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VIRTUAL STUDIES IN GRATING- BASED PHASE-CONTRAST IMAGING Janne Vignero 1 INTRODUCTION Talbot-Lau Interferometry (TLI) Transmission Image Differential phase Image Dark Field Image 2 INTRODUCTION TLI

  1. TALBOT-LAU INTERFEROMETRY (TLI) Also referred to as ‘grating - based’ phase -contrast imaging Periodic x-ray field is created by a grating; ‘the Talbot effect’ Periodic x-ray field is measured by a grating Pseudo coherent beam created by grating Conventional x-ray tubes are not coherent ▫ ▪ ▫ ▫ ▫ ▫ 27 INTRODUCTION TLI SIMULATIONS DETECTABILITY STUDY APPLICATIONS CONCLUSION

  2. TALBOT-LAU INTERFEROMETRY (TLI) Also referred to as ‘grating - based’ phase -contrast imaging Periodic x-ray field is created by a grating; ‘the Talbot effect’ Periodic x-ray field is measured by a grating Pseudo coherent beam created by grating Conventional x-ray tubes are not coherent ▫ ▪ ▫ ▫ ▫ ▫ 28 INTRODUCTION TLI SIMULATIONS DETECTABILITY STUDY APPLICATIONS CONCLUSION

  3. TALBOT-LAU INTERFEROMETRY (TLI) Also referred to as ‘grating - based’ phase -contrast imaging Periodic x-ray field is created by a grating; ‘the Talbot effect’ Periodic x-ray field is measured by a grating Pseudo coherent beam created by grating Conventional x-ray tubes are not coherent ▫ ▪ ▫ ▫ ▫ ▫ 29 INTRODUCTION TLI SIMULATIONS DETECTABILITY STUDY APPLICATIONS CONCLUSION

  4. TALBOT-LAU INTERFEROMETRY (TLI) Also referred to as ‘grating - based’ phase -contrast imaging Periodic x-ray field is created by a grating; ‘the Talbot effect’ Periodic x-ray field is measured by a grating Pseudo coherent beam created by grating Conventional x-ray tubes are not coherent ▫ ▪ ▫ ▫ ▫ ▫ 30 INTRODUCTION TLI SIMULATIONS DETECTABILITY STUDY APPLICATIONS CONCLUSION

  5. TALBOT-LAU INTERFEROMETRY (TLI) Also referred to as ‘grating - based’ phase -contrast imaging Periodic x-ray field is created by a grating; ‘the Talbot effect’ Periodic x-ray field is measured by a grating Pseudo coherent beam created by grating Conventional x-ray tubes are not coherent ▫ ▪ ▫ ▫ ▫ ▫ 31 INTRODUCTION TLI SIMULATIONS DETECTABILITY STUDY APPLICATIONS CONCLUSION

  6. TALBOT-LAU INTERFEROMETRY (TLI) ▫ ▪ ▫ ▫ ▫ ▫ 32 INTRODUCTION TLI SIMULATIONS DETECTABILITY STUDY APPLICATIONS CONCLUSION

  7. TALBOT-LAU INTERFEROMETRY (TLI) For each pixel we measure an average intensity pattern with and without object ▫ ▪ ▫ ▫ ▫ ▫ 33 INTRODUCTION TLI SIMULATIONS DETECTABILITY STUDY APPLICATIONS CONCLUSION

  8. TALBOT-LAU INTERFEROMETRY (TLI) For each pixel we measure 3 parameters 3 images can be constructed ▫ ▪ ▫ ▫ ▫ ▫ 34 INTRODUCTION TLI SIMULATIONS DETECTABILITY STUDY APPLICATIONS CONCLUSION

  9. TALBOT-LAU INTERFEROMETRY (TLI) Differential phase Image Transmission Image Dark Field Image ▫ ▪ ▫ ▫ ▫ ▫ 35 INTRODUCTION TLI SIMULATIONS DETECTABILITY STUDY APPLICATIONS CONCLUSION

  10. TALBOT-LAU INTERFEROMETRY (TLI) Differential phase Image Transmission Image 𝑇 𝑒𝑄 = 2𝜌𝑒 tan 𝜖𝜀𝑢 S Tr = exp −𝜈𝑢 = exp −2𝑙𝛾𝑢 𝑞 2 𝜖𝑦 ▫ ▪ ▫ ▫ ▫ ▫ 36 INTRODUCTION TLI SIMULATIONS DETECTABILITY STUDY APPLICATIONS CONCLUSION

  11. RESEARCH QUESTION How to quantitatively compare Tr and dP imaging? Transmission Image Differential phase Image ▫ ▪ ▫ ▫ ▫ ▫ 37 INTRODUCTION TLI SIMULATIONS DETECTABILITY STUDY APPLICATIONS CONCLUSION

  12. TRANSMISSION VERSUS DIFFERENTIAL PHASE IMAGING Transmission (Tr) Differential phase (dP) 𝑇 𝑒𝑄 = 2𝜌𝑒 tan 𝜖𝜀𝑢 S Tr = exp −𝜈𝑢 Signal 𝑞 2 𝜖𝑦 = exp −2𝑙𝛾𝑢 1 1 ⋅ 1 Noise 𝜏 𝑈𝑠 ∝ 𝜏 𝑒𝑄 ∝ 𝑤 𝑄𝑊 𝑄𝑊 ▫ ▪ ▫ ▫ ▫ ▫ 38 INTRODUCTION TLI SIMULATIONS DETECTABILITY STUDY APPLICATIONS CONCLUSION

