Diffusion MRI harmonization via personalized template mapping

Abstract

One fundamental challenge in diffusion magnetic resonance imaging (dMRI) harmonization is to disentangle the contributions of scanner‐related effects from the variable brain anatomy for the observed imaging signals. Conventional harmonization methods rely on establishing an atlas space to resolve anatomical variability and generate a unified inter‐site mapping function. However, this approach is limited in accounting for the misalignment of neuroanatomy that still widely persists even after registration, especially in regions close to cortical boundaries. To overcome this challenge, we propose a personalized framework in this paper to more effectively address the confounding from the misalignment of neuroanatomy in dMRI harmonization. Instead of using a common template representing site‐effects for all subjects, the main novelty of our method is the adaptive computation of personalized templates for both source and target scanning sites to estimate the inter‐site mapping function. We integrate our method with the rotation invariant spherical harmonics (RISH) features to achieve the harmonization of dMRI signals between sites. In our experiments, the proposed approach is applied to harmonize the dMRI data acquired from two scanning platforms: Siemens Prisma and GE MR750 from the Adolescent Brain Cognitive Development dataset and compared with a state‐of‐the‐art method based on RISH features. Our results indicate that the proposed harmonization framework achieves superior performance not only in reducing inter‐site variations due to scanner differences but also in preserving sex‐related biological variability in original cohorts. Moreover, we assess the impact of harmonization on the estimation of fiber orientation distributions and show the robustness of the personalized harmonization procedure in preserving the fiber orientation of original dMRI signals.

We proposed a personalized framework to effectively address the confounding caused by the misalignment of neuroanatomy in dMRI harmonization. This approach is applied to harmonize the dMRI data from the Adolescent Brain Cognitive Development study. We demonstrated that our method achieved superior performance in reducing inter‐site variations and preserving sex‐related biological variability.

1. INTRODUCTION

Diffusion magnetic resonance imaging (dMRI) (Basser et al., 1994) allows the probing of brain microstructure in vivo and plays a key role in brain mapping research. With the widespread use of large‐scale dMRI data from various studies (Casey et al., 2018; Mueller et al., 2005; Van Essen et al., 2013), the harmonization of dMRI data across acquisition protocols, sites, and vendors is a critical yet challenging problem (Magnotta et al., 2012; Vollmar et al., 2010; Zhu et al., 2011). One fundamental difficulty in dMRI harmonization is disentangling scanner‐related effects from anatomical variations on the local appearance of imaging signals. To this end, we propose a novel personalized framework that better resolves the impact of anatomical variability on the estimation of inter‐site mapping and advances the state‐of‐the‐art in dMRI harmonization.

With the goal of limiting the impact of anatomical variability on the estimation of scanner effects, prevailing dMRI harmonization approaches rely on the co‐registration of dMRI data across sites into a common atlas space. Then, spatial/regional mapping for dMRI harmonization can be estimated as the confounding of anatomy is expected to be removed. Following this registration‐based framework, several statistical normalization approaches including Removal of Artificial Voxel Effect by Linear regression (Fortin et al., 2016), Surrogate Variable Analysis (Leek & Storey, 2007), and ComBat (Johnson et al., 2007) were examined in (Fortin et al., 2017) for the harmonization of diffusion tensor imaging (DTI) features. The ComBat method has been shown to be highly effective for multi‐site DTI data pooling. For the direct harmonization of dMRI signals, the rotation invariant spherical harmonics (RISH) feature‐based method was proposed (Mirzaalian et al., 2015) and embedded in a registration framework to achieve voxel‐wise harmonization in a template space (Cetin Karayumak et al., 2019; Mirzaalian et al., 2018). Similarly, a method of moments was proposed (Huynh et al., 2019) to achieve the harmonization of dMRI signals after registration to an atlas space by comparing the spherical moments of dMRI signals across sites to estimate a linear mapping function.

Despite the essential role of co‐registration in previous harmonization methods, little work has been done to examine its reliability in building anatomical correspondences across subjects in dMRI harmonization. In fact, the inter‐subject variability in neuroanatomy and hence the possible lack of one‐to‐one correspondences across subjects will inevitably complicate the construction of anatomical correspondences essential for the validity of existing harmonization models. This difficulty will be especially evident in regions surrounding the cortical boundaries, where the high variability across subjects has been well‐known (Thompson et al., 1996; Uylings et al., 2005). As illustrated in Figure 1a, there are obvious anatomical differences between the two Adolescent Brain Cognitive Development (ABCD) (Casey et al., 2018) subjects even after they have been co‐registered to the template image in Figure 1b. Because harmonization algorithms rely on pooling data across subjects from different sites at locations with corresponding anatomy, this type of mismatch, shown in Figure 1, would make the estimation of the inter‐site mapping function much less reliable and lead to invalid harmonization of the dMRI data at affected locations.

FIGURE 1.

Inter‐subject anatomical variability and the resulting mismatch between individual subjects and the sample mean template. (a) Fractional anisotropy (FA) images of two Adolescent Brain Cognitive Development (ABCD) subjects co‐registered to the template space. Top: NDARINV15MFU6UZ acquired from a GE MR750 scanner; bottom: NDARINV1NW3HM13 scanned on a Siemens Prisma scanner. (b) A template image constructed from the FA images of 100 ABCD subjects. Left column: axial slices of the two ABCD subjects and the template. For each axial slice, zoomed views of the regions of interest (ROIs) highlighted by yellow and blue boxes are shown in the middle and right columns, respectively, where the variations of the brain anatomy are noticeable.

To overcome this fundamental problem in establishing anatomically consistent correspondences for the estimation of inter‐site mapping functions, we develop a personalized template estimation framework in this paper to abridge the anatomical gaps between population‐based templates and individual subjects to be harmonized. We also integrate this personalized analysis framework with RISH features (Cetin Karayumak et al., 2019; Mirzaalian et al., 2018) to achieve voxel‐wise harmonization of dMRI signals across scanners. Figure 2a shows the overall harmonization framework. To integrate the feature representations of reference subjects from both source and target scanning sites for each query subject, we introduce a personalized pooling tensor for each site. As illustrated in Figure 2b, the pooling tensor of a site consists of weight vectors computed via solving a convex optimization problem at each voxel based on the similarity of the local anatomy between the query subject and the reference subjects, which are representative of a site. Once the pooling tensors are estimated, site‐specific templates will be estimated in a personalized manner for computing the inter‐site mapping function for each feature representation. By combining the transferred feature representations, we achieve personalized harmonization of the dMRI data from the source to the target site for the query subject.

FIGURE 2.

An overview of our personalized diffusion magnetic resonance imaging (dMRI) harmonization method. (a) The overall framework for the estimation of personalized templates and inter‐site mapping functions to achieve the harmonization from the source to the target site. (b) Details about the estimation of the personalized pooling tensors (${\mathcal{W}}_{\mathrm{src}}$ and ${\mathcal{W}}_{\mathrm{tar}}$) by computing a weight vector $w$ at each voxel as the solution of a convex optimization problem based on local similarity of the anatomy between the query subject and reference subjects of each site.

