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# Genetic and functional insights into the fractal structure of the heart

## Abstract

The inner surfaces of the human heart are covered by a complex network of muscular strands that is thought to be a remnant of embryonic development1,2. The function of these trabeculae in adults and their genetic architecture are unknown. Here we performed a genome-wide association study to investigate image-derived phenotypes of trabeculae using the fractal analysis of trabecular morphology in 18,096 participants of the UK Biobank. We identified 16 significant loci that contain genes associated with haemodynamic phenotypes and regulation of cytoskeletal arborization3,4. Using biomechanical simulations and observational data from human participants, we demonstrate that trabecular morphology is an important determinant of cardiac performance. Through genetic association studies with cardiac disease phenotypes and Mendelian randomization, we find a causal relationship between trabecular morphology and risk of cardiovascular disease. These findings suggest a previously unknown role for myocardial trabeculae in the function of the adult heart, identify conserved pathways that regulate structural complexity and reveal the influence of the myocardial trabeculae on susceptibility to cardiovascular disease.

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## Data availability

The genetic and phenotypic UK Biobank data presented in this study are available to any bona fide researcher upon application to UK Biobank (https://bbams.ndph.ox.ac.uk/ams/). The GWAS summary level data used in this study are publicly available: per-slice and meta-analysis summary statistics of fractal dimension can be accessed through the GWAS catalogue (https://www.ebi.ac.uk/gwas; accession numbers GCST90000287–GCST90000296), LD score regression traits are available at http://ldsc.broadinstitute.org and heart failure summary statistics can be found at http://www.hermesconsortium.org/. Figs. 1, 3 and 4 contain raw data that are provided as source data unless prior application to UK Biobank is required. Source data are provided with this paper.

## Code availability

The analysis code is freely available on GitHub (https://doi.org/10.5281/zenodo.3698268).

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## Acknowledgements

The research was supported by the UK Medical Research Council (MC-A651-53301); British Heart Foundation (NH/17/1/32725, RG/19/6/34387, RE/18/4/34215); Wellcome Trust (107469/Z/15/Z); National Institute of Environmental Health Sciences (R01 ES029917-02); Heidelberg University; the Simons Center for Quantitative Biology at Cold Spring Harbor Laboratory; and the National Institute for Health Research Biomedical Research Centre based at Imperial College Healthcare NHS Trust and Imperial College London. P.M.M. has also received personal and research support from the Edmond J. Safra Foundation and Lily Safra, an NIHR Senior Investigator’s Award, the Medical Research Council and the UK Dementia Research Institute. R.T.L. is supported by a UKRI Health Data Research Rutherford Fellowship (MR/S003754/1). A.H. is supported by a BHF PhD studentship. J.G. is supported by a Research Center for Molecular Medicine (HRCMM) Career Development Fellowship, the MD/PhD program of the Medical Faculty Heidelberg, the Deutsche Herzstiftung (S/02/17) and by an Add-On Fellowship for Interdisciplinary Science of the Joachim Herzstiftung. Research funding for cohorts used in Mendelian Randomization: NIHR Cardiovascular Biomedical Research Unit of Royal Brompton and Harefield NHS Foundation Trust (DCM cohort). Funding information for HERMES-participating studies is described elsewhere20. Data aggregation and downstream bioinformatics were funded through grants from the MRC Proximity to Discovery scheme, the NIHR UCLH Biomedical Research Centre and the EU/EFPIA Innovative Medicines Initiative 2 Joint Undertaking BigData@Heart grant no. 116074. We thank H. Suzuki for his work on preprocessing the image data, R. Fumero for advice on the finite element modelling, V. Uhlmann for advice on radial image registration, L. Schertel and C. Baader for sgRNA production, members of the Wittbrodt Laboratory for discussion and support and B. Statton and M. Thanaj for assisting with data preprocessing.