  13. TRANSMISSION VERSUS DIFFERENTIAL PHASE IMAGING 1. Beta versus delta Transmission (Tr) Differential phase (dP) 𝑇 𝑒𝑄 = 2𝜌𝑒 tan 𝜖𝜀𝑢 S Tr = exp −𝜈𝑢 Signal 𝑞 2 𝜖𝑦 = exp −2𝑙𝛾𝑢 1 1 ⋅ 1 Noise 𝜏 𝑈𝑠 ∝ 𝜏 𝑒𝑄 ∝ 𝑤 𝑄𝑊 𝑄𝑊 ▫ ▪ ▫ ▫ ▫ ▫ 39 INTRODUCTION TLI SIMULATIONS DETECTABILITY STUDY APPLICATIONS CONCLUSION

  14. 1. BETA VERSUS DELTA (H 2 0, 30 keV) 𝜺 For soft tissues 𝜀 ≈ 1000 ⋅ 𝛾 ≠ 1000 times better performance 𝜸 of dP in comparison to Tr ▫ ▪ ▫ ▫ ▫ ▫ 40 INTRODUCTION TLI SIMULATIONS DETECTABILITY STUDY APPLICATIONS CONCLUSION

  15. TRANSMISSION VERSUS DIFFERENTIAL PHASE IMAGING 1. Beta versus delta Transmission (Tr) Differential phase (dP) 𝑇 𝑒𝑄 = 2𝜌𝑒 tan 𝜖𝜀𝑢 S Tr = exp −𝜈𝑢 Signal 𝑞 2 𝜖𝑦 = exp −2𝑙𝛾𝑢 1 1 ⋅ 1 Noise 𝜏 𝑈𝑠 ∝ 𝜏 𝑒𝑄 ∝ 𝑤 𝑄𝑊 𝑄𝑊 ▫ ▪ ▫ ▫ ▫ ▫ 41 INTRODUCTION TLI SIMULATIONS DETECTABILITY STUDY APPLICATIONS CONCLUSION

  16. TRANSMISSION VERSUS DIFFERENTIAL PHASE IMAGING 1. Beta versus delta 2. ‘ 𝒆, 𝒒 𝟑 ’ the sensitivity Transmission (Tr) Differential phase (dP) 𝑇 𝑒𝑄 = 2𝜌𝑒 tan 𝜖𝜀𝑢 S Tr = exp −𝜈𝑢 Signal 𝑞 2 𝜖𝑦 = exp −2𝑙𝛾𝑢 1 1 ⋅ 1 Noise 𝜏 𝑈𝑠 ∝ 𝜏 𝑒𝑄 ∝ 𝑤 𝑄𝑊 𝑄𝑊 ▫ ▪ ▫ ▫ ▫ ▫ 42 INTRODUCTION TLI SIMULATIONS DETECTABILITY STUDY APPLICATIONS CONCLUSION

  17. 3. THE SYSTEM SENSITIVITY 𝑇 𝑒𝑄 = 2𝜌𝑒 tan 𝜖𝜀𝑢 S Tr = exp −𝜈𝑢 = exp −2𝑙𝛾𝑢 𝑞 2 𝜖𝑦 ▫ ▪ ▫ ▫ ▫ ▫ 43 INTRODUCTION TLI SIMULATIONS DETECTABILITY STUDY APPLICATIONS CONCLUSION

  18. 3. THE SYSTEM SENSITIVITY The G1-to-G2 distance ‘d’ The system sensitivity 2𝜌𝑒 𝑞 2 ▫ ▪ ▫ ▫ ▫ ▫ 44 INTRODUCTION TLI SIMULATIONS DETECTABILITY STUDY APPLICATIONS CONCLUSION

  19. 3. THE SYSTEM SENSITIVITY The G1-to-G2 distance ‘d’ The system sensitivity 2𝜌𝑒 𝑞 2 ▫ ▪ ▫ ▫ ▫ ▫ 45 INTRODUCTION TLI SIMULATIONS DETECTABILITY STUDY APPLICATIONS CONCLUSION

  20. 3. THE SYSTEM SENSITIVITY The G1-to-G2 distance ‘d’ The period of the interference pattern ‘p 2 ’ The system sensitivity 2𝜌𝑒 𝑞 2 ▫ ▪ ▫ ▫ ▫ ▫ 46 INTRODUCTION TLI SIMULATIONS DETECTABILITY STUDY APPLICATIONS CONCLUSION

  21. TRANSMISSION VERSUS DIFFERENTIAL PHASE IMAGING 1. Beta versus delta 2. ‘ 𝑒, 𝑞 2 ’ the system sensitivity Transmission (Tr) Differential phase (dP) 𝑇 𝑒𝑄 = 2𝜌𝑒 tan 𝜖𝜀𝑢 S Tr = exp −𝜈𝑢 3. ‘ 𝒘 ’, the system visibility Signal 𝑞 2 𝜖𝑦 = exp −2𝑙𝛾𝑢 1 1 ⋅ 1 Noise 𝜏 𝑈𝑠 ∝ 𝜏 𝑒𝑄 ∝ 𝑤 𝑄𝑊 𝑄𝑊 ▫ ▪ ▫ ▫ ▫ ▫ 47 INTRODUCTION TLI SIMULATIONS DETECTABILITY STUDY APPLICATIONS CONCLUSION