The rest of this paper is organized as follows. Section 2 introduces the personalized dMRI harmonization framework and related numerical algorithms. Experimental results are presented in Section 3 to demonstrate that the proposed personalized method is able to achieve much‐improved performance in comparison with the state‐of‐the‐art method based on RISH feature mapping. Finally, discussions and conclusions are made in Section 4.

2. METHODS

2.1. Diffusion MRI harmonization in a common space

Given dMRI data from a source and target site, the goal of the harmonization task is to estimate a mapping function: $\widehat{S}=\mathrm{\Psi }\left(S\right)$ for each subject in the source site, where $S$ denotes the diffusion signal of a subject from the source site and $\mathrm{\Psi }$ denotes the inter‐site mapping function to the target site. For the estimation of the inter‐site mapping function, sets of reference subjects from the source and target sites are typically needed to represent the scanner‐dependent variations. In addition, it is important to consider the anatomical variations across subjects and the spatial heterogeneity of scanner differences.

To this end, nonlinear image registration has played a key role in minimizing the impact of anatomical differences across subjects and allowing the pooling of information from representative reference subjects for the characterization of site‐effects. Within a common space constructed through nonlinear registration of the anatomical images of subjects from both sites, the harmonization mapping function $\mathrm{\Psi }$ can be determined by comparing the rotation invariant diffusion features, such as RISH features (Cetin Karayumak et al., 2019) and diffusion moments (Huynh et al., 2019), across sites. For each feature, a population‐based template $\mathbf{E}$ is first constructed for both the source and target sites by evenly pooling the co‐registered feature images of the reference subjects from each site:

$$\mathbf{E}=\frac{1}{N}\sum _{i=1}^N{\mathbf{R}}^i,$$ (1)

where ${\mathbf{R}}^i$ is the diffusion feature image of the i‐th reference subject from a given site. Using the population‐based feature templates from both the source and target site, the harmonization mapping function $\mathrm{\Psi }$ can be estimated at each location in the common space, which can then be applied to all source subjects for their harmonization to the target site (Cetin Karayumak et al., 2019; Huynh et al., 2019).

2.2. Personalized template estimation

While the common space from nonlinear registration can greatly reduce inter‐subject variations, significant anatomical differences remain, especially around the cortical areas. For a given query subject from the source site to be harmonized, this type of anatomical misalignment will no doubt introduce significant bias to the estimation of feature templates and consequently affect the harmonization mapping function. To avoid the confounding caused by the anatomical misalignment in harmonization, we develop a personalized approach for template estimation by adaptively integrating the feature representations from the reference subjects of a given site in the common space according to localized anatomical similarity. For a given query subject $\mathcal{Q}$ from the source site, we compute a personalized pooling tensor ${\mathcal{W}}^{\mathcal{Q}}$ for the estimation of a personalized template ${\mathbf{E}}^{\mathcal{Q}}$:

$${\mathbf{E}}^{\mathcal{Q}}=\mathrm{ℛ}\odot {\mathcal{W}}^{\mathcal{Q}},$$ (2)

where $\mathrm{ℛ}=\left[{\mathbf{R}}^1\dots {\mathbf{R}}^N\right]$ denotes the feature images of $N$ reference subjects from a given site. At a location $x$ in the common space, the uneven pooling of references is performed by a weighted sum:

$${\mathbf{E}}^{\mathcal{Q}}\left(x\right)={\mathcal{W}}^{\mathcal{Q}}{\left(x\right)}^T\mathrm{ℛ}\left(x\right),$$ (3)

where ${\mathcal{W}}^{\mathcal{Q}}\left(x\right)={\left[w_1\left(x\right),\dots ,w_N\left(x\right)\right]}^T$ is a weight vector, with $w_i\left(x\right)>0$ for $i=1,\dots ,N$ and ${\sum }_i^N{w}_i\left(x\right)=1$ and $\mathrm{ℛ}\left(x\right)={\left[{\mathbf{R}}^1\left(x\right),\dots ,{\mathbf{R}}^N\left(x\right)\right]}^T$ is the local reference vector containing diffusion features sampled from the reference subjects.

For the calculation of the weight tensor ${\mathcal{W}}^{\mathcal{Q}}$, we compute the reference weight vector ${\mathcal{W}}^{\mathcal{Q}}\left(x\right)$ adaptively at each location $x$ in the common space by solving a convex optimization problem. Let's denote the co‐registered anatomical image of the source query subject in the common space as $U$ and those of the $N$ reference subjects as $\mathcal{V}=\left\{V_1,V_2,\dots ,V_N\right\}$. For numerical implementation, we use fractional anisotropy (FA) image as the anatomical image of each subject in this work. At each point $x$ in the common space, the local anatomical similarity measure between the query subject and a reference subject is denoted as $\mathrm{sim}\left(U\left(x\right),V\left(x\right)\right)$, which we define based on the cross‐correlation of local patches: $\mathrm{sim}\left(U\left(x\right),V\left(x\right)\right)=\left({\sum }_{y_j\in \mathbf{P}}\left(U\left(y_j\right)-{\mu }_U\right)\left(V\left(y_j\right)-{\mu }_V\right)\right)/{\sigma }_U{\sigma }_V$, where $\mathbf{P}$ is a 3D patch of size $3\times 3\times 3$ centered at the voxel $x$ in both $U$ and $V$, ${\mu }_U$ and ${\mu }_V$ are the mean FA value within the patch, and ${\sigma }_U$ and ${\sigma }_V$ are the standard deviations. To ensure that the personalized templates are representative of reference subjects with similar anatomy at each point, we introduce a Laplacian regularizer across reference subjects in the cost function. This regularizer can encourage the reference subjects with highly similar anatomy to be assigned with similar weights. Furthermore, we include a spatial consistency term in the cost function to consider the local spatial dependencies in adjacent locations. The weight vector estimation is then formulated as the following convex optimization problem:

$$\begin{array}{l}\underset{\mathbf{w}}{\max }{\mathbf{p}}^T\mathbf{w}-{\gamma }_1{\mathbf{w}}^T\mathbf{Lw}+{\gamma }_2{\mathbf{q}}^T\mathbf{w}\\ s.t.\mathbf{w}\ge 0,{\mathbf{1}}^T\mathbf{w}=1,\end{array}$$ (4)

where $\mathbf{w}={\mathcal{W}}^{\mathcal{Q}}\left(x\right)$ is the weight vector at $x$ and $\mathbf{p}={\left[\mathrm{sim}\left(U\left(x\right),V_1\left(x\right)\right),\dots ,\mathrm{sim}\left(U\left(x\right),V_N\left(x\right)\right)\right]}^T$ is the query‐to‐reference similarity vector at $x$. In the Laplacian regularization term ${\mathbf{w}}^T\mathbf{Lw}$, $\mathbf{L}=\mathbf{D}-\mathbf{A}$ is a Laplacian matrix, where $\mathbf{A}$ is the inter‐reference similarity matrix with entry $\mathbf{A}\left(i,j\right)=\mathrm{sim}\left(V_i\left(x\right),V_j\left(x\right)\right)$, and $\mathbf{D}$ is the degree matrix. We can trade‐off between the potential mismatch of brain anatomy and the reliability in template estimation by tuning the parameter ${\gamma }_1$. By increasing the parameter ${\gamma }_1$, the weights would be propagated to more reference subjects, which would enlarge the sample size and improve the reliability of the personalized templates. On the other hand, an overly large parameter ${\gamma }_1$ could result in assigning non‐negligible weights to all reference subjects and bring the misregistration problem back to template construction. The third term of the cost function is designed to encourage the spatial consistency of the weight vectors, where the neighborhood similarity vector for the query location $x$ is defined as

$$\mathbf{q}=\frac{{\sum }_{x^{\prime }\in \mathcal{N}\left(x\right)}\mathrm{sim}\left(U\left(x\right),U\left(x^{\prime }\right)\right)\mathbf{p}\left(x^{\prime }\right)}{{\sum }_{x^{\prime }\in \mathcal{N}\left(x\right)}\mathrm{sim}\left(U\left(x\right),U\left(x^{\prime }\right)\right)}.$$ (5)

