多變量體積型態法用於磁振造影影像群組間結構差異性之定量分析

Abstract

以體素為基礎的型態計量學（voxel-based morphometry, VBM），近年來已被廣泛應用在許多腦部結構研究上，以統計的方式量化、比較兩組人腦結構每一體素之型態是否具有顯著的差異。體素型態學使用單變異量統計，對於較為集中且巨大的差異具有簡單有效的優點。但是由於此方法沒有考慮相鄰體素間的連帶關係，因此可能無法找出差異量較為分散且微小的腦部區域。

本研究中我們提出了一個新的腦部結構評估技術—多變量體積形態法 （multivariate volumetric morphometry, MVM），以運用於磁振造影影像群組間結構差異性之定量分析。相對於以體素為基礎的型態計量學，多變量體積形態法採用線性鑑別度分析（linear discriminant analysis, LDA）作為多變量的估計方法來取代單變量的分析。此方法能同時考慮全部的體素，以找出對於群組間結構差異性最具鑑別力的投影軸。位於該投影軸上之每一元素即代表相對應體素具有的鑑別力比重（discrimination weight），且此鑑別力比重可被視為用來評估磁振造影影像群組間結構差異之程度等級(significance level)。此種多變量的計量方法能突顯群組間較為細微的結構性差異，很適合用於分析腦部結構差異的研究。此外，我們也證明了不論使用原始的磁振造影影像或是平滑化過後的影像，此方法所能達到的最大區辨能力是一樣的，因此可以直接在原始影像而非在人工處理平滑化後的影像上推論分析結果。相反地，以體素為基礎的型態計量學卻必須使用平滑化的處理來增加分析的正確性，同時加強相鄰體素間的連帶關係。然而使用平滑化處理時，要決定其恰當的影響範圍是很困難的一個問題，因為較大範圍的平滑化處理雖然可降低影像雜訊，但卻必須付出細部資訊被模糊的代價。

透過模擬小腦周圍區域萎縮的實驗，我們驗證了多變量體積形態法的有效性與正確性。比起以體素為基礎的型態計量學，該方法確實更有能力可偵測到群組間細微的腦部結構差異之處。應用在脊髓小腦運動失調症（spinocerebellar ataxia, SCA）的結構差異分析上，多變量體積形態法也比以體素為基礎的型態計量學更明顯地找出和病理相關的腦部結構組織。

Recently, voxel-based morphometry (VBM) has been widely applied to statistically infer the structural anomalies between the brains of two subject groups, in a voxel-by-voxel manner. This method is effective for mapping massive and centralized discrepancy. However, it may suffer from the poor sensitivity to subtle and widely-distributed discrepancy in brain structures.

In this work, we propose a novel multivariate morphometry (MVM) method that can be used to delineate the anatomical discrepancy between two groups of MR images. Rather than voxel-by-voxel manner in VBM, the proposed MVM simultaneously considers all of the voxels in MR volumes and map the group differences by using the linear discriminant analysis to determine the most discriminant projection vector. Each element in the projection vector represents the discrimination weight of the corresponding voxel involved in the combination of the most discriminant components. This weight can thus be regarded as the significance level of the corresponding voxel when differentiating two groups of MR volumes. This multivariate approach is appropriate to characterize group discrepancy, particularly when the brain atrophy distributes widely. Moreover, we prove that the discriminability remains the same no matter the projection vector is calculated from the original MR volumes or from the smoothed ones. Hence we can simply use the original data without the interference of the blurring artifact caused by the smoothing operation. On the contrary, VBM method applies the Gaussian smoothing filter to reduce image noise as well as to incorporate spatial support from neighboring voxels. It is difficult to determine an appropriate kernel size for the smoothing filter because larger kernel can reduce more noise, but with the penalty of more smeared image.

According to our experiments, we demonstrate the effectiveness of the proposed method by using the simulation data set containing artificial atrophy around the cerebellum area. Compared to the VBM method, the proposed MVM method can achieve a better sensitivity to subtle and widely-distributed variation of brain structure. When applied to a clinical study of SCA3 disease, the MVM method clearly reveals more significant atrophy in the disease-related areas within the brain volumes of the patient group, than the VBM method does.