ADC Estimation in Multi-scan DWMRI Abhinav K. Jha 1* , Matthew A. Kupinski 1 , Jeffrey J. Rodríguez 2 , Renu M. Stephen 3 and Alison T. Stopeck 3 1 College of Optical Sciences, University of Arizona, Tucson, AZ, USA 2 Dept. of Electrical and Computer Engineering, University of Arizona, Tucson, AZ, USA 3 Arizona Cancer Center, University of Arizona, Tucson, AZ, USA * Corresponding author: akjha@email.arizona.edu Abstract: A maximum-likelihood-based scheme for estimating the Apparent Diffusion Coeffi- cient (ADC) value in diffusion-weighted MRI is presented, using which data from multiple scans acquired at the same diffusion-gradient value can be used for accurate ADC computation. c  2010 Optical Society of America OCIS codes: 110.2960 Image analysis; (170.3880) Medical and biological imaging 1 Introduction The apparent diffusion coefficient (ADC) obtained using diffusion weighted magnetic resonance imaging (DWMRI) is emerging as a potentially novel non-invasive imaging bio-marker for prediction and monitoring of anti-cancer therapy response [1,2]. The ADC value of a lesion is computed using the signal strength of the lesion at two different magnetic diffusion gradient values (b values). To measure ADC accurately, multiple scans of a patient at the same magnetic b value are carried out. However due to certain variations across scans, the ADC values estimated are not the same for different scans. We propose a maximum-likelihood- based scheme to use the data from all the scans to estimate a single, accurate and reliable ADC value. Our method takes into account the variance in the signal strengths that are estimated in different scans, and uses this information to output a more reliable ADC estimate. The results section illustrates how our method yields accurate ADC values. 2 Methods In a study at the Arizona Cancer Center, DWMRI is being examined as a potential imaging biomarker to monitor therapeutic response in breast cancer patients with metastases to the liver. Diffusion weighted single-shot echo-planar imaging (DW-SSEPI) using b values of 0 and 450 s/mm 2 is performed. This scan is repeated in triplicate for each b value. To make the problem general, let us assume that each scan has been done at M b values, and K is the number of scans at each b value. Denoting each of these b values by b i , in our case, b 1 = 0 s/mm 2 and b 2 = 450 s/mm 2 , M = 2 and K = 3. A diffusion-map based approach can be taken to estimate the ADC of the lesion [2]. To accomplish this, first we take the mean of the K scans at each b value and therefore determine an average scan at each b value. We then segment the lesion in this average scan, and since we have the signal strength for each lesion pixel at two b values, therefore by using the basic ADC equation [1], we can obtain the ADC value of each lesion pixel. Although the averaging of scans increases the Signal- to-Noise-ratio, but due to variations like visceral organ motion, patient movement across scans and other effects like non-linearity of scanner, flow effects around the organ this method would output inaccurate ADC values [2]. Also due to these reasons, the ADC values computed from different scans will be different, while ideally we would like to get a single ADC value from all the measurements. To solve this issue, we propose a maximum-likelihood-estimation(MLE) based method. Consider the lesion pixel at b value b i . Let S k iq be the random variable(RV) that denotes the intensity of pixel q and let ¯ S i k denote the mean signal intensity of the lesion for the k th scan. We can show using the central limit theorem that ¯ S i k is a Gaussian RV [3]. To use the MLE approach to solve the problem of ADC estimation, let us take the mean of ¯ S i k to be S 0 exp(-ab i ), by using the basic ADC equation [1], where a a339_1.pdf OSA / DIPA 2010 DTuB3.pdf