Here $\mathcal{N}\left(x\right)$ is the neighborhood centered at $x$ and $\mathbf{p}\left(x^{\prime }\right)={\left[\mathrm{sim}\left(U\left(x^{\prime }\right),V_1\left(x^{\prime }\right)\right),\dots ,\mathrm{sim}\left(U\left(x^{\prime }\right),V_N\left(x^{\prime }\right)\right)\right]}^T$ is the query‐to‐reference similarity vector of the neighboring voxel $x^{\prime }\in \mathcal{N}\left(x\right)$. Note that the contributions of spatial neighborhoods are proportional to their anatomical similarity with the query location to accommodate the anatomical inconsistencies that may arise in neighborhood patches located at tissue boundaries. The tuning parameter ${\gamma }_2$ controls the involvement of neighborhood information in the estimation of weight assignment. Overall, this quadratic programming problem is solved by using the embedded conic solver (ECOS) (Diamond & Boyd, 2016; Domahidi et al., 2013).

For dMRI harmonization, personalized templates will be computed for each query subject with respect to the reference subjects from both the source and target site, respectively. This procedure will be performed for all pertinent diffusion image features, which characterize the scanner effects for the source and target sites. Subsequently, the inter‐site mapping function for harmonizing the dMRI signal to the target site can be estimated, as we will describe below.

2.3. Personalized harmonization based on mapping spherical harmonics features

To demonstrate the application of our personalized template estimation for dMRI harmonization, we integrate it with the RISH features from the LinearRISH harmonization method (Cetin Karayumak et al., 2019). To compute the RISH features, the dMRI signals at each voxel are first represented by the spherical harmonics (SPHARM) as $S\simeq {\sum }_{\mathit{lm}}{C}_{\mathit{lm}}{Y}_{\mathit{lm}}$, where $Y_{\mathit{lm}}$ and $C_{\mathit{lm}}$ are the SPHARM basis and corresponding coefficient of order $l$ and degree $m$. The RISH features characterize the energy distribution of the dMRI signal at each order $l$ and are defined as $R_l={\sum }_m{C}_{\mathit{lm}}^2$. In a common space constructed by nonlinear registration, the LinearRISH method computes a template from the source and target site for each RISH feature and calculates a scale factor ${\mathrm{\Phi }}_l$ at each location, which is then applied to scale the SPHARM coefficients at the same order $l$: ${\widehat{C}}_{\mathit{lm}}={\mathrm{\Phi }}_l{C}_{\mathit{lm}}$ to realize the harmonization. Note that the template and scale factors are the same for all subjects from the source site.

For the personalized harmonization of dMRI data from a source site ($\mathrm{src}$) to a target site ($\mathrm{tar}$) in our proposed method, the mapping function ${\mathbf{\Phi }}_l$ is estimated separately for each query subject $\mathcal{Q}$ at each SPHARM order:

$${\mathbf{\Phi }}_l\left(x\right)=\sqrt{\frac{{\mathbf{E}}_l^{\mathrm{tar}}\left(x\right)}{{\mathbf{E}}_l^{\mathrm{src}}\left(x\right)}},$$ (6)

where ${\mathbf{E}}_l^{\mathrm{tar}}$ and ${\mathbf{E}}_l^{\mathrm{src}}$ are the personalized template of the RISH feature at the order $l$ for the target and source sites, respectively. Compared with the conventional LinearRISH method, the main novelty of our method is that the RISH feature templates are estimated by solving (4) and hence emphasize reference subjects with similar anatomy to boost consistency. The mapping image ${\mathbf{\Phi }}_l$ is then warped back to the subject space of the query individual. At each voxel in the query space, the SPHARM coefficient $C_{\mathit{lm}}^{\mathcal{Q}}$ of the dMRI signal is scaled by the mapping function at the order $l$ as ${\widehat{C}}_{\mathit{lm}}^{\mathcal{Q}}={\mathrm{\Phi }}_l{C}_{\mathit{lm}}^{\mathcal{Q}}$. Finally, the harmonized dMRI signal ${\widehat{S}}^{\mathcal{Q}}$ is generated by using the scaled SPHARM coefficients:

$${\widehat{S}}^{\mathcal{Q}}=\sum _{\mathit{lm}}{\widehat{C}}_{\mathit{lm}}^{\mathcal{Q}}{Y}_{\mathit{lm}}.$$ (7)

By repeating this process for all voxels, we obtain the harmonization of the query subject from the source to the target site.

3. EXPERIMENTAL RESULTS

To demonstrate the efficacy of the proposed personalized dMRI harmonization framework, we apply the proposed method to harmonize dMRI data acquired from two scanning systems: Siemens Prisma (SIEMENS) and GE MR750 from the ABCD study (Casey et al., 2018) and compare the performance with the state‐of‐the‐art LinearRISH method (Cetin Karayumak et al., 2019). The results are organized as follows. In Section 3.1, we describe the dMRI dataset and the implementation details of harmonization experiments. An illustration of the weight assignment for personalized template construction in our method and a comparison with the template from LinearRISH are presented in Section 3.3. Next, we discuss the selection of regularization parameters for our method in Section 3.4. In Section 3.5, we present a comprehensive comparison of the proposed harmonization framework with LinearRISH in terms of reducing the inter‐site variation of DTI features. Then, we assess the impact of available reference subjects on the performance of our personalized harmonization framework in Section 3.6. In Section 3.7, we focus on the regional distribution of DTI features in cortical gray matter areas to further demonstrate the effectiveness of our personalized harmonization method in disentangling site‐effects from variable brain anatomy. In Section 3.8, we examine the impact of dMRI harmonization on the estimation of fiber orientation distribution (FOD). Finally, we investigate the preservation of sex‐related biological variability after harmonization and compare the performance of both methods in Section 3.9.

