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Validating a novel normalization method - 'Pscore' to assess individual deviations using diffusion MRI data from the Human Connectome Project

Rakibul Hafiz¹, M. Okan Irfanoglu¹, Amritha Nayak^1,2,3, and Carlo Pierpaoli¹
¹Quantitative Medical Imaging, NIBIB, NIH, Bethesda, MD, United States, ²Military Traumatic Brain Injury Initiative, Bethesda, MD, United States, ³The Henry Jackson Foundation for the Advancement of Military Medicine, Bethesda, MD, United States

Synopsis

Keywords: Diffusion Analysis & Visualization, Diffusion/other diffusion imaging techniques, Statistical Analysis, Normalization Techniques, Zscore, Pscore, Human Connectome Project

Motivation: Conventional methods like Zscores are often used to evaluate individual patients against a normative distribution. This can lead to biased estimations when distributions are skewed. We showed this in a pilot study using 48 controls and proposed a novel metric - 'Pscore', to address this bias. We aimed to reproduce these results systematically using a larger dataset.

Goal(s): Validate the 'Pscore' approach on a large-scale high resolution neuroimaging dataset.

Approach: Diffusion MRI data from the Human Connectome Project (HCP) was used to test various normalization methods

Results: Pscores demonstrate symmetric distributions and no systematic biases observed in Zscores of all diffusion MRI derived metrics.

Impact: The non-Gaussian nature of neuroimaging data has implications for building normative databases and their use to assess abnormalities in individual subjects. The proposed 'Pscore' approach reliably addresses this, which implies its usefulness for individual assessments even in smaller neuroimaging datasets.

INTRODUCTION

Normative modeling is often used to assess individuals.^1-3 Quantitative MRI metrics hold the potential to assess individual deviations and typically incorporate the Zscore approach. A fundamental assumption for such parametric models is that the data is normally distributed. However, neuroimaging metrics, such as those derived from diffusion MRI (dMRI), often do not conform to Gaussianity, even in large-scale datasets.⁴ Biases are introduced when inferences are made from such skewed distributions.⁵ In ISMRM 2023, we also reported similar skews and biases in Zscores using dMRI data from 48 controls and how the proposed Pscore approach accounts for it.⁶ We showed that when the normative distribution itself is skewed and an individual is assessed against such a distribution, the direction of skew causes an extreme value bias in the corresponding tails. But these findings were from a small sample and normative models are typically built using larger datasets. Therefore, we designed this work based on two important questions – (a) do these inconsistencies in Zscores persist in large-scale datasets? If so, how well does the Pscore approach account for it? We address this by using dMRI data from an effective sample of 960 healthy young adults from the Human Connectome Project (HCP).⁷

METHODS

We used the latest version of our robust TORTOISEV4⁸ pipeline to preprocess the dMRI data. Four diffusion tensor (DT)^{9, 10} and five mean apparent propagator (MAP)¹¹ voxelwise metrics were computed and average values within atlas ROIs¹² generated from the same dataset (see Figure1), were extracted. The method delineating the computation of Pscores is detailed in our pilot work.⁶ The 'Pscore' approach uses the median as the reference and incorporates percentile ranks computed from the normative sample. It normalizes the difference between a subject's position and the median of the distribution with the corresponding difference between the 5^th/95^th percentile edge values. Other normalization techniques like ‘Log’ transformations and standardized ‘Zscores’ were also tested ROIwise. The distributions from the raw data were compared against distributions from these three normalization techniques. Particularly, Zscores and Pscores from the entire sample were taken across all white matter ROIs to evaluate two parameters: (a) the total percentage (%) of positive and negative values around the 0-line, and (b) the percentage (%) of extreme values above and below the 95^th and 5^th percentiles, respectively. The first parameter identifies the skewness in the normative distribution and the second parameter quantifies the bias introduced in extreme values at the left/right tails.