  22. 3. THE SYSTEM VISIBILITY 𝑤 = 𝑏 1 /𝑏 0 The visibility Decreased by - Polychromatic source - Finite width G0 slits 𝑏 1 - Finite height G2 grating - Beam divergence 𝑏 0 ▫ ▪ ▫ ▫ ▫ ▫ 48 INTRODUCTION TLI SIMULATIONS DETECTABILITY STUDY APPLICATIONS CONCLUSION

  23. 3. THE SYSTEM VISIBILITY 𝑤 = 𝑏 1 /𝑏 0 The visibility Determines noise in dP image 𝑏 1 𝑏 0 ▫ ▪ ▫ ▫ ▫ ▫ 49 INTRODUCTION TLI SIMULATIONS DETECTABILITY STUDY APPLICATIONS CONCLUSION

  24. 3. THE SYSTEM VISIBILITY 𝑤 = 𝑏 1 /𝑏 0 The visibility Determines noise in dP image 𝑏 1 𝑏 0 ▫ ▪ ▫ ▫ ▫ ▫ 50 INTRODUCTION TLI SIMULATIONS DETECTABILITY STUDY APPLICATIONS CONCLUSION

  25. 3. THE SYSTEM VISIBILITY 𝑤 = 𝑏 1 /𝑏 0 The visibility Determines noise in dP image 𝑏 1 𝑏 0 ▫ ▪ ▫ ▫ ▫ ▫ 51 INTRODUCTION TLI SIMULATIONS DETECTABILITY STUDY APPLICATIONS CONCLUSION

  26. 3. THE SYSTEM VISIBILITY 𝑤 = 𝑏 1 /𝑏 0 The visibility Determines noise in dP image 𝑏 1 𝑏 0 ▫ ▪ ▫ ▫ ▫ ▫ 52 INTRODUCTION TLI SIMULATIONS DETECTABILITY STUDY APPLICATIONS CONCLUSION

  27. TRANSMISSION VERSUS DIFFERENTIAL PHASE IMAGING Benchmarking the CH-TLI setup 1. Beta versus delta 2. ‘ 𝑒, 𝑞 2 ’ the system sensitivity 3. ‘ 𝑤 ’, the system visibility ▫ ▪ ▫ ▫ ▫ ▫ 53 INTRODUCTION TLI SIMULATIONS DETECTABILITY STUDY APPLICATIONS CONCLUSION

  28. TRANSMISSION VERSUS DIFFERENTIAL PHASE IMAGING 1. Beta versus delta 2. ‘ 𝑒, 𝑞 2 ’ the system sensitivity Transmission (Tr) Differential phase (dP) 𝑇 𝑒𝑄 = 2𝜌𝑒 tan 𝜖𝜀𝑢 S Tr = exp −𝜈𝑢 3. ‘ 𝑤 ’, the system visibility Signal 𝑞 2 𝜖𝑦 = exp −2𝑙𝛾𝑢 1 1 ⋅ 1 Noise 𝜏 𝑈𝑠 ∝ 𝜏 𝑒𝑄 ∝ 𝑤 𝑄𝑊 𝑄𝑊 4. Projection vs differential ▫ ▪ ▫ ▫ ▫ ▫ 54 INTRODUCTION TLI SIMULATIONS DETECTABILITY STUDY APPLICATIONS CONCLUSION

  29. 2. PROJECTION VERSUS DIFFERENTIAL IMAGING S Tr = exp −𝜈𝑢 Transmission = exp −2𝑙𝛾𝑢 𝑇 𝑒𝑄 = 2𝜌𝑒 tan 𝜖𝜀𝑢 Differential phase 𝑞 2 𝜖𝑦 ▫ ▪ ▫ ▫ ▫ ▫ 55 INTRODUCTION TLI SIMULATIONS DETECTABILITY STUDY APPLICATIONS CONCLUSION

  30. 2. PROJECTION VERSUS DIFFERENTIAL IMAGING S Tr = exp −𝜈𝑢 Transmission = exp −2𝑙𝛾𝑢 𝑇 𝑒𝑄 = 2𝜌𝑒 tan 𝜖𝜀𝑢 Differential phase 𝑞 2 𝜖𝑦 ▫ ▪ ▫ ▫ ▫ ▫ 56 INTRODUCTION TLI SIMULATIONS DETECTABILITY STUDY APPLICATIONS CONCLUSION

  31. 2. PROJECTION VERSUS DIFFERENTIAL IMAGING S Tr = exp −𝜈𝑢 Transmission = exp −2𝑙𝛾𝑢 𝑇 𝑒𝑄 = 2𝜌𝑒 tan 𝜖𝜀𝑢 Differential phase 𝑞 2 𝜖𝑦 Contrast-to-noise metrics are not applicable So, even theoretically, how to compare Tr and dP? ▫ ▪ ▫ ▫ ▫ ▫ 57 INTRODUCTION TLI SIMULATIONS DETECTABILITY STUDY APPLICATIONS CONCLUSION