3.1. Dataset and implementation details

3.1.1. Subjects and dMRI data

In our experiments, we used data acquired on two scanning systems: SIEMENS and GE Discovery MR750 (GE) from the ABCD Study (Casey et al., 2018). A total of 200 subjects at baseline were selected from the ABCD study, with balanced sample sizes for each scanner, including 100 subjects scanned on SIEMENS and another 100 subjects on GE, which we denote as the SIEMENS and GE cohort in our experiments, respectively. To control for confounding effects of age and gender, all selected participants are 9 years old and well‐matched for gender, consisting of 50 females and 50 males in each cohort. For both scanners, the ABCD dMRI data used in harmonization experiments were acquired at b = 3000 s/mm² from 60 gradient directions using multiband EPI (Setsompop et al., 2012). All dMRI data have an isotropic spatial resolution of 1.7 mm. The sequence parameters, repetition time (TR), time to echo (TE), and flip angle, are scanner‐specific. See Table 1 for detailed dMRI sequence parameters for the SIEMENS and GE scanners.

TABLE 1.

Diffusion magnetic resonance imaging parameters for the Siemens Prisma (SIEMENS) and GE MR750 (GE) scanner in the Adolescent Brain Cognitive Development study.

Scanner	TR (ms)	TE (ms)	Flip angle (°)
SIEMENS	4100	88	90
GE	4100	81.9	77

Abbreviations: TE, time to echo; TR, repetition time.

Furthermore, all data used in our experiments are part of the ABCD Data Release 4.0 from the National Institute of Mental Health (NIMH) Data Archive and have been preprocessed by the ABCD study. Quality control and preprocessing were performed to minimize the influence of poor image quality and artifacts prior to harmonization (Hagler Jr et al., 2019). For eddy current correction, distortions on the diffusion gradients were estimated using the approach in Zhuang et al. (2006). The echo‐planar imaging distortions were corrected for each acquisition using the reversing gradient method with FSL's TOPUP (Andersson et al., 2003, 2012). The head motion correction and diffusion gradient adjustment were performed following procedures in (Hagler Jr et al., 2009). Additionally, to minimize the impact of noise on the RISH based harmonization (Cetin Karayumak et al., 2019; Mirzaalian et al., 2016), the diffusion‐weighted images were denoised via the over‐complete local PCA‐based method (Manjón et al., 2013).

3.1.2. Implementation details of dMRI harmonization

For both our method and the LinearRISH method for comparison, we calculated five RISH features for SPHARM orders of $l=\left\{\mathrm{0,2,4,6,8}\right\}$ for the harmonization of dMRI signals at each voxel. For the generation of the common space for computing the harmonization mapping function, we applied the template construction tool “antsMultiVariateTemplateConstruction” from Advanced Normalization Tools (Avants et al., 2009) to FA and zeroth order RISH images of all subjects, using cross‐correlation as the similarity metric for nonlinear registration. The generated deformation fields were used to perform inter‐subject alignment of the RISH and DTI features in all harmonization and evaluation experiments. For our method, all subjects from the source or target site (SIEMENS or GE) served as reference subjects for the construction of personalized RISH feature templates and the estimation of mapping functions.

3.2. Local reference selection and personalized template construction

Personalized template construction is achieved by adaptively assigning pooling weights at each voxel according to the anatomical similarities between the query subject and reference subjects from each site. First, we illustrate how the weight assignment was conducted at two typical locations with parameters: ${\gamma }_1=0.1$ and ${\gamma }_2=2.0$. Figure 3a presents a location centered in a white matter region where the anatomical mismatching problem is relatively mild. In this example, both the query subject and reference subjects were from the GE cohort. As can be seen in the top row on the right of Figure 3a, reference patches with high anatomical similarity were assigned high weights and included for template construction. On the other hand, reference patches with low similarity (shown in the bottom row of Figure 3a) were assigned zero weights and excluded from template estimation at the current voxel. Figure 3b shows another example at the boundary of gray and white matter with higher inter‐subject anatomical variability. Here, the query subject was from the GE cohort and the reference subjects were from the SIEMENS cohort. The top row on the right of Figure 3b presents the instances of selected reference patches with non‐zero weights. Compared to the results shown in Figure 3a, it is observable that the pooling weights are more concentrated over well‐aligned references because a more limited number of references share similar anatomy to the query subject at the highlighted location on the cortical boundary. As shown in the bottom row on the right of Figure 3b, noticeable dissimilarities exist between the query and reference patches. With zero weights assigned to those references, our method effectively alleviates the confounding due to the misalignment of brain anatomy in template construction.

FIGURE 3.

An illustration of selected and discarded references at two representative locations. In each subfigure (a) and (b), the results are organized as follows. Left: the transverse slice of the fractional anisotropy image indicating the location of the query patch in the common space (highlighted in red); middle: a zoomed view of the query patch (in red box); right (top row): top‐4 reference patches ordered by their pooling weights; right (bottom row): discarded reference patches with zero weights. The assigned weights and the query‐reference anatomical similarity are displayed above each reference patch in the form of “weight (anatomical similarity).”

By performing the personalized weight assignment at each voxel for reference subjects from the source or target site, personalized templates can be generated for a given query subject to characterize site‐effects in dMRI signals. Figure 4 displays the zeroth‐order RISH feature of a query subject (Subject ID: NDARINV15MFU6UZ) and the corresponding templates estimated by the LinearRISH method based on the sample mean and the proposed personalized method. In contrast to the conventional templates from LinearRISH (first row on the right) for both the GE and SIEMENS cohort, we can see the personalized templates from our method (second row on the right) capture much more cortical folding details (circled by red dashed lines) that align very well with the query subject.

FIGURE 4.

A comparison of site‐specific templates estimated by the LinearRISH method based on sample mean and our personalized method for the zeroth‐order RISH feature. Left: a transverse slice of the zeroth‐order rotation invariant spherical harmonics (RISH) feature of a query subject (GE Subject ID: NDARINV15MFU6UZ). Right (top row): the corresponding slice of templates estimated from the GE MR750 (GE) and Siemens Prisma (SIEMENS) cohort by the LinearRISH method. Right (bottom row): the corresponding slice of the templates estimated from the GE and SIEMENS cohort by our personalized method.

3.3. Regularization parameters

3.3.1. Across‐reference regularization

In the proposed personalized harmonization framework, the number of selected references primarily depends on the underlying query‐to‐reference anatomical similarity at each voxel and the choice of ${\gamma }_1$. We investigated the spatial distribution of the average number of selected references per query subject with varying ${\gamma }_1$ while keeping ${\gamma }_2=2.0$. Because anatomical similarity across subjects varies in different brain regions, the average number of references used for personalized template estimation differs spatially. For two harmonization experiments: GE toward SIEMENS and SIEMENS toward GE, the spatial distribution of reference number for the estimation of site‐specific templates are plotted in Figure 5 under different parameter choices of ${\gamma }_1$. From the results, we can observe that white matter areas consistently have a higher reference number than cortical gray matter regions. This suggests that gray matter regions with higher inter‐subject variability tend to have fewer qualified references. Furthermore, an increase of ${\gamma }_1$ enlarges the size of the reference set. By tuning ${\gamma }_1$, we trade‐off between the potential mismatch to references and the reliability achieved through the availability of a sufficient number of references to represent site‐specific characteristics at each location. Upon examining the distribution of reference numbers with ${\gamma }_1=0.1$, the number of references typically exceeds 20 in white matter regions, which is more than sufficient for a reliable representation of population characteristics in harmonization (Cetin Karayumak et al., 2019). For gray matter regions with more severe misalignment in brain anatomy, there are still on average at least 10–15 references available for template construction. Based on these observations, we set ${\gamma }_1=0.1$ for the rest of our experiments.

