium-82/rubidium-82 generators and
`quality control of rubidium-82 chloride for myocardial perfusion
`imaging in patients using positron emission tomography(cid:148), Appl.
`Radiat. Isot., Vol. 50, pp 1015-1023, 1999.
`[4] Y. Yano, (cid:147)Essentials of a Rubidium-82 generator for nuclear
`medicine(cid:148), Appl. Radiat. Isot., Vol 38, No 3, pp. 205-211, 1987.
`[5] V. Dhawan, (cid:147)Model for 82Sr/82Rb generator elution profiles: A
`second approach to radioawway/dosimetry(cid:148), Appl. Radiat. Isot.,
`Vol. 38, No. 3, pp. 233-239, 1987.
`[6] T. Imaizumi, O. Oyama, Yoshimitsu T., (cid:147)Study of pneumatic
`servo system employing solenoid valve instead of proportional
`valve by keeping the solenoid valve plunger to be floating(cid:148),
`Flucom Symposium Proceedings, article 076, 2000.
`
`
`
`
`
`
`
`Desired Dose
`(% calibration
`activity)
`
` TABLE I
`CONSTANT FLOW RATE RESULTS
`
`Elution Time
`Error (%)
`
`Eluted Dose
`Error
`(%)
`
`Mean Squared
`Errors (%)
`[steady-state]
`Threshold Comparison Control
`9.8
`31.6
`-6.7
`5.5
`33.9
`-13.3
`3.6
`34.0
`0.0
`7.3
`26.6
`-3.3
`Predictive-Corrective Control with PWM
`42.4
`[42.9]
`16.7
`5.0
`21.6
`[15.7]
`-3.3
`3.9
`27.6
`[8.8]
`-3.3
`6.2
`37.7
`[25.5]
`26.7
`2.3
`
`10
`30
`50
`70
`
`10
`30
`50
`70
`
`Activity Rate (MBq/s)
`
`Activity Rate (MBq/s)
`
`Instantaneous Activity at Patient Outlet - Threshold Comparison Control
`
`0123
`
`10
`
`15
`
`20
`
`25
`
`30
`
`40
`
`45
`
`50
`
`55
`
`60
`
`35
`Time (s)
`Instantaneous Activity at Patient Outlet - Predictive-Corrective Control and PWM
`
`15
`
`20
`
`25
`
`30
`
`40
`
`45
`
`50
`
`55
`
`60
`
`
`
`0123
`
`10
`
`35
`Time (s)
`Fig. 7 - Similar elutions at 50% generator capacity using the threshold
`comparison algorithm (top) and the adaptive-corrective control with PWM
`valve control (bottom). The dotted lines show the desired profile.
`
`
`from waste to patient outlet, resulting in a surge of active
`saline from the generator. Fig. 7 demonstrates sample
`elutions of 50% generator activity. The threshold control
`results in a MSE of 34.0%. With the exception of the initial
`peak during the first 4 s, the steady state MSE is only 8.8%
`and results partly from correction of the initial peak.
`As mentioned above, the high duty-cycle threshold,
`Tmin, required to vibrate the valve significantly limits the
`resolution of variable valve implementation. To date we
`have implemented the vibration control in software. Future
`improvements would implement the PWM in hardware
`using a timer. With counters running in the MHz range, the
`control signal resolution would be 3 orders of magnitude
`higher than our current implementation, and may help to
`further reduce the steady state MSE.
`
`C. Breakthrough Sr Activity
`
`
`Elution of 82Sr and 85Sr isotopes (half-life 25 and 65
`days respectively) to the patient is undesired, as Sr tends to
`accumulate in the bone marrow, which is particularly
`radiation sensitive.
`Daily calibration samples are used to test for the
`breakthrough of Sr activity. Our generator is limited to 20 L
`of elution for clinical use. After expiry we continued testing
`
`4 of 4
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