The osteoporosis dataset included 1,011,300 participants from three public summary-statistics resources. The GWAS Catalog contributed 456,348 participants, FinnGen Round 8 contributed 342,499 participants, and the IEU Open GWAS project contributed 212,453 participants. A fixed-effects inverse-variance-weighted meta-analysis was performed in METAL^[19]. Before meta-analysis, variants were harmonized by genomic position, effect allele, non-effect allele, effect estimate, standard error, and, where available, allele frequency. Palindromic variants with unresolved strand orientation or inconsistent allele frequencies were excluded. Participant-level overlap across the contributing cohorts could not be quantified directly from the released summary statistics and is therefore acknowledged as a potential source of residual bias. All three data sources were restricted to European-ancestry samples. Summary statistics for total body bone mineral density, femoral neck bone mineral density, lumbar spine bone mineral density, forearm bone mineral density, and heel bone mineral density were obtained from the Genetic Factors for Osteoporosis consortium.

Summary statistics for the 3,935 UK Biobank imaging-derived phenotypes were obtained from the published resource reported by Smith et al.^[20]. The dataset integrates raw and processed imaging measures, along with related non-imaging variables, released through the UK Biobank imaging pipeline. The present study used publicly available summary statistics from the GWAS Catalog and related public repositories rather than newly accessed individual-level UK Biobank data. Figure 1 summarizes the overall study workflow and is cited here before the primary Mendelian randomization results. Supplementary Table 1 presents the identifier-to-trait mapping and imaging-location characteristics for the 3,935 imaging-derived phenotypes.

Genetic variants were used as instrumental variables to evaluate genetically predicted associations between imaging-derived phenotypes and osteoporosis^[21]. Three core assumptions were considered: relevance, independence from major confounders, and the absence of direct paths from the instrumental variables to the outcome outside the exposure^[22]. All 3,935 imaging-derived phenotypes were screened as exposures against the meta-analyzed osteoporosis dataset. Generalized summary-data-based Mendelian randomization was used as the primary screening method. Two-sample Mendelian randomization with inverse-variance weighting was then applied to the prioritized imaging-derived phenotypes, followed by weighted median, MR-Egger^[23], and Mendelian Randomization Pleiotropy RESidual Sum and Outlier (MR-PRESSO) as sensitivity analyses. Cochran’s Q statistic was used to assess heterogeneity. Reverse Mendelian randomization analyses were subsequently performed with osteoporosis as the exposure and the 16 validated imaging-derived phenotypes as the outcomes. Because several imaging-derived phenotypes required relaxed instrument thresholds and included variants with F statistics below 10, those findings were interpreted as exploratory throughout the manuscript. The extent of sample overlap between UK Biobank-derived imaging GWAS data and the public osteoporosis or bone mineral density datasets could not be quantified directly from the available summary statistics and remains an acknowledged limitation of the MR framework used here.

Linkage disequilibrium score regression was used to estimate genetic correlation from summary statistics. For two traits with nonzero genetic correlation, the product of Z-scores across variants is regressed on linkage-disequilibrium scores to estimate the genetic covariance component.

In linkage disequilibrium score regression, sample overlap is expected to affect the intercept more than the slope, reducing but not eliminating concern about overlap-related bias. This property is specific to linkage disequilibrium score regression and should not be extrapolated to Mendelian randomization analyses^[24]. Therefore, potential overlap between UK Biobank-derived imaging data and osteoporosis or bone mineral density datasets remains a recognized limitation of the Mendelian randomization framework used in this study.

Imaging-derived phenotypes with the strongest genetic correlation with osteoporosis were taken forward for pleiotropy analysis under the composite null hypothesis. Single-nucleotide polymorphisms that met genome-wide significance at P < 5 × 10^-8 were classified as pleiotropic candidates. Functional mapping and GWAS annotation were used to identify pleiotropic loci. Bayesian colocalization^[25] was then applied to distinguish provisional pleiotropic signals from higher-confidence shared causal regions. The pooled genome-wide association results for osteoporosis were annotated using FUMA^[26] with default settings. Within each locus, the nearest gene and the top-ranked Polygenic Priority Score^[27] gene within a 500-kb window were recorded for interpretation. Colocalization support was defined as PP.H4 > 0.75.

Genes prioritized by pleiotropy analysis under the composite null hypothesis and colocalization were evaluated as candidate mediators of the BrainSegVol-to-eTIV association with osteoporosis. Tissue-specific cis-expression quantitative trait loci were obtained from the GTEx v8 resource. For the primary mediation model, whole-blood cis-expression quantitative trait loci were selected a priori because the working biological hypothesis centered on immune regulation relevant to systemic bone remodeling. Independent whole-blood cis-expression quantitative trait loci that met a false discovery rate threshold of 0.05 or lower were used as instruments in the primary mediation analysis. GTEx served here as the source of tissue-specific instrument panels rather than as the basis for a formal genome-wide tissue-enrichment analysis. Steiger filtering was applied as a directionality screen during instrument selection, whereas reverse-direction testing was evaluated separately. Two-step Mendelian randomization was then used to estimate the effect of BrainSegVol-to-eTIV on each mediator, the effect of each mediator on osteoporosis conditional on BrainSegVol-to-eTIV, and the corresponding indirect effect and mediation proportion. The two-step mediation workflow is shown in Supplementary Figure 1. Confidence intervals for the mediated effects were derived with the delta method^[18]. Given the complexity of linkage disequilibrium and pleiotropy in the HLA region, the mediation analysis was interpreted as evidence supporting a putative candidate mediator rather than a confirmed biological mechanism.

Instrument selection began at P < 5 × 10^-8. When fewer than four variants were available for a given imaging-derived phenotype, a secondary threshold of P < 1 × 10^-6 was used as an exploratory instrument-retention strategy. Variants were clumped at r² < 0.001 within a 10,000-kb window. Variants absent from the outcome dataset, variants with unresolved strand ambiguity, and palindromic variants with inconsistent allele information were excluded. The GWAS Catalog was queried to remove variants associated with major confounders, including alcohol dependence, body fat percentage, body mass index, body height, lean body mass, and body weight, as summarized in Supplementary Table 2. Instrument strength was evaluated with F statistics greater than 10.

All analyses were conducted using TwoSampleMR, gsmr2, GenomicSEM, MRPRESSO, plinkbinr, ieugwasr, dplyr, coloc, and base packages in R version 4.4.1. Multiple-testing control was applied in a staged manner across the analytical pipeline. We conducted an initial discovery screen of imaging-derived phenotypes. We retained traits that showed nominal significance, with concordant directions across generalized summary-data-based Mendelian randomization and inverse-variance-weighted analyses. False discovery rate correction^[28] was then applied at the validation stage, and prioritized traits were required to retain support across the osteoporosis and bone mineral density analyses. Pleiotropic loci were defined at the conventional genome-wide significance threshold of P < 5 × 10^-8, and colocalization required PP.H4 > 0.75. For reverse Mendelian randomization, false discovery rate correction was applied across the 16 primary inverse-variance-weighted tests.

Using the meta-analyzed osteoporosis dataset as the outcome, discovery Mendelian randomization screening identified 180 imaging-derived phenotypes with nominal evidence of association. The full GSMR screening results are provided in Supplementary Table 3. Seventy-five imaging-derived phenotypes showed concordant support across generalized summary-data-based Mendelian randomization and inverse-variance-weighted analyses and were retained for validation, as summarized in Supplementary Table 4. After cross-validation against five bone mineral density traits with false discovery rate control, 16 imaging-derived phenotypes remained supported, and the confirmatory MR results across the five bone mineral density traits are presented in Supplementary Table 5. Seven imaging-derived phenotypes showed evidence of genetic correlation with osteoporosis, as summarized in Supplementary Table 6. Detailed PLACO and colocalization results are summarized in Supplementary Table 7. Instrument-strength assessment for the 16 validated imaging-derived phenotypes (IDPs) is summarized in Supplementary Table 8, and SNP-level instrument parameters are provided in Supplementary Table 9. Thirteen of the 16 validated IDPs showed low weak-instrument risk, whereas three traits, specifically GCST90006352, GCST90006346, and GCST90004325, used the relaxed threshold and included at least one SNP with an F statistic below 10. We therefore treated these findings as exploratory in the subsequent interpretation. Figure 2A summarizes the screening workflow, and Figure 2B shows the outcome-specific effect estimates. Seven imaging-derived phenotypes were validated in forearm bone mineral density, seven in femoral neck bone mineral density, seven in lumbar spine bone mineral density, three in total body bone mineral density, and four in heel bone mineral density. BrainSegVol-to-eTIV (GCST90002612) and ThalamNuclei lh volume CL (GCST90002729) showed the most consistent pattern across osteoporosis and all five bone mineral density outcomes [Table 1].