FIGURE 5.

The spatial distribution of reference numbers in personalized and site‐specific template construction with different choices of the regularization parameter ${\gamma }_1$. (a) Query subjects from the GE MR750 (GE) cohort and Reference subjects from the Siemens Prisma (SIEMENS) cohort. (b) Query subjects from the SIEMENS cohort and reference subjects from the GE cohort.

3.3.2. Spatial smoothness regularization

We further examined the effect of the regularization parameter ${\gamma }_2$ on the spatial consistency of reference selection. For each query subject $\mathcal{Q}$, the 4D personalized pooling tensor ${\mathcal{W}}^{\mathcal{Q}}$ is composed of multiple 3D weight images $W_i^{\mathcal{Q}}$: ${\mathcal{W}}^{\mathcal{Q}}=\left[W_1^{\mathcal{Q}},\dots ,W_N^{\mathcal{Q}}\right]$, where $N$ is the size of the reference set from a site. For each weight image, we used the magnitude of its Laplacian to quantify the smoothness of weight assignment (Xue et al., 2014). Overall, the spatial smoothness of reference selection for a query subject is computed as follows:

$${\eta }^{\mathcal{Q}}=\sum _i^N\sum _{j\in \mathrm{\Omega }}\mid \mathrm{\Delta }{W}^{\mathcal{Q}}\left(j\right)\mid ,$$ (8)

where $\mathrm{\Delta }{W}^{\mathcal{Q}}=\left({\partial }^2{W}^{\mathcal{Q}}/\partial x^2\right)+\left({\partial }^2{W}^{\mathcal{Q}}/\partial y^2\right)+\left({\partial }^2{W}^{\mathcal{Q}}/\partial z^2\right)$ is the Laplacian of a 3D weight image and $\mathrm{\Omega }$ denotes the location set of the whole brain region in the common space. In Figure 6, we demonstrate the relationship between the parameter ${\gamma }_2$ and the overall smoothness of weight assignment in situations where query and reference subjects are from different sites while maintaining ${\gamma }_1=0.1$. It can be observed that increasing ${\gamma }_2$ leads to a noticeable improvement in the spatial smoothness of weight assignment. After ${\gamma }_2$ reaches $1.0$, its impact on the smoothness reaches a region of relative stability. The turning point is at ${\gamma }_2=2.0$ and larger values of ${\gamma }_2$ result in a tendency toward less spatial consistency. Thus, it is reasonable to choose ${\gamma }_2$ around 2.0. In the following experiments, we set ${\gamma }_2=2.0$ for the regularization of spatial consistency.

FIGURE 6.

Spatial consistency regularization by changing the parameter ${\gamma }_2$. For query subjects from the GE MR750 (GE) cohort and reference subjects from the Siemens Prisma (SIEMENS) cohort, the mean values of the weight smoothness measure across all query subjects with respect to varying ${\gamma }_2$ are plotted in red. Similarly, the green curve shows the results under an alternative setting (query subjects from the SIEMENS and reference set from the GE cohort).

3.4. Inter‐site variation and harmonization

To quantitatively evaluate the performance of harmonization methods, we calculated the inter‐site coefficients of variation (CoVs) for diffusion features, including FA and mean diffusivity (MD), before and after harmonization. The coefficient of variation, defined as the ratio of the standard deviation to the mean of a feature, quantifies the dispersion of a distribution. The inter‐site CoVs, reflecting the discrepancy of integrated datasets, are expected to be reduced after harmonization. For a qualitative evaluation, Figure 7 presents the voxel‐wise CoVs of merged dMRI data in the template space for the following combinations: (1) original SIEMENS and GE data (SIEMENS + GE), (2) original SIEMENS and harmonized GE data using SIEMENS as the target site (SIEMENS + harmonized GE), and (3) original GE and harmonized SIEMENS data using GE as the target site (GE + harmonized SIEMENS).

FIGURE 7.

Inter‐site coefficients of variation (CoVs) of fractional anisotropy (FA) and mean diffusivity (MD) before and after harmonization. The results for original datasets before harmonization, Siemens Prisma (SIEMENS) + harmonized GE MR750 (GE), and GE + harmonized SIEMENS are shown in the left, middle, and right panel. In the second and third panel, the results of LinearRISH, our method, and the improvement rate (${\mathrm{IR}}_{\mathrm{CoV}}$) are displayed from left to right, respectively.

To clearly demonstrate the improvement achieved by our proposed method, we calculated the local improvement rate (${\mathrm{IR}}_{\mathrm{CoV}}$) defined as follows:

$${\mathrm{IR}}_{\mathrm{CoV}}=\frac{{\mathrm{CoV}}_{\mathrm{org}}-{\mathrm{CoV}}_{\mathrm{a}}}{\max \left({\mathrm{CoV}}_{\mathrm{org}}-{\mathrm{CoV}}_{\mathrm{b}},\epsilon \right)},$$ (9)

where ${\mathrm{CoV}}_{\mathrm{org}}$, ${\mathrm{CoV}}_{\mathrm{b}}$, and ${\mathrm{CoV}}_{\mathrm{a}}$ were the CoVs before harmonization, after harmonization using the baseline method (LinearRISH), and using the proposed method. To ensure a positive denominator, $\epsilon$ was set to be 0.001. A value of ${\mathrm{IR}}_{\mathrm{CoV}}>1$ indicates superior performance by our method in reducing the CoV of the integrated data from the GE and SIEMENS cohort. The voxel‐wise ${\mathrm{IR}}_{\mathrm{CoV}}$ images for FA and MD are shown in the fourth and last column in Figure 7 for two harmonization tasks: harmonizing GE data to SIEMENS (SIEMENS + harmonized GE) and harmonizing SIEMENS data to GE (GE + harmonized SIEMENS). We can clearly see that our method achieved better performance than LinearRISH in most brain regions, especially in areas close to cortical gray matter. In other white matter regions, the two methods achieve comparable performance in both harmonization tasks.

Besides, we calculated the average CoV and the negative rate ($r_{\mathrm{N}}$) of CoV after harmonization across the whole brain, white matter, and cortical gray matter regions to quantify the overall performance of the two harmonization methods. The negative rate ($r_{\mathrm{N}}$) of CoV is defined as the ratio of the number of voxels with increasing or equal CoV after harmonization to the total number of voxels in the common space. It represents the failure rate in terms of reducing the inter‐site variability. Table 2 summarizes the quantitative results for both harmonization tasks: SIEMENS + harmonized GE and GE + harmonized SIEMENS using the proposed method and LinearRISH. A paired t‐test was used to compare the performance of harmonization using different methods for each DTI feature. The tests reveal that all improvements are statistical significant with $p<{10}^{-15}$. This further demonstrates the much improved performance by our personalized harmonization framework in reducing the inter‐site variation and the negative rate ($r_{\mathrm{N}}$) for both the FA and MD features.