  32. TRANSMISSION VERSUS DIFFERENTIAL PHASE IMAGING 1. Beta versus delta 2. ‘ 𝑒, 𝑞 2 ’ the system sensitivity Transmission (Tr) Differential phase (dP) 𝑇 𝑒𝑄 = 2𝜌𝑒 tan 𝜖𝜀𝑢 S Tr = exp −𝜈𝑢 3. ‘ 𝑤 ’, the system visibility Signal 𝑞 2 𝜖𝑦 = exp −2𝑙𝛾𝑢 1 1 ⋅ 1 Noise 𝜏 𝑈𝑠 ∝ 𝜏 𝑒𝑄 ∝ 𝑤 𝑄𝑊 𝑄𝑊 4. Projection vs differential ▫ ▪ ▫ ▫ ▫ ▫ 58 INTRODUCTION TLI SIMULATIONS DETECTABILITY STUDY APPLICATIONS CONCLUSION

  33. RESEARCH QUESTION How to quantitatively compare Tr and dP imaging? Transmission Image Differential phase Image Comparing experimental data will be very hard, but even for theoretical data (where the ground truth is known) there is no approach available as we cannot compare 𝑇 𝑈𝑠 with 𝑇 𝑒𝑄 . ▫ ▪ ▫ ▫ ▫ ▫ 59 INTRODUCTION TLI SIMULATIONS DETECTABILITY STUDY APPLICATIONS CONCLUSION

  34. RESEARCH QUESTION How to quantitatively compare Tr and dP imaging? Performance metric: Relative dose required for a lesion to be detectable in Tr and dP Use virtual studies to benchmark the dP performance against the Tr performance  Requires a simulation platform to produce rapidly ‘realistic’ dP and Tr images ▪ ▫ ▫ ▫ ▫ ▫ 60 INTRODUCTION TLI SIMULATIONS DETECTABILITY STUDY APPLICATIONS CONCLUSION

  35. OUTLINE ― Talbot-Lau interferometry ― A hybrid simulation framework – generate ‘realistic’ imagines that match those of a TLI scanner ― A detectability study – a task-based study – human reader studies (4-AFC) ― Application: mammography ▫ ▫ ▪ ▫ ▫ ▫ 61 INTRODUCTION TLI SIMULATIONS DETECTABILITY STUDY APPLICATIONS CONCLUSION

  36. HYBRID IMAGE MODELLING Numerical wave propagation Hybrid image modelling Computationally expensive, not practical Combining analytical equations with for virtual studies where you need a lot of experimentally measured metrics data and large fields of view. 4 𝜈 m ▫ ▫ ▪ ▫ ▫ ▫ 62 INTRODUCTION TLI SIMULATIONS DETECTABILITY STUDY APPLICATIONS CONCLUSION

  37. HYBRID IMAGE MODELLING Expected signal S Tr = exp −𝜈𝑢 = exp −2𝑙𝛾𝑢 𝑇 𝑒𝑄 = 2𝜌𝑒 tan 𝜖𝜀𝑢 𝑞 2 𝜖𝑦 Expected noise level 𝜏 𝑈𝑠 = 𝑇 𝑈𝑠 1 + 1 𝑇 𝑈𝑠 𝑄𝑊 1 2 1 + 1 1 𝜏 𝑒𝑄 = 1 + 𝑤 2 𝑇 𝑈𝑠 𝐸 2 𝑇 𝑈𝑠 𝑄𝑊 Chabior et al. [2012] ▫ ▫ ▪ ▫ ▫ ▫ 63 INTRODUCTION TLI SIMULATIONS DETECTABILITY STUDY APPLICATIONS CONCLUSION

  38. HYBRID IMAGE MODELLING Detector and focal spot blur Expected signal 𝑇 𝑈𝑠 ℱ −1 ℱ 𝑇 ⋅ 𝑁𝑈𝐺 ⋅ 𝐻 𝐺𝑇 Image 𝑇 + 𝑂 Expected noise Correlate and scale noise ℱ −1 ℱ 𝑆 ⋅ 𝜏 𝑈𝑠 𝑂𝑄𝑇 ⋅ 𝜏 ▫ ▫ ▪ ▫ ▫ ▫ 64 INTRODUCTION TLI SIMULATIONS DETECTABILITY STUDY APPLICATIONS CONCLUSION

  39. HYBRID IMAGE MODELLING Detector and focal spot blur Expected signal 𝑇 𝑈𝑠 ℱ −1 ℱ 𝑇 ⋅ 𝑁𝑈𝐺 ⋅ 𝐻 𝐺𝑇 Image 𝑇 + 𝑂 Expected noise Correlate and scale noise ℱ −1 ℱ 𝑆 ⋅ 𝜏 𝑈𝑠 𝑂𝑄𝑇 ⋅ 𝜏 S Tr = exp −𝜈𝑢 = exp −2𝑙𝛾𝑢 ▫ ▫ ▪ ▫ ▫ ▫ 65 INTRODUCTION TLI SIMULATIONS DETECTABILITY STUDY APPLICATIONS CONCLUSION

  40. HYBRID IMAGE MODELLING Detector and focal spot blur Expected signal 𝑇 𝑈𝑠 ℱ −1 ℱ 𝑇 ⋅ 𝑁𝑈𝐺 ⋅ 𝐻 𝐺𝑇 Image 𝑇 + 𝑂 Expected noise Correlate and scale noise ℱ −1 ℱ 𝑆 ⋅ 𝜏 𝑈𝑠 𝑂𝑄𝑇 ⋅ 𝜏 MTF : measured G FS : analytical ▫ ▫ ▪ ▫ ▫ ▫ 66 INTRODUCTION TLI SIMULATIONS DETECTABILITY STUDY APPLICATIONS CONCLUSION

