1. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Adaptive Weighted Deconvolution Model to Estimate the Cerebral Blood Flow Function in Dynamic Susceptibility Contrast MRI Jiaping Wang, Ph.D Department of Mathematical Science University of North Texas at Denton Joint work with Drs. Hongtu Zhu and Hongyu An from UNC-CH

2. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Outline Background and Motivation Adaptive Weighted De-convolution Model Simulation Studies Real Data Analysis

3. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Part 1. Background and Motivation

4. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Dynamic Susceptibility Contrast (DSC) Perfusion MRI measures the passage of a bolus of a non-diffusible contrast through the brain. The signal decreases as the bolus passes through the imaging slices. Background

5. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Convolution Relationship

6. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Deconvolution Techniques Fourier Transformation SVD TSVD at 0.01 TSVD at 0.05 TSVD at 0.1 TSVD at 0.2

7. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Part 2. Part 2. Adaptive Weighted Deconvolution Model

8. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Notations D : 3D volume N : the number of points on D d : a voxel in D : : spatial-temporal process : error process : AIF function, constant along space : Residue function D : 3D volume N : the number of points on D d : a voxel in D : : spatial-temporal process : error process : AIF function, constant along space : Residue function

9. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Voxel-wise Approach Frequency-Domain Frequency-Domain Temporal-Domain Temporal-Domain

10. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Discrete Continuous Key Assumptions:

11. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Two Main Steps (Spatial Adaptive Approach): 1. Transform the time series into the Fourier or Wavelet domain. 2. Smoothing the curves in the frequency domain by involving the local neighborhood information. Two Main Steps (Spatial Adaptive Approach): 1. Transform the time series into the Fourier or Wavelet domain. 2. Smoothing the curves in the frequency domain by involving the local neighborhood information. Voxel-wise vs. Spatio-Interdependence Jumping SpaceIrregular Boundary

12. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Unknown Approximation Spatial-Adaptive Approach

13. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Weighted LSE Estimated HRF

14. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Being Hierarchical Drawing nested spheres with increasing radiuses at each voxel and each frequency Drawing nested spheres with increasing radiuses at each voxel and each frequency …

15. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Sequentially determine weights Adaptively update Sequentially determine weights Adaptively update Being Adaptive Stopping Statistics

16. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL How to determine ?

17. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL

23. Part 3. Part 3. Simulations

24. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL (i) A temporal cut of the true images ; (ii) The true curves C(t) (iii) The true curves R(t) Simulation Set-up The true residue curves (iv) The AIF Curve (i)(ii)(iii) (iv)

25. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Simulation Results Result from SWADM Cluster Result Mean Curves of Clusters from SWADM

26. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL (1) Comparison with SVD ; Comparison Results (2) Comparison with TSVD at 0.01 ; (3) Comparison with TSVD at 0.05 ; (4) Comparison with TSVD at 0.1 ; (5) Comparison with TSVD at 0.2 ; (6) Comparison with Voxel-wise IFT ;

27. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Comparison along SNRs Average of D d along different SNRsOne sample t test for D d TSVD at 0.01 TSVD at 0.05 TSVD at 0.1 TSVD at 0.2 Voxel-wise IFT SVD

28. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Part 4. Part 4. Real Data

29. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL (e) The DSC PWI data set obtained from an acute ischemic stroke patient at Washington University in St. Louis after receiving a signed consent form with Institutional Review Board approval. MR images were acquired on a 3T Siemens whole body Trio system (Siemens Medical Systems, Erlangen, Germany). PWI images were acquired with a T2*-weighted gradient echo EPI sequence (TR/TE= 1500/43 ms,14 slices with a slice thickness of 5 mm, matrix= 128x128). This sequence was repeated 50 times and Gadolinium diethylenetriamine penta-acetic acid (Gd-DTPA, 0.1 mmol/kg) was injected at the completion of the 5th measure. Data Description

30. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Slices from C(t) images Sample of C(t) curves, the largest one can be considered as AIF. Clustered pattern Mean curves of clusters Clustering Results

31. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Estimation Results from Different Methods The curves from same voxel in Cluster I The curves from same voxel in Cluster II

32. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Thank You!