TABLE 2.

Inter‐site coefficients of variation and negative rates ($r_{\mathrm{N}}$) after harmonization for fractional anisotropy (FA) and mean diffusivity (MD).

ROI	Dataset	FA CoV ($r_{\mathrm{N}}$)	MD CoV ($r_{\mathrm{N}}$)
WB a	SIEMENS + GE	0.404 ± 0.160 (−)	0.090 ± 0.052 (−)
	SIEMENS + GE (LinearRISH)	0.361 ± 0.132 (9.83%)	0.087 ± 0.047 (15.47%)
	SIEMENS + GE (our method)	0.332 ± 0.121 (2.27%)	0.080 ± 0.043 (3.14%)
	GE + SIEMENS (LinearRISH)	0.409 ± 0.172 (30.04%)	0.096 ± 0.064 (65.71%)
	GE + SIEMENS (our method)	0.367 ± 0.150 (11.58%)	0.088 ± 0.055 (15.56%)
GM	SIEMENS + GE	0.483 ± 0.109 (−)	0.097 ± 0.044 (−)
	SIEMENS + GE (LinearRISH)	0.435 ± 0.087 (12.02%)	0.093 ± 0.040 (11.11%)
	SIEMENS + GE (our method)	0.396 ± 0.082 (2.00%)	0.085 ± 0.037 (0.96%)
	GE + SIEMENS (LinearRISH)	0.486 ± 0.128 (31.75%)	0.104 ± 0.057 (71.70%)
	GE + SIEMENS (our method)	0.433 ± 0.112 (10.10%)	0.094 ± 0.048 (16.37%)
WM	SIEMENS + GE	0.303 ± 0.124 (−)	0.064 ± 0.026 (−)
	SIEMENS + GE (LinearRISH)	0.283 ± 0.120 (5.24%)	0.065 ± 0.030 (26.25%)
	SIEMENS + GE (our method)	0.267 ± 0.109 (0.84%)	0.060 ± 0.026 (7.58%)
	GE + SIEMENS (LinearRISH)	0.284 ± 0.122 (6.16%)	0.064 ± 0.027 (58.52%)
	GE + SIEMENS (our method)	0.274 ± 0.114 (3.46%)	0.061 ± 0.026 (11.41%)

Note: The bold values are just used to highlight our results that are different from other methods.

Abbreviations: CoV, coefficients of variation; GE, GE MR750; SIEMENS, Siemens Prisma.

^a WB, WM, and GM denote the whole brain, white matter, and cortical gray matter, respectively.

3.5. Number of available references

When constructing personalized templates in our method, having an adequate number of reference subjects from each site is beneficial to cover the variability of neuroanatomy, especially in regions where the anatomical structures are not shared by the majority of the population. In this experiment, we assessed the impact of the number of available references on harmonization performance. The same parameter settings were used with ${\gamma }_1=0.1$ and ${\gamma }_2=2.0$. For both the GE and SIEMENS scanners, we randomly selected subsets, varying in size from 20 to 100, of the GE and SIEMENS cohorts as references for personalized template construction. For both the GE and SIEMENS scanners, the same number of references was used in all experiments. Figure 8 shows that the inter‐site CoVs (in red) and the negative rates ($r_{\mathrm{N}}$) of CoV (in blue) for both FA and MD decrease as the size of the reference set increases for both harmonization tasks. This indicates that sufficient references (≥60) are crucial for adaptive template construction and the success of dMRI harmonization.

FIGURE 8.

Inter‐site coefficients of variation (CoVs) for fractional anisotropy (FA) and mean diffusivity (MD) with varying numbers of available references. (a) and (b) Display the inter‐site CoVs (in red line) and the negative rates of CoV (in blue line) of FA and MD with Siemens Prisma (SIEMENS) + harmonized GE MR750 (GE) data. (c) and (d) show the corresponding results for GE + harmonized SIEMENS data. The inter‐site CoVs and the negative rates of CoV for the results produced by LinearRISH with 100 references from each platform are in red dashed‐line and blue dashed‐line, respectively, in each panel.

3.6. Impact of personalized harmonization on DTI feature distribution in cortical gray matter regions

In Section 3.5, we presented the overall performance enhancement achieved by our method and qualitatively visualized the major improvement in cortical gray matter regions. To further assess the performance of harmonization, we analyzed the distribution of DTI features in cortical lobes before and after harmonization. As we noticed that the task of harmonizing GE toward SIEMENS data achieved lower inter‐site CoVs in Section 3.5, we focused on DTI features computed from harmonized GE data toward SIEMENS by our method and LinearRISH. As shown in Figure 9, four histograms of the FA feature (SIEMENS, GE, harmonized GE by our method, harmonized GE by LinearRISH) within the gray matter voxels of each cortical lobe (frontal, parietal, temporal, and occipital) of the left hemisphere are plotted. The cortical lobes were defined by merging parcellated ROIs from FreeSurfer (Fischl, 2012). By comparing the respective FA feature distribution curves in Figure 9, we observe that both our method and LinearRISH can reduce the noticeable discrepancies between the original GE (blue curves) and SIEMENS (red curves) data before harmonization. However, it is evident that our method achieves better performance as the FA histograms of harmonized data using our method (purple curves) align more closely with the target histograms (red) than those produced by LinearRISH (cyan curves).

FIGURE 9.

Fractional anisotropy (FA) distributions before and after harmonization. The density curves of FA within the frontal, occipital, parietal, and temporal lobes of the left hemisphere are shown in (a), (b), (c), and (d), respectively. GE, GE MR750; SIEMENS, Siemens Prisma.

We can quantify the difference of feature distributions across scanners using the Jensen–Shannon divergence (JSD) (Lin, 1991):

$$\mathrm{JSD}\left(P\parallel Q\right)=\frac{1}{2}\mathrm{KLD}\left(P\parallel M\right)+\frac{1}{2}\mathrm{KLD}\left(Q\parallel M\right),$$ (10)

where $\mathit{JSD}\left(P\parallel Q\right)$ is the JSD of distributions $P$ and $Q$, the average distribution $M=\left(1/2\right)\left(P+Q\right)$, and $\mathrm{KLD}\left(\cdot \parallel \cdot \right)$ indicates the Kullback–Leibler divergence. The JSD is a symmetric measure for comparing two distributions. A lower JSD value indicates a higher resemblance between the two distributions. To quantify the harmonization performance from the perspective of feature distributions, we computed the JSD of FA and MD distributions across scanners for all four major cortical lobes. The results were summarized in Tables 3 and 4 for FA and MD features. We note that our method achieves lower JSD values for both FA and MD features in nearly all cortical regions as compared to results from the LinearRISH method. This reaffirms the efficacy of our method in improving the performance of dMRI harmonization.

TABLE 3.

Jensen–Shannon divergence of fractional anisotropy features across scanners before (Orig) and after harmonization (LinearRISH and our method). Results from both the left and right hemispheres are listed.