  41. HYBRID IMAGE MODELLING Detector and focal spot blur Expected signal 𝑇 𝑈𝑠 ℱ −1 ℱ 𝑇 ⋅ 𝑁𝑈𝐺 ⋅ 𝐻 𝐺𝑇 Image 𝑇 + 𝑂 Expected noise Correlate and scale noise ℱ −1 ℱ 𝑆 ⋅ 𝜏 𝑈𝑠 𝑂𝑄𝑇 ⋅ 𝜏 R = random generated values with a zero mean and a unit variance ▫ ▫ ▪ ▫ ▫ ▫ 67 INTRODUCTION TLI SIMULATIONS DETECTABILITY STUDY APPLICATIONS CONCLUSION

  42. HYBRID IMAGE MODELLING Detector and focal spot blur Expected signal 𝑇 𝑈𝑠 ℱ −1 ℱ 𝑇 ⋅ 𝑁𝑈𝐺 ⋅ 𝐻 𝐺𝑇 Image 𝑇 + 𝑂 Expected noise Correlate and scale noise ℱ −1 ℱ 𝑆 ⋅ 𝜏 𝑈𝑠 𝑂𝑄𝑇 ⋅ 𝜏 NPS : measured 𝜏 𝑈𝑠 = 𝑇 𝑈𝑠 1 + 1 PV: measured 𝑇 𝑈𝑠 𝑄𝑊 ▫ ▫ ▪ ▫ ▫ ▫ 68 INTRODUCTION TLI SIMULATIONS DETECTABILITY STUDY APPLICATIONS CONCLUSION

  43. HYBRID IMAGE MODELLING Detector and focal spot blur Expected signal 𝑇 𝑈𝑠 ℱ −1 ℱ 𝑇 ⋅ 𝑁𝑈𝐺 ⋅ 𝐻 𝐺𝑇 Image 𝑇 + 𝑂 Expected noise Correlate and scale noise ℱ −1 ℱ 𝑆 ⋅ 𝜏 𝑈𝑠 𝑂𝑄𝑇 ⋅ 𝜏 ▫ ▫ ▪ ▫ ▫ ▫ 69 INTRODUCTION TLI SIMULATIONS DETECTABILITY STUDY APPLICATIONS CONCLUSION

  44. HYBRID IMAGE MODELLING Detector and focal spot blur Expected signal 𝑇 𝑈𝑠 ℱ −1 ℱ 𝑇 ⋅ 𝑁𝑈𝐺 ⋅ 𝐻 𝐺𝑇 Image 𝑇 + 𝑂 Expected noise Correlate and scale noise ℱ −1 ℱ 𝑆 ⋅ 𝜏 𝑈𝑠 𝑂𝑄𝑇 ⋅ 𝜏 − log() ▫ ▫ ▪ ▫ ▫ ▫ 70 INTRODUCTION TLI SIMULATIONS DETECTABILITY STUDY APPLICATIONS CONCLUSION

  45. HYBRID IMAGE MODELLING Detector and focal spot blur Expected signal 𝑇 𝑒𝑄 ℱ −1 ℱ 𝑇 ⋅ 𝑁𝑈𝐺 ⋅ 𝐻 𝐺𝑇 Image 𝑇 + 𝑂 Expected noise Correlate and scale noise ℱ −1 ℱ 𝑆 ⋅ 𝜏 𝑒𝑄 𝑂𝑄𝑇 ⋅ 𝜏 𝑇 𝑒𝑄 = 𝟑𝝆𝒆 tan 𝜖𝜀𝑢 𝒒 𝟑 𝜖𝑦 ▫ ▫ ▪ ▫ ▫ ▫ 71 INTRODUCTION TLI SIMULATIONS DETECTABILITY STUDY APPLICATIONS CONCLUSION

  46. HYBRID IMAGE MODELLING Detector and focal spot blur Expected signal 𝑇 𝑒𝑄 ℱ −1 ℱ 𝑇 ⋅ 𝑁𝑈𝐺 ⋅ 𝐻 𝐺𝑇 Image 𝑇 + 𝑂 Expected noise Correlate and scale noise ℱ −1 ℱ 𝑆 ⋅ 𝜏 𝑒𝑄 𝑂𝑄𝑇 ⋅ 𝜏 MTF : measured G FS : analytical ▫ ▫ ▪ ▫ ▫ ▫ 72 INTRODUCTION TLI SIMULATIONS DETECTABILITY STUDY APPLICATIONS CONCLUSION

  47. HYBRID IMAGE MODELLING Detector and focal spot blur Expected signal 𝑇 𝑒𝑄 ℱ −1 ℱ 𝑇 ⋅ 𝑁𝑈𝐺 ⋅ 𝐻 𝐺𝑇 Image 𝑇 + 𝑂 Expected noise Correlate and scale noise ℱ −1 ℱ 𝑆 ⋅ 𝜏 𝑒𝑄 𝑂𝑄𝑇 ⋅ 𝜏 R = random generated values with a zero mean and a unit variance ▫ ▫ ▪ ▫ ▫ ▫ 73 INTRODUCTION TLI SIMULATIONS DETECTABILITY STUDY APPLICATIONS CONCLUSION

