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Timing-pulse measurement and detector calibration for the OsteoQuant®.

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Dead-Time and Beam-Hardening correction methods

Dead-Time and Beam-Hardening correction methods

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  • Works on the translate-rotate principleThese movements are achieved through a combination of high-precision mechanical hardware and stepping motors.The three orthogonal movements in the scanner are the translation and rotation of the source and detector and the axial positioning of the gantry.
  • The motor moves the scanner at a required speed and acceleration. The motion-control system generates the necessary pulses to rotate the motor shaft for the required measurement interval. The data collected is irrelevant unless the motor and data collection timing pulses are correlatedAs we do not know the relative phase of the two pulse trains and do not want to assume consistency between the two frequenciesProvides a reference between the two pulse events, to relate a motor position to a detector frame.
  • This kind of data transfer can be achieved using a counter with a universal serial bus (USB) interface combined with a temporary storage buffer. Fast event notification speed from the counters to the computer should be in milliseconds or less to register all events.
  • Start pulse generated from CNTR3 of module 1. Produces a pulse after 65ms.The start pulse from CNTR 3 sets a FF, which enables the counting of an 8 bit counter at 1 MHz. 128ms later, the counter MSB transitions to a high state which resets the flip flop and thereby reshapes the input signal.
  • The synch pulse acts as a common point of reference to the two pulse trains. After a delay of 0.5ms after the synch pulse, the OR gates are activated and the counting starts.
  • Motor pulses were simulated using a function generator.Sync time pulses are the raw pulses subtracted from the start pulse. The start pulse is the only common time stamp for both modules.
  • There are certain general properties that apply to all types of radiation detectors.Some of these properties can cause loss in expected photon counts. These lossesare often modeled as being caused by dead-time and may result in errors in thereconstructed image if left uncorrected.
  • This charge is collected applying an electric field across the detector. The time taken to recover from an event registration is dead timeA problem occurs if another event happens during the time required to create the electric signal. The occurrence of a radiation quantum is a random event governed by Poisson statistics. and these losses become severe for larger event rates.
  • The consequence of dead-time is shown here.The scanner is to be operated at 1mA. Hence the expected counts according to the slope equation is 72,000.
  • In CT reconstruction, the reconstructed image values are assumed to be linearly proportional to the density of the object scanned, which is fulfilled if a mono-energetic x-ray source is used. However, use of a poly-energetic x-ray source results in wrongly estimated density values in some parts of the reconstructed image.
  • . The anode material is a compound made of tungsten, molybdenum and rhodiumEach slab measures 10.5 cm x 6.5 cm, with the thickness of an individual slab being 1.62 mm for aluminum and 7.8 mm for Plexig10 slab pairs simulate the arm, 19 leg
  • y_i is the modeled uncorrected tube current vs. photon count response. Y_i is the ideal response. y_i can be mathematically modeled as a function of beta, where x is the independent variable and y is the dependant variable.Slope is calculated from the linear part of the response.The fourth degree polynomial equation returns four root values out of which the complex and negative roots are ignored. The real root closest to the expected linear line is chosen.
  • Stability was tested using same and different date corrections.Coefficient vectors from 22 dates for data sets collected over nine months. For same-date corrections n is 64 x 10 . For diff date, it varies with the number of data sets. The results are discussed later
  • Corrections: Same date and Different date
  • In CT reconstruction, the reconstructed image values are assumed to be linearly proportional to the density of the object scanned.According to Beer’s Law, the projection values of the x-ray beam passing through an object are linearly proportional to μ(E). For a monoenergetic x-ray source, the effective attenuation coefficient μeff is a function of the average energy of the x-ray spectrum (Bremsstrahlung). The projection values are generally linearized to a linear line of slope μeff
  • Purely a mathematical modelThe robustness of the different polynomial fits was measured using the F-test for a 99% confidence interval. Mathematical model is linearized. 5 root values
  • For lower energies, the equation is the same as Beer’s law. The author knows his energy and m1, m2 valueare equated to zero and the minimum squared error associated with each unknown are calculated.