Lobe	Hemi	Orig	LinearRISH	Our method
Frontal	Left	0.048	0.011	0.007
	Right	0.050	0.011	0.006
Parietal	Left	0.062	0.014	0.008
	Right	0.056	0.012	0.007
Temporal	Left	0.034	0.009	0.003
	Right	0.033	0.010	0.004
Occipital	Left	0.037	0.008	0.004
	Right	0.031	0.006	0.002

Note: The bold values are just used to highlight our results that are different from other methods.

TABLE 4.

Jensen–Shannon divergence of mean diffusivity features across scanners before (Orig) and after harmonization (LinearRISH and our method). Results from both the left and right hemispheres are listed.

Lobe	Hemi	Orig	LinearRISH	Our method
Frontal	Left	0.052	0.053	0.044
	Right	0.046	0.049	0.043
Parietal	Left	0.038	0.039	0.032
	Right	0.029	0.033	0.029
Temporal	Left	0.039	0.037	0.023
	Right	0.039	0.044	0.024
Occipital	Left	0.024	0.014	0.014
	Right	0.011	0.011	0.010

Note: The bold values are just used to highlight our results that are different from other methods.

3.7. Preservation of fiber orientation distribution

To understand the impact of harmonization on the analysis of structural connectivity, we examined the changes in FOD before and after harmonization. First, we estimated the FOD from the original and harmonized dMRI data (Tran & Shi, 2015) and extracted the largest FOD peak at each voxel for quantitative comparison. To measure the impact of harmonization on FODs, we computed the cosine similarity of corresponding FOD peak directions estimated from dMRI signals at each voxel before and after harmonization. The average voxel‐wise cosine similarity across the white matter was calculated for each subject. For the GE and SIEMENS cohort, the mean and the standard deviation of cosine similarity measures from different harmonization experiments are listed in Table 5. As can be observed from the second and the fourth row in Table 5, the proposed method induces minimal changes in the FOD peaks for both cohorts. These results also closely align with those obtained by LinearRISH, shown in the first and the third row, which suggests that both our method and LinearRISH are able to preserve the fiber orientations of the original dMRI.

TABLE 5.

Fiber orientation distribution peaks before and after harmonization. Row 1 and 2: harmonized GE MR750 (GE) toward Siemens Prisma (SIEMENS); row 3 and 4: harmonized SIEMENS toward GE.

Dataset	Cosine similarity
GE (LinearRISH)	0.995 ± 0.001
GE (our method)	0.996 ± 0.001
SIEMENS (LinearRISH)	0.996 ± 0.001
SIEMENS (our method)	0.996 ± 0.001

3.8. Preservation of sex effects on DTI features

Preserving the inter‐subject biological variability in original data is essential during the harmonization of data across scanners. To evaluate the impact of harmonization procedures on the preservation of biological variability, we examined sex differences in white matter microstructure properties as such group differences have been found significant and replicable in the baseline cohort of the ABCD study (Lawrence et al., 2023). More specifically, we calculated the effect sizes of sex differences for the GE cohort before and after harmonization toward the SIEMENS cohort. The effect sizes are quantified using Cohen's d (Cohen, 2013):

$$d=\frac{{\mu }_{\mathrm{f}}-{\mu }_{\mathrm{m}}}{s_{\text{pooled}}},$$ (11)

where ${\mu }_f$ and ${\mu }_m$ are the mean feature values for the female and male subjects, respectively. $s_{\text{pooled}}=\sqrt{\left(\left(N_{\mathrm{f}}-1\right){\sigma }_{\mathrm{f}}^2+\left(N_{\mathrm{m}}-1\right){\sigma }_{\mathrm{m}}^2\right)/\left(N_{\mathrm{f}}+N_{\mathrm{m}}-2\right)}$ is the pooled standard deviation, where $N$ and $\sigma$ denote the number of subjects and the standard deviation of a specific gender group.

Considering the sex differences are region‐specific (Gong et al., 2009; Hsu et al., 2008; López‐Vicente et al., 2021), we examined the effect sizes for all major lobes. The ROIs were delineated by merging the subcortical white matter parcellations extracted by FreeSurfer (Fischl, 2012). The mean values of FA in each ROI were computed to reflect the regional white matter maturation. Figure 10 displays the effect sizes of sex differences in FA across brain regions for the GE cohort before and after they were harmonized to the SIEMENS cohort. Compared with LinearRISH, it is evident that our method is more effective in preserving the sex differences after harmonization in most brain regions. It is also notable that the proposed approach is able to preserve effect sizes in all regions with absolute differences ($\mathrm{\Delta }d$) of effect sizes before and after harmonization no greater than 0.035.

FIGURE 10.

Preservation of sex differences during harmonization. The effect sizes of sex differences in fractional anisotropy (FA) before (blue), after harmonization using LinearRISH (orange), and our method (green) for the GE MR750 (GE) cohort. The quantitative values of effect sizes ($d$) and the absolute differences ($\mathrm{\Delta }d$) between the effect sizes before and after harmonization are annotated in the form of “$d\left(\mathrm{\Delta }d\right)$.”

3.9. Computation cost

We implemented the personalized harmonization framework using Python on a workstation configured with AMD Ryzen Threadripper 3960X CPUs and 256 GB RAM. The estimation of personalized template with 100 reference images took an average of 2407 s (±98 s). The entire personalized harmonization process took approximately 4930 ± 134 s, showcasing a reasonable execution time for handling dMRI harmonization.

4. DISCUSSIONS AND CONCLUSIONS

In this paper, we introduced the personalized idea to dMRI harmonization and comprehensively examined the importance of establishing reliable anatomical correspondences for dMRI harmonization. To mitigate the confounding effects due to the entanglement of inter‐subject anatomical variability and site‐specific variations in dMRI signals, we presented a personalized template estimation framework and integrated it with RISH features to realize the personalized harmonization of dMRI data. By applying the proposed framework to harmonize dMRI data acquired from Siemens Prisma and GE MR750 scanners in the ABCD study, we demonstrated that our method achieved much improved performance in reducing scanner differences in dMRI signals and preserving sex‐related biological variability in original cohorts.

Although the personalized harmonization framework presented in this work employs RISH features for inter‐site mapping estimation, the proposed personalized template estimation method is general and can be integrated with other dMRI harmonization techniques for the refinement of anatomical correspondences in different harmonization scenarios. For instance, when there are large variations in the number of gradient directions between the source and target site, the moment‐based method (Huynh et al., 2019) might be preferable as it is independent of the matching of spherical harmonic coefficients. Investigating the effectiveness of embedding the proposed approach in other dMRI harmonization frameworks such as the moment‐based method is a direction of our future work.

By leveraging geometric information, surface‐based registration methods can facilitate the alignment of cortical folding patterns and improve the quality of volumetric registration (Ahmad et al., 2019). However, due to inter‐subject topographic variations of cortical folding, the geometric correspondences achieved by surface‐based registration cannot ensure the validity of the corresponding anatomy (Wu et al., 2019; Zhang & Shi, 2021, 2023). For example, sulcal and gyral regions could be mismatched across subjects after registration (Zhang & Shi, 2023). From the perspective of harmonization, this anatomical misalignment problem can bias site‐effect estimation and in turn skew the harmonization mapping process. To this end, we proposed a personalized template estimation framework to overcome this fundamental problem via adaptive integration of feature representation of reference subjects to disentangle scanner‐related effects from variable brain anatomy. In this work, we examined and demonstrated its impact on the dMRI harmonization of multi‐site data from the ABCD study.