  48. HYBRID IMAGE MODELLING Detector and focal spot blur Expected signal 𝑇 𝑒𝑄 ℱ −1 ℱ 𝑇 ⋅ 𝑁𝑈𝐺 ⋅ 𝐻 𝐺𝑇 Image 𝑇 + 𝑂 Expected noise Correlate and scale noise ℱ −1 ℱ 𝑆 ⋅ 𝜏 𝑒𝑄 𝑂𝑄𝑇 ⋅ 𝜏 NPS : measured 𝜏 𝑒𝑄 = 𝑇 𝑈𝑠 2 1 + 1 1 PV: measured 1 + 𝒘 2 𝑇 𝑈𝑠 𝐸 2 𝑇 𝑈𝑠 𝑸𝑾 𝑤 : measured ▫ ▫ ▪ ▫ ▫ ▫ 74 INTRODUCTION TLI SIMULATIONS DETECTABILITY STUDY APPLICATIONS CONCLUSION

  49. HYBRID IMAGE MODELLING Detector and focal spot blur Expected signal 𝑇 𝑒𝑄 ℱ −1 ℱ 𝑇 ⋅ 𝑁𝑈𝐺 ⋅ 𝐻 𝐺𝑇 Image 𝑇 + 𝑂 Expected noise Correlate and scale noise ℱ −1 ℱ 𝑆 ⋅ 𝜏 𝑒𝑄 𝑂𝑄𝑇 ⋅ 𝜏 ▫ ▫ ▪ ▫ ▫ ▫ 75 INTRODUCTION TLI SIMULATIONS DETECTABILITY STUDY APPLICATIONS CONCLUSION

  50. HYBRID IMAGE MODELLING PMMA sphere ▫ ▫ ▪ ▫ ▫ ▫ 76 INTRODUCTION TLI SIMULATIONS DETECTABILITY STUDY APPLICATIONS CONCLUSION

  51. HYBRID IMAGE MODELLING In vivo scan mouse Model is based on segmented uCT data ▫ ▫ ▪ ▫ ▫ ▫ 77 INTRODUCTION TLI SIMULATIONS DETECTABILITY STUDY APPLICATIONS CONCLUSION

  52. RESEARCH QUESTION How to quantitatively compare Tr and dP imaging? Transmission Image Differential phase Image ▫ ▫ ▫ ▪ ▫ ▫ 78 INTRODUCTION TLI SIMULATIONS DETECTABILITY STUDY APPLICATIONS CONCLUSION

  53. OUTLINE ― Talbot-Lau interferometry ― A hybrid simulation framework – generate ‘realistic’ imagines that match those of a TLI scanner ― A detectability study – a task-based study – human reader studies (4-AFC) ― Application: mammography ▫ ▫ ▪ ▫ ▫ ▫ 79 INTRODUCTION TLI SIMULATIONS DETECTABILITY STUDY APPLICATIONS CONCLUSION

  54. TASK BASED DETECTABILITY STUDY Relative dose required for a lesion to be detectable = measure of relative performance Via a four alternative forced choice study ▫ ▫ ▫ ▪ ▫ ▫ 80 INTRODUCTION TLI SIMULATIONS DETECTABILITY STUDY APPLICATIONS CONCLUSION

  55. 4-AFC Four alternative forced choice (4-AFC) Zhang et al., SPIE proceedings (2016) ▫ ▫ ▫ ▪ ▫ ▫ 81 INTRODUCTION TLI SIMULATIONS DETECTABILITY STUDY APPLICATIONS CONCLUSION

  56. 4-AFC Four alternative forced choice (4-AFC) Zhang et al., SPIE proceedings (2016) ▫ ▫ ▫ ▪ ▫ ▫ 82 INTRODUCTION TLI SIMULATIONS DETECTABILITY STUDY APPLICATIONS CONCLUSION

  57. 4-AFC Four alternative forced choice (4-AFC) Zhang et al., SPIE proceedings (2016) ▫ ▫ ▫ ▪ ▫ ▫ 83 INTRODUCTION TLI SIMULATIONS DETECTABILITY STUDY APPLICATIONS CONCLUSION

  58. 4-AFC Four alternative forced choice (4-AFC) Zhang et al., SPIE proceedings (2016) ▫ ▫ ▫ ▪ ▫ ▫ 84 INTRODUCTION TLI SIMULATIONS DETECTABILITY STUDY APPLICATIONS CONCLUSION

  59. 4-AFC Four alternative forced choice (4-AFC) Zhang et al., SPIE proceedings (2016) ▫ ▫ ▫ ▪ ▫ ▫ 85 INTRODUCTION TLI SIMULATIONS DETECTABILITY STUDY APPLICATIONS CONCLUSION

  60. 4-AFC Four alternative forced choice (4-AFC) Psychometric curve fit 𝑐 %𝐷𝑝𝑠𝑠 = 1 − 0.75 ⋅ exp − 𝑒𝑝𝑡𝑓 𝑏 Zhang et al., SPIE proceedings (2016) ▫ ▫ ▫ ▪ ▫ ▫ 86 INTRODUCTION TLI SIMULATIONS DETECTABILITY STUDY APPLICATIONS CONCLUSION