  • To prove that the appropriate relationship between E2 and E1 exists for our data, a random 19-platedata set was chosen to calculate the fitting parameters and estimate the energies. A random 19-plate data set was chosen to calculate the fitting parameters and energies.
  • The idea of different date corrections was suggested because setting the parameters for correction prior to every scan is a tedious process especially beam hardening.If there is no drift in the detector response, the correction from another day can be used.Different date corrections are the correction coefficients from from the data collected on a different date applied on another data set.
  • Measuring the plates to calculate the parameters necessary for the primary correction every day is a tedious process.
  • The same-date and different-date corrections are assumed to be stable if their residuals are less than or equal to 350.
  • as the photon energy is a major factor in defining the attenuation properties
  • Transcript

    • 1. BMIL
      Timing Pulse Measurement and Detector Calibration for the OsteoQuant®
      Advisor: Dr. Thomas N. Hangartner
      By: Binu Enchakalody
      1
    • 2. The OsteoQuant®
      pQCTscanner which can provide precise density assessment of the trabecular and cortical regions of bone.
      Currently being upgraded to a x-ray tube source and a CZT semiconductor detector.
      2
      Ref: http://www.wright.edu/academics/bmil/bmil1.htm
    • 3. Objective
      Implement a system capable of registering the motor- and detector timing-pulses of the Osteoquant® using a common time-base in microsecond resolution.
      2a. Correct the photon-count loss due to dead time to an error level of less than 0.5% of the maximum expected photon counts.
      2b. Correct the non-linearity of the projection values due to beam hardening to an error level of less than 1% of the expected maximum projection value.
      3
    • 4. Timing-Pulse Measurement for the OsteoQuant®
      4
    • 5. Need for Timing-Pulse Measurement
      Data collected is only useful if there is synchronization between the motor- and detector-timing pulses.
      The motor- and detector timing-pulses have to be well synchronized to assure correlation between the data collected and the measurement interval.
      Aim
      Each detector frame should be accurately related to a motor position.
      Solution
      Measure time stamps using a common time base to relate a motor position to a detector frame.
      5
    • 6. Timing-Pulse Measurement: Analyzing the problem
      Sample Detector Timing-Pulse
      0 2 4 6 8 10 12 ms
      Sample Motor Timing-Pulse
      0 3 6 9 12 ms
      Common Time-Base (1/1000 resolution)
      1 µs
      µs
      3000
      6000
      8000
      12000
      0
      2000
      4000
      10000
      9000
      6
    • 7. Timing-Pulse Measurement: Requirement
      Requires counters working at clock frequencies of 1 MHz or above.
      High data transfer speed
      Fast event notification
      Solution
      The USB-4301 is a low-power USB-2.0-compliant, 16-bit, 5 channel, up-down binary counter, capable of operating at frequencies as high as 5 MHz can be used in event counting and pulse generating applications.
      7
    • 8. Setup
      • Motor- and detector-timing pulses are assigned to separate modules
      • 9. Modules are daisy chained to form 32-bit counters
      • 10. Terminal count is achieved in ~72 minutes
      8
    • 11. External Circuit Components
      Synchronization Circuit
      9
    • 12. External Circuit Components
      10
    • 13. Timing Diagram
      11
    • 14. Flow chart
      External Circuitry
      • Pulse Shaping Circuit
      • 15. Start Pulse
      • 16. Synchronization Circuit
      • 17. Interrupt Mask
      • 18. Combined Circuit
      Counter Programming
      12
    • 22. Error Range of Measured Time Periods
      Interrupt signal of 2.22 ± 0.003 ms
      Relative error : 0.13%
      13
    • 23. Sample Spreadsheet
      14
    • 24. Detector Calibration for the OsteoQuant®
      15
    • 25. Detector Calibration: Dead Time
      Dead Time
      An event occurs at the detector is converted into an electrical signal depending on the intensity and duration of the event.