We used linkage disequilibrium score regression to evaluate genetic correlation between osteoporosis and the 16 validated imaging-derived phenotypes. A nominal significance level of P < 0.05 was used as the screening threshold in this step. Seven imaging-derived phenotypes showed evidence of genetic correlation with osteoporosis [Figure 3 and Supplementary Table 6], including ()) aseg global volume-ratio BrainSegVol-to-eTIV (id: GCST90002612); (2) HippSubfield lh volume HATA (id: GCST90002686); (3) ThalamNuclei lh volume CL (id: GCST90002729); (4) aparc-Desikan lh volume postcentral (id: GCST90002789); (5) aparc-a2009s lh volume G-precentral (id: GCST90002953); (6) aparc-pial lh area postcentral (id: GCST90003162); and (7) aparc-a2009s lh thickness S-precentral-inf-part (id: GCST90003670).

BrainSegVol-to-eTIV showed convergent support in the Mendelian randomization and linkage disequilibrium score regression analyses. We therefore conducted pleiotropy screening between this phenotype and osteoporosis. The quantile-quantile plot showed no early deviation from the null distribution [Supplementary Figure 2]. Pleiotropy analysis under the composite null hypothesis identified 40 loci at P < 5 × 10^-8 [Figure 4]. Six loci showed strong colocalization support with PP.H4 > 0.75, as illustrated in Figure 5A-F. The pleiotropic loci and prioritized genes are summarized in Table 2. Detailed PLACO and colocalization results are summarized in Supplementary Table 7. The remaining loci showed weaker evidence and require cautious interpretation.

We next evaluated whether the pleiotropic genes prioritized by pleiotropy analysis under the composite null hypothesis and colocalization contributed to the association between BrainSegVol-to-eTIV and osteoporosis. Six genes were evaluated in the mediation framework: IL12RB2, HLA-DRB1, ESR1, PPP6R3, PLEKHG1, and NCAM1. Gene-specific Mendelian randomization results for these pleiotropic candidates are shown in Supplementary Figure 3. Among them, using whole-blood cis-expression quantitative trait loci derived from GTEx v8, HLA-DRB1 showed evidence of partial mediation, with an estimated mediation proportion of 41.8% and a 95% confidence interval of 19.90% to 63.70%. The corresponding Mendelian randomization diagnostics are shown in Figure 6A-C; the colocalization result is shown in Figure 6D; and the indirect-effect estimate is summarized in Figure 6E.

Reverse Mendelian randomization analyses with osteoporosis as the exposure and the 16 validated IDPs as the outcomes are summarized in Supplementary Table 10. None of the reverse analyses remained significant after false discovery rate correction. Nominal inverse variance weighted associations were observed for QC SWI-to-T1 linear alignment discrepancy, aseg lh intensity Lateral-Ventricle, QC T1-to-standard nonlinear alignment discrepancy, and HippSubfield lh volume HATA, but none survived multiple-testing correction. Detailed sensitivity diagnostics for the 16 primary IDP-to-osteoporosis analyses are summarized in Supplementary Table 11 and Supplementary Figures 4-48. MR-Egger intercept tests and HEIDI tests did not indicate material directional pleiotropy or marked heterogeneity across the 16 analyses. Fourteen analyses were judged robust, whereas the two QC-related traits GCST90006352 and GCST90006346 showed minor heterogeneity. In both cases, the listed candidate outlier variants did not yield significant MR-PRESSO distortion tests, and post-removal Cochran’s Q statistics were attenuated.