In this paper, we examined the effectiveness of the personalized harmonization framework using the single‐shell data acquired at b = 3000 s/mm² from the ABCD study. Data from this shell were acquired from 60 gradient directions and thus provides the sufficient angular resolution for the reliable calculation of high order RISH features based on SPHARM. On the other hand, ABCD data acquired on b = 500, b = 1000, and b = 2000 s/mm² shells only contain limited gradient directions (≤15) and are insufficient for the accurate calculation of RISH features. Non‐Gaussian behavior of data acquired at high b‐values can potentially lead to inaccuracies in the estimation of features such as FA and MD (Hui et al., 2010; Jones & Basser, 2004). Many previous studies, however, showed that DTI features derived from high b‐values were still highly sensitive to pathological changes in white matter and gray matter (Dudink et al., 2008; Mayzel‐Oreg et al., 2007; Seo et al., 2008; Tachibana et al., 2013). High b‐value DTI features were also reported to be closely associated with neurite orientation dispersion and density imaging (NODDI) based neurite density index features (Fukutomi et al., 2019). Thus, DTI features from high b‐value data as used in our experiments, though not comparable with their low b‐value counterparts, can still effectively characterize dMRI data and valuable for demonstrating inter‐site discrepancies for the validation of our harmonization method.

The ${\gamma }_1$ parameter controls the scope of reference for estimating a personalized template. The choice of ${\gamma }_1$ is primarily determined by examining the number of selected references in brain regions with high variability. In our experiment of harmonizing multi‐site dMRI data from the ABCD study, we observed that, given ${\gamma }_2=2.0$, setting ${\gamma }_1=0.1$ ensures a minimum of 10 references across brain regions for the reliable estimation of personalized templates. This parameter setting is typically recommended for the personalized template construction when a substantial number of reference subjects (≥60) is available.

The ventricle regions are filled with cerebrospinal fluid (CSF). Owing to potential temporal drift and variations across different gradient directions, dMRI signals in the CSF are prone to high variation (Hansen et al., 2019), which consequently leads to high CoVs of the DTI features such as MD in ventricles. The isotropic diffusion characteristic of CSF tends to let noise predominate in the estimation of SPHARM coefficients of dMRI signal, which undermines RISH feature estimation in each subject. In addition, the high variation of dMRI signals in CSF further compromises the reliability of RISH templates at the population level. Eventually, these fluctuations impact the estimation of harmonization mapping functions and undermine the performance of dMRI harmonization in the ventricles as reflected by the large CoVs of MD feature even after harmonization in Figure 7.

For the voxel‐wise comparison of harmonization performances, we followed previous approaches (Huynh et al., 2019) to calculate CoVs in the template space and compare the performance of our method and LinearRISH. We acknowledge that the misalignment problem can contribute to the estimation of inter‐site CoVs in the template space. However, it is important to note that such misalignment issues have nearly common effects on the estimation of CoVs both before and after harmonization. As our primary focus is on the reduction of CoV rather than its absolute magnitude when examining harmonization performance, the CoVs due to anatomical misalignment would not compromise the fidelity of comparison results reported in Figure 7 and Table 2. To further eliminate the impact of misalignment on the evaluation of harmonization performance, we also analyzed the distribution of DTI features within cortical lobes, employing subject space parcellation via FreeSurfer in Section 3.7. The observations presented in this section reaffirm the findings in Section 3.5, that the personalized harmonization framework enhances harmonization performance, particularly in cortical regions.

The JSD values presented in Tables 3 and 4 are scalar measures, which indicate the resemblance of regional DTI feature distributions between two sites. In evaluating harmonization performances, even a minor numerical improvement in JSD can be non‐trivial. As shown in Table 3, both our method and LinearRISH notably reduced the JSD of FA distributions in all regions. From Figure 9a, we can see that even a minor improvement in JSD, such as from 0.011 to 0.007 in the first row of Table 3, can reflect substantial differences in feature distributions. It is also important to note that reductions in JSD are an anticipated outcome of harmonization. For the MD results in Table 4, we note that our method consistently reduces JSD in all brain regions. On the other hand, it is crucial to note that LinearRISH incorrectly enlarges the JSD values of MD even after harmonization for many cortical regions.

In Section 3.9, we examined whether harmonization procedures can properly preserve sex differences in the original data. The results in Figure 10 demonstrate that both LinearRISH and our method can preserve the sex differences because the numerical changes of the Cohen's d before and after harmonization are well below the typical threshold of Cohen's d used for small effect size (0.2). This suggests harmonization based on RISH features can properly preserve the biological variability, which aligns with previous observations reported in (Cetin Karayumak et al., 2019).

Besides the conventional frameworks (Fortin et al., 2017; Huynh et al., 2019; Mirzaalian et al., 2016) that explicitly estimate the harmonization mapping function, many learning‐based methods were developed recently. With scans of traveling subjects obtained from multiple sites, the dMRI harmonization problem could be formulated as a paired image‐to‐image translation problem (Cetin Karayumak et al., 2018; Hansen et al., 2022; Koppers et al., 2019; Nath et al., 2019). In addition, several unsupervised harmonization methods that do not require explicitly paired scans were proposed for dMRI harmonization (Moyer et al., 2020; St‐Jean et al., 2020). While in principle, sophisticated inter‐site transformation, learned with deep neural architectures, is beneficial for dMRI harmonization, the inter‐subject variability and misalignment of brain anatomy still have significant impacts on these methods as the heterogeneity in anatomy (e.g., in cortical gray matter regions) can complicate the learning of inter‐site transformation and potentially result in the mismatch of training and testing data, which can hinder the reliability of harmonization (Ning et al., 2020; Tax et al., 2019). For our future work, we are also interested in extending our method by developing learning based harmonization algorithms that take into account the inter‐subject variability of neuroanatomy.

In the current framework, multiple healthy controls, carefully matched for confounding effects, for example, age and gender, from each scanning platform are required to avoid bias from confounding variables in the reliable estimation of harmonization mapping functions. For the harmonization of dMRI data from different cohorts with a limited overlap of related confounding variables such as age, our method can be extended to consider these confounding variables as additive terms in a regression model. Similar to the ComBat method (Fortin et al., 2016), the reference features can be adjusted by regressing out the confounding variables to reveal site‐specific characteristics for harmonization. This possible extension will be another direction for our future work.

CONFLICT OF INTEREST STATEMENT

The authors have no conflict of interest.

Xia, Y. , & Shi, Y. (2024). Diffusion MRI harmonization via personalized template mapping. Human Brain Mapping, 45(5), e26661. 10.1002/hbm.26661

DATA AVAILABILITY STATEMENT

The scripts and code used in this study will be shared publicly upon publication of the article. The data used in this paper are part of the Adolescent Brain Cognitive Development (ABCD) Data Release 4.0 from the NIMH Data Archive (NDA).