      The time required to collect this charge depends on certain characteristics (mobility, distance to collection electrodes, etc.) of the detector itself and on the subsequent electronics.
      Due to the random nature governed by Poisson statistics, there is always a probability that the detector misses a true event that follows a recorded event.
      The missed true events are called dead-time losses
      16
    • 26. Need for Dead-Time Correction
      Operating Parameters:
      Tube Voltage : 45 kVp
      Tube Current: 0 – 1 mA
      Photon accumulation time : 50 ms
      Aim:
      Correct the photon-count loss due an error level of less than 0.5% of the maximum expected photon counts (0.5% of 72,000) ± 350 counts.
      The photon counts-vs.-tube current response plot is mathematically modeled and then linearized.
      The measured non-linear and the expected linear photon counts for varying tube currents of one detector element from a sample data set
      17
    • 27. Detector Calibration: Beam Hardening
      Beam Hardening
      X-ray beams used in CT are usually polychromatic
      When the photon beam passes through material, it tends to preferentially loose its lower energy photons, hardening the beam in the process.
      Lower-energy x-rays are more prone to attenuation, and the average energy of a polychromatic beam varies with increasing thickness of the material, thereby making the beam harder.
      18
    • 28. Beam Hardening
      Operating Parameters:
      Tube Voltage : 45 kVp
      Tube Current: 1 mA
      Photon accumulation time : 50 ms
      Aim:
      Correct the non-linearity of the projection values due to beam hardening to an error level of less than 1% of the expected maximum projection value (1% of 5 projection value units) ± 0.05.
      The projections-vs.-thickness plot is mathematically modeled and then linearized.
      The measured non-linear and expected linear projection values for varying absorber thicknesses.
      19
    • 29. Experimental Setup
      Source : The tube can operate at a maximum anode voltage of 50 kVp and a maximum anode current of 1 mA, at a maximum operating temperature of 55oC.
      Detector : The detector is a CZT semi-conductor cuboid of 64 pixilated elements composed of 50% tellurium, 5% zinc and 45% cadmium.
      Slabs : Slabs are used in the beam hardening experiment as a substitute for the bone and soft-tissue in human-body (aluminum and Plexiglas). A total on 19 pairs of these slabs were used.
      Data was collected on 22 dates over a span of nine months.
      20
    • 30. Dead-Time Correction: Steps
      Modeling using the fourth-degree polynomial function
      Linearization of the model
      Drift and stability analysis of the correction
      Same-date Correction
      Different-date Correction
      21
    • 31. Dead-Time Correction: Modeling and linearization
      For dead-time correction
      22
    • 32. Stability of the Dead-Time Correction
      • Fit-coefficient vectors were collected
      • 33. Corrections applied to the data collected at the same date (same-date corrections) and a different-date (different-date corrections).
      • 34. The stability was analyzed by comparing the residuals
      • 35. The corrections were declared stable if their residuals < 350.
      • 36. The least expected residuals are those from the same-date corrections
      23
    • 37. Beam-Hardening Correction: Steps
      Fifth-Degree Polynomial Model
      Modeling using the polynomial function for 10- and 19-plate data sets
      Linearizing the mathematical model
      Corrections applied on the 10- and 19-plate data sets
      Bimodal-Energy Model
      Modeling using the bimodal-energy model for 10- and 19-plate data sets
      Linearizing the mathematical model
      Corrections applied on the10- and 19-plate data sets
      Compare the stability analysis between both models
      24
    • 38. Beam-Hardening Correction
      According to Beer’s Law, the projection values of the x-ray beam passing through an object are linearly proportional to μ(E).
      The projection values are generally linearized to a linear line.
      i: 1, 2, 3, ... 19 for the number of slab pairs used
      I0 : counts collected with no object in the beam path
      Ii: counts collected with i number of slab pairs
      µeff: linear attenuation coefficient for Al and Pl
      di : thickness of i number of slab pairs
      25
    • 39. Linearization Using the Polynomial Model
      Based on the projection value-vs.-slab thickness plots, it was decided that an 5th-degree polynomial fit can model these data.
      Each detector element’s data was fitted using a second to a sixth-degree polynomial function.
      26
    • 40. Bimodal-Energy Model
      The bimodal energy model* suggests that the attenuation is a function of predominantly two energies, a dominant energy (E2) and a lower energy (E1).
      • The projection values can be modeled using μ1, μ2and α.
      • 41. μ2is the slope by E2 for large thicknesses
      • 42. μ1 is the slope by E1 for smaller thicknesses.
      To solve for the unknowns, the non-linear least squares method is used.
      The equation system was iteratively solved using a Matlab script by assuming initial values for the unknown fitting parameters.
      Ref: de Casteele, E. V., Dyck, D. V., Sijbers, J., and Raman, E. 2002. An energy-based beam hardening model in tomography. Phys Med Biol 47, 23–30.
      27
    • 43. Bimodal-Energy Model
      • The slab pairs were treated as a homogenous material by calculating the thickness ratio for a slab pair.
      • 44. Energies E2 and E1 are not predetermined.
      • 45. Estimate of the expected lower and upper bound for μ1 and μ2.
      • 46. E2 proved to be greater than E1
      Linear attenuation coefficient (μ(E)) vs. energy for the Al/Pl slabs.
      28
    • 47. Linearization Using the Bimodal-Energy Model
      • The corrected projection values were obtained by solving till convergence, with an acceptable error < 0.01 (1%).
      • 48. Linearization using both models satisfy the required error criterion
      • 49. The stability of the beam-hardening corrections were analyzed by evaluating the error statistics of the same-date and different-date corrected values.
      29
    • 50. Secondary Correction
      Primary correction every day is a tedious process.
      Apply primary corrections from one particular date to the data sets collected from other dates and following this with a secondary correction (3rd degree polynomial) based only on a few plates (0, 6, 14, 19 or 0, 3, 7, 9) measured on the specific date.
      Without Secondary Correction With Secondary Correction
      30
    • 51. Stability analysis for beam-hardening corrections
      Same-date and different-date corrections.
      Same-date primary
      Different-date primary
      Different-date-primary followed by secondary
      Data collected on 22 dates, during nine months.
      134 coefficient matrices for the 10-plate data sets.
      5 coefficient matrices for the 19-plate data sets.
      Stability for the correction method is assumed if the residuals of the same-date and different-date corrections are less than 0.05.
      31
    • 52. Results: Dead-Time Correction
      Linearization using the fourth-degree model for a data set. Histogram of the individual residuals using a fourth-degree polynomial correction for a data set
      32
    • 53. Same-Date Corrections: 10 plate data-set
      33
      Corrected projection values and their histograms for the polynomial and
      the bimodal-energy model
    • 54. Different-date corrections: 10 plate data-set
      Corrected projection values and their histograms for the polynomial and the
      bimodal-energy model
      34
    • 55. Different-date primary followed by secondary correction: 10 plate data-set
      35
      Corrected projection values and their histograms for the polynomial and the bimodal-energy model
    • 56. Summary: Correction Methods
      Summary of the same-date and different-date primary (Prim) corrections using the fifth degree
      polynomial and bimodal-energy models, and the same-date and different-date primary corrections using both models followed by the secondary (Sec) corrections. The checked cells represent the methods that produced residuals lower than 0.05.
      36
    • 57. Detector Calibration: Summary
      The same-date dead-time corrections were all within the expected residual value.
      The data collection required for the dead-time corrections can be automated.
      Same-date primary corrections consistently produced corrected projection values that were well within the expected residual of 0.05.
      Most of the residuals for the different-date bimodal corrections were below 0.05, whereas the residual values for the different-date polynomial corrections were above 0.05.
      Future Work
      Using the non-paralyzable dead-time model.
      Beam hardening corrections should be studied with different tube voltages.
      Stability of the corrections over a shorter time period can be studied
      37