RESULTS AND DISCUSSION

Figure2 shows how the Pscore approach compares against other normalization methods within a representative ROI: left Superior Longitudinal Fasciculus. Pscores (Figure2.(d)) of fractional anisotropy (FA) attain a closer fit to a normal distribution compared to the other methods (Figure2.(b) and (c)). The mean, mode and median of the Pscore distribution nicely align at the 0-line, unlike the 'Log' transform and 'Zscore' distributions. When assessed over all white matter ROIs from the entire sample (Figure 3), Zscores of propagator anisotropy (PA) (Figure 3(e)) demonstrated the highest skew (59% positive vs. 41% negative Zscores) among the metrics shown. Such imbalances in positive and negative Zscores were observed at various levels for all dMRI metrics. Contrarily, the Pscore distributions maintain a balanced 50% positive and negative scores around the 0-line for all dMRI metrics. The skews observed in Zscore distributions introduced extreme value bias in the tails of these distributions. These biases were quantified in Table1, which shows that Zscores from both DT and MAP metrics have an unbalanced percentage of extreme values (P_>95(%) and P_<5(%) ≠ 5%). On the other hand, Pscores from the same metrics maintain 5% extreme values in both tails. Therefore, when comparing individuals to a skewed normative distribution, Pscores provide a more robust and accurate estimation. This can have useful applications in neuroimaging, where normative models use Zscores to assess individual deviations.^{4, 13} Furthermore, our pilot work⁶ showed Pscores robustly account for such biases even in smaller samples (n = 48). Therefore, Pscores can also prove very useful when assessing individual deviations using neuroimaging datasets with more practical sample sizes e.g., 50-100 subjects.

CONCLUSION

We used a large sample of high resolution dMRI data from the HCP⁷ to test the ‘Pscore’ approach and reproduce our previous findings.⁶ We propose the use of this novel metric: ‘Pscore’, to accurately assess individual deviations with respect to a normative distribution, especially, when the normative data have skewed distributions. Even though diffusion MRI was used to showcase the ‘Pscore’ approach, it is not data-selective, and should be reliably applicable to any data from clinical and research paradigms.

Acknowledgements

Data were provided [in part] by the Human Connectome Project, WU-Minn Consortium (Principal Investigators: David Van Essen and Kamil Ugurbil; 1U54MH091657) funded by the 16 NIH Institutes and Centers that support the NIH Blueprint for Neuroscience Research; and by the McDonnell Center for Systems Neuroscience at Washington University.

References

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6. Hafiz R, Nayak A, Irfanoglu MO, Chan L, Pierpaoli C. Using ‘P-scores’: a novel percentile-based normalization method to accurately assess individual deviation in heavily skewed neuroimaging data. 2023 ISMRM & ISMRT Annual Meeting & Exhibition, Toronto, Canada, Program Abstract Number #3781, ISSN# 1545-4428 | Published date: 19 May, 2023.

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Figures

Figure1. Axial montage of regions of interest (ROIs) used in the current study. A 5 x 2 montage was created in the axial plane to show the spatial extent of the ROIs overlayed on the average connectome DT FA template. The slice labels are provided on the top-left of each image in the montage. The “A”, “P”, “I”, “S”, “L” and “R” are the anterior, posterior, inferior, superior, left and right directions, respectively.

Figure2. Comparing raw distribution of average FA values from the left superior longitudinal fasciculus, against distributions from the three normalization techniques tested. The distributions from ‘Raw’, ‘Log’ and ‘Zscore’ panels are asymmetric. Their histograms do not closely fit the normal density curve (dashed purple). The ‘mean’ (dashed green) overestimates the most common values and appears separated from the median (dashed red) and the mode (tallest bar). The ‘Pscore’ panel shows correct alignment of the mean, mode and median and a proper fit to the normal density curve.

Figure3. Zscores vs. Pscores distributions across all ROIs and dMRI metrics. For each metric, two histograms are shown – top, light red: Zscores and bottom, light blue: Pscores. The normal density curves help assess the closeness to a Gaussian fit. Zscore distributions for FA, PA and NG show negative skew (positive > 50% and negative < 50%), whereas Zscores from MD, RD, RTAP, RTOP and RTPP show positive skew (negative > 50% and positive < 50%). However, Pscore distributions are symmetric and consistently maintain 50% negative and positive values on either side for all metrics.

Table1. Extreme value bias assessment between Zscores and Pscores. The table quantifies the number (N_>95, N_<5) and percentage (P_>95(%), P_<5(%)) of extreme values above/below the 95th/5th percentile values (Z = ±1.645), respectively, for the Zscore and Pscore distributions shown in Figure3. N_Total is the total number of values across all ROIs in the entire sample. Zscores from FA, PA and NG show a negative bias (P_<5 > P_>95), whereas, Zscores from MD, RD, RTAP, RTOP and RTPP show a positive bias (P_>95 > P_<5). Contrarily, Pscores maintain 5% extreme values in both tails for the same metrics.

Proc. Intl. Soc. Mag. Reson. Med. 32 (2024)

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DOI: https://doi.org/10.58530/2024/2140