## Author information

Authors

### Contributions

H.V.M. and T.J.W.D. performed the formal analysis and co-wrote the manuscript; M.S. and M.L.C. performed the in silico modelling; T.J.W.D. and A.d.M. collected and analysed image data; R.T.L., A.H., J.S.W. and S.K.P. collected and analysed the clinical data; W.B., P.T., J.C. and D.R. developed the computational phenotyping; J.G., T.T. and J.W. detailed the experimental strategy for the medaka validation; J.G. and T.T. designed and performed CRISPR–Cas9 knockout experiments and conducted phenotypic analysis under the guidance of J.W.; J.G. acquired light sheet microscopy recordings, and analysed and plotted the medaka knockout and imaging data. P.M.M., E.B., S.A.C. and D.P.O. provided interpretation of the results; E.B., S.A.C. and D.P.O. conceived the study, managed the project and revised the manuscript. All authors reviewed the final manuscript.

### Corresponding authors

Correspondence to Hannah V. Meyer or Declan P. O’Regan.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

## Additional information

Peer review information Nature thanks Tim Leiner, Christopher Newton-Cheh and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Extended data figures and tables

### Extended Data Fig. 1 The ethnicities of participants in the discovery and replication cohorts.

a, b, Principal components 1 and 2 of the principal component analysis of the combined genotypes of the HapMap III datasets (n = 1,184 individuals) and the UK Biobank discovery cohort (a; n = 19,262 individuals; 159,243 independent genetic variants) or the UK Digital Heart study (b; n = 2,985 individuals; 149,707 independent genetic variants). Data from the UK Biobank (a) or UK Digital Heart cohort (b) are depicted in blue, HapMap individuals are coloured by their ethnicity. Cohort individuals within 1.5 standard deviations distance from the centre of the European HapMap individuals (grey) are selected for further analyses.

### Extended Data Fig. 2 Fractal dimension phenotypes.

a, The distribution of CMR image slices for which the fractal dimensions were measured in the n = 19,761 UK Biobank individuals. Missing fractal dimension measurements per slice can arise because a slice was not measured (NA), or the estimation of the fractal dimension failed owing to poor image quality or the estimated fractal dimension failing quality control (NaN). b, The correlation between fractal dimension summary measures derived from the observed fractal dimension slice measurements and interpolated fractal dimension measurements per sample. Interpolated fractal dimension measurements per sample were derived by using a Gaussian kernel local fit to different numbers of slice templates, allowing for direct slice comparisons across individuals. Different numbers of slices for interpolation were tested (rows; 7–12 slices). Columns show different summary measures: the mean fractal dimension across all measured slices (MeanGlobalFD) or mean fractal dimension per slice region (MeanBasalFD, MeanMidFD, MeanApicalFD) were analysed. Linear model of measured~interpolated (r2) values of the summary measures between measured and interpolated fractal dimensions in the UK Biobank (n = 19,761 individuals).

### Extended Data Fig. 3 Acquisition and processing of phenotypes.

a, Fractal dimension analysis on cardiac computed tomography images. The fractal dimension was calculated using the same method as for CMR, but with manual regions of interest, in a set of gated cardiac computed tomography images. Top, analogous processing as described in Fig. 1c, using edge detection of the trabeculae and subsequent box counting across a range of sizes. Bottom, analogous to Fig. 2a, box plots of the fractal dimension measurements for 20 individuals per slice, colour-coded by cardiac region. The lower and upper hinges in the box plot correspond to the 25th and 75th percentiles (IQR), the horizontal line in the box plot indicates the median. The lower and upper whiskers extend from the hinge to the smallest and largest values that are no further than 1.5× the IQR. b, Myocardial strain. Global longitudinal Lagrangian strain at each cardiac phase for all UK Biobank participants with CMR imaging (n = 26,893). Individual data points shown with a smoothed mean and density contours. c, Principal component analysis of fractal dimension measurements across all 9 slices in the 18,096 individuals of the UK Biobank discovery cohort. Proportion of variance explained for each principal component (left). Biplot of the first and second (middle) or third and fourth (right) principal components of each individual (grey points). The corresponding loadings for the fractal dimension of slices 1–9 are shown as vectors. d, Genotype, fractal dimension and trabeculation outlines for rs35006907. