VIRTUAL STUDIES IN GRATING- BASED PHASE-CONTRAST IMAGING Janne - PowerPoint PPT Presentation

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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