  61. 4-AFC Four alternative forced choice (4-AFC) Psychometric curve fit – threshold at 62.5% 𝑐 %𝐷𝑝𝑠𝑠 = 1 − 0.75 ⋅ exp − 𝑒𝑝𝑡𝑓 𝑏 Zhang et al., SPIE proceedings (2016) ▫ ▫ ▫ ▪ ▫ ▫ 87 INTRODUCTION TLI SIMULATIONS DETECTABILITY STUDY APPLICATIONS CONCLUSION

  62. 4-AFC Four alternative forced choice (4-AFC) Psychometric curve fit – threshold at 62.5% 𝑐 %𝐷𝑝𝑠𝑠 = 1 − 0.75 ⋅ exp − 𝑒𝑝𝑡𝑓 𝑏 Zhang et al., SPIE proceedings (2016) If you want to do this for every task it is very time consuming. Make it more general. ▫ ▫ ▫ ▪ ▫ ▫ 88 INTRODUCTION TLI SIMULATIONS DETECTABILITY STUDY APPLICATIONS CONCLUSION

  63. GENERALIZED TASK BASED DETECTABILITY STUDY Liver in adipose bg with blood in muscle bg with radiation dose of x radiation dose of y Definitions FOM 𝐺𝑃𝑁 𝑈𝑠 = min 𝐽 𝑈𝑠 − max 𝐽 𝑈𝑠 𝜏 𝑈𝑠 𝐺𝑃𝑁 𝑒𝑄 = max(∫ |𝑇 𝑒𝑄 |𝑒𝑦) 𝜏 𝑒𝑄 Liver in adipose bg with blood in muscle bg with radiation dose of w radiation dose of z Should scale with detectability ▫ ▫ ▫ ▪ ▫ ▫ 89 INTRODUCTION TLI SIMULATIONS DETECTABILITY STUDY APPLICATIONS CONCLUSION

  64. GENERALIZED TASK BASED DETECTABILITY STUDY Liver in adipose bg with radiation dose of x Definitions FOM 𝐺𝑃𝑁 𝑈𝑠 = min 𝐽 𝑈𝑠 − max 𝐽 𝑈𝑠 𝜏 𝑈𝑠 𝐺𝑃𝑁 𝑒𝑄 = max(∫ |𝑇 𝑒𝑄 |𝑒𝑦) 𝜏 𝑒𝑄 Liver in adipose bg with radiation dose of w Should scale with detectability Only valid for same task shape! ▫ ▫ ▫ ▪ ▫ ▫ 90 INTRODUCTION TLI SIMULATIONS DETECTABILITY STUDY APPLICATIONS CONCLUSION

  65. GENERALIZED TASK BASED DETECTABILITY STUDY For a certain task shape 1. Simulate . Simulate set of Tr and dP images (bg and obj) with Transmission Diff. Phase signal and noise combinations ranging between undetectable to detectable 2. FOM. 3. 4AFC. 4. Thresholds. 5. EAK(62.5%). 6. RP. ▫ ▫ ▫ ▪ ▫ ▫ 91 INTRODUCTION TLI SIMULATIONS DETECTABILITY STUDY APPLICATIONS CONCLUSION

  66. GENERALIZED TASK BASED DETECTABILITY STUDY For a certain task shape 1. Simulate . Simulate set of Tr and dP images (bg and obj) with Transmission Diff. Phase signal and noise combinations ranging between undetectable to detectable 2. FOM. Calculate the FOM of each of the images . 3. 4AFC. 𝐺𝑃𝑁 𝑒𝑄 = max(∫ |𝑇 𝑒𝑄 |𝑒𝑦) 𝐺𝑃𝑁 𝑈𝑠 = min 𝐽 𝑈𝑠 − max 𝐽 𝑈𝑠 𝜏 𝑒𝑄 𝜏 𝑈𝑠 4. Thresholds. 5. EAK(62.5%). 6. RP. ▫ ▫ ▫ ▪ ▫ ▫ 92 INTRODUCTION TLI SIMULATIONS DETECTABILITY STUDY APPLICATIONS CONCLUSION

  67. GENERALIZED TASK BASED DETECTABILITY STUDY For a certain task shape 1. Simulate . Simulate set of Tr and dP images (bg and obj) with Transmission Diff. Phase signal and noise combinations ranging between undetectable to detectable 2. FOM. Calculate the FOM of each of the images . 3. 4AFC. Use these images in a 4afc human reader study (one for Tr 𝐺𝑃𝑁 𝑒𝑄 = max(∫ |𝑇 𝑒𝑄 |𝑒𝑦) 𝐺𝑃𝑁 𝑈𝑠 = min 𝐽 𝑈𝑠 − max 𝐽 𝑈𝑠 𝜏 𝑒𝑄 𝜏 𝑈𝑠 and one for dP) as a function of the FOM 4. Thresholds. 5. EAK(62.5%). FOM FOM 6. RP. ▫ ▫ ▫ ▪ ▫ ▫ 93 INTRODUCTION TLI SIMULATIONS DETECTABILITY STUDY APPLICATIONS CONCLUSION

  68. GENERALIZED TASK BASED DETECTABILITY STUDY For a certain task shape 1. Simulate . Simulate set of Tr and dP images (bg and obj) with Transmission Diff. Phase signal and noise combinations ranging between undetectable to detectable 2. FOM. Calculate the FOM of each of the images . 3. 4AFC. Use these images in a 4afc human reader study (one for Tr 𝐺𝑃𝑁 𝑒𝑄 = max(∫ |𝑇 𝑒𝑄 |𝑒𝑦) 𝐺𝑃𝑁 𝑈𝑠 = min 𝐽 𝑈𝑠 − max 𝐽 𝑈𝑠 𝜏 𝑒𝑄 𝜏 𝑈𝑠 and one for dP) as a function of the FOM 4. Thresholds. Calculate the threshold FOM Tr and FOM dP 5. EAK(62.5%). FOM FOM 6. RP. ▫ ▫ ▫ ▪ ▫ ▫ 94 INTRODUCTION TLI SIMULATIONS DETECTABILITY STUDY APPLICATIONS CONCLUSION

  69. GENERALIZED TASK BASED DETECTABILITY STUDY For a certain task shape 1. Simulate . Simulate set of Tr and dP images (bg and obj) with Transmission Diff. Phase signal and noise combinations ranging between undetectable to detectable 2. FOM. Calculate the FOM of each of the images . 3. 4AFC. Use these images in a 4afc human reader study (one for Tr 𝐺𝑃𝑁 𝑒𝑄 = max(∫ |𝑇 𝑒𝑄 |𝑒𝑦) 𝐺𝑃𝑁 𝑈𝑠 = min 𝐽 𝑈𝑠 − max 𝐽 𝑈𝑠 𝜏 𝑒𝑄 𝜏 𝑈𝑠 and one for dP) as a function of the FOM 4. Thresholds. Calculate the threshold FOM Tr and FOM dP 5. EAK(62.5%). Calculate the EAK Tr and EAK dP for a given FOM FOM application (combination of bg and obj materials) to reach e.g. for tumor lesion in adipose e.g. for tumor lesion in adipose tissue which EAK required to tissue which EAK required to respectively the FOMTr and FOMdP reach FOM Tr = FOM Tr62.5% reach FOM dP = FOM dP62.5% 6. RP. ▫ ▫ ▫ ▪ ▫ ▫ 95 INTRODUCTION TLI SIMULATIONS DETECTABILITY STUDY APPLICATIONS CONCLUSION

  70. GENERALIZED TASK BASED DETECTABILITY STUDY For a certain task shape 1. Simulate . Simulate set of Tr and dP images (bg and obj) with Transmission Diff. Phase signal and noise combinations ranging between undetectable to detectable 2. FOM. Calculate the FOM of each of the images . 3. 4AFC. Use these images in a 4afc human reader study (one for Tr 𝐺𝑃𝑁 𝑒𝑄 = max(∫ |𝑇 𝑒𝑄 |𝑒𝑦) 𝐺𝑃𝑁 𝑈𝑠 = min 𝐽 𝑈𝑠 − max 𝐽 𝑈𝑠 𝜏 𝑒𝑄 𝜏 𝑈𝑠 and one for dP) as a function of the FOM 4. Thresholds. Calculate the threshold FOM Tr and FOM dP 5. EAK(62.5%). Calculate the EAK Tr and EAK dP for a given FOM FOM application (combination of bg and obj materials) to reach e.g. for tumor lesion in adipose e.g. for tumor lesion in adipose tissue which EAK required to tissue which EAK required to respectively the FOMTr and FOMdP reach FOM Tr = FOM Tr62.5% reach FOM dP = FOM dP62.5% 𝑆𝑄 = 𝐹𝐵𝐿 𝑈𝑠 62.5% 6. RP. The relative performance of an application = EAK Tr /EAK dP 𝐹𝐵𝐿 𝑒𝑄 62.5% ▫ ▫ ▫ ▪ ▫ ▫ 96 INTRODUCTION TLI SIMULATIONS DETECTABILITY STUDY APPLICATIONS CONCLUSION

  71. OUTLINE ― Talbot-Lau interferometry ― A hybrid simulation framework – generate ‘realistic’ imagines that match those of a TLI scanner ― A detectability study – a task-based study – human reader studies (4-AFC) ― Application: mammography ▫ ▫ ▪ ▫ ▫ ▫ 97 INTRODUCTION TLI SIMULATIONS DETECTABILITY STUDY APPLICATIONS CONCLUSION

  72. APPLICATIONS Application 1. Sphere/lesions of different sizes 5.3 mm diam 2.6 mm diam 1.3 mm diam Lesion Shaheen E. et al. , Med. Phys. 41(8), 2014 ▫ ▫ ▫ ▫ ▪ ▫ 98 INTRODUCTION TLI SIMULATIONS DETECTABILITY STUDY APPLICATIONS CONCLUSION

  73. APPLICATIONS Application 1. Sphere/lesions of different sizes 5.3 mm diam ▫ ▫ ▫ ▫ ▪ ▫ 99 INTRODUCTION TLI SIMULATIONS DETECTABILITY STUDY APPLICATIONS CONCLUSION

  74. APPLICATIONS: HOMOGENEOUS BG Application 1. Sphere/lesions of different sizes Transmission Differential phase 1. Simulate . 2. FOM. 3. 4AFC . 4. Thresholds. 5. EAK(62.5%). 6. RP. 8 different FOM values 8 different FOM values 15 signal present & 45 signal absent per dose 15 signal present & 45 signal absent per dose ▫ ▫ ▫ ▫ ▪ ▫ 100 INTRODUCTION TLI SIMULATIONS DETECTABILITY STUDY APPLICATIONS CONCLUSION

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