## 1 Introduction  
Computer aided diagnosis (CADx) can be defined as a diagnosis that is made by a radiologist who uses the output from a computerized analysis of medical images as a \"second opinion\" in both detecting lesions and making diagnostic decisions [1]. One aim of the typical CADx system is to extract and analyze the characteristics of benign and malignant lesions in an objective manner to aid the radiologist. Here, the \"diagnostic\" decision relates to treatment response and early classification of drug responders versus non-responders, and we name our proposed system as computer-aided therapeutic response (CADrx) system. Glioblastoma multiforme (GBM) is the most aggressive and lethal primary brain tumor in human. Anti-angiogenesis drugs are increasingly being explored in clinical trials as therapeutic options. In a phase II _in vivo_ clinical trial, the conventional way to assess treatment response is the tumor size change after chemotherapy or radiotherapy based on Macdonald criteria and evaluated on T1-weighted contrast enhanced (T1 wCE) MR images. However, efficacy can only be evaluated at least 8-10 weeks after treatment. Diffusion weighted magnetic resonance imaging (DW-MRI) has the potential to work as a surrogate biomarker to reveal changes in the tumor microenvironment that precede morphologic tumor changes [2]. DW-MRI depends on the microscopic mobility of water. This mobility, classically called Brownian motion, is due to thermal agitation and is highly influenced by the cellular environment of water. Because water diffusion is strongly affected by molecular viscosity and membrane permeability between intra- and extracellular compartments, DW-MRI can be used to characterize highly cellular regions of tumors versus acellular regions. Treatment response detection can be manifested as a change in tumor cellularity, which may precede tumor size changes. Thus, findings on DW-MRI could be an early sign of biologic changes. [3]  
The purpose of this study is to use apparent diffusion coefficient (ADC), derived from DW-MR images, for early prediction of the tumor volume change on a later scan. There are two main parts to this computer-aided treatment response evaluation system. First, a semi-automated segmentation algorithm is applied to segment the GBM brain tumors on T1 wCE images. Then, the tumor ROI is mapped onto derived ADC maps and the histogram of tumor ADC values will be extracted for automatic treatment response prediction. Computer-aided detection and segmentation of GBM brain tumors is a challenging problem and in Table 1 we present a concise review of the prior art in automatic tumor segmentation. Fuzzy clustering and knowledge-based analysis are popular methods explored by the early pioneers [4-6]. Voxel-based classification method using statistical pattern classification techniques are explored by others [7-15]. Most of the studies above use multiple MRI sequences (T1w, T2w, proton density weighted, and Flair) for the automatic tumor and edema detection and segmentation. [PERSON] _et al._[16] developed an interactive system adapting the fuzzy connectedness using multiple MRI sequences. [PERSON] _et al._[17,18] used texture features and segmentation by the weighted aggregation (SWA) method for the GBM tumor segmentation on T1 wCE images which is similar to part of our study. In our study, we developed semi-automated method to segment tumors on T1 wCE images; in addition, we mapped the tumor contours onto ADC maps. Computer-aided diagnosis (CADx) in GBM brain tumor is an active research area, and many promising MR methods have been developed for detecting and characterizing cancer, its treatments and adverse effects, e.g. T1-weighted MR, T2-weighted MR, MR spectroscopy, perfusion-weighted MR, and diffusion-weighted MR. In our study, we focused on T1-weighted and DW-MRI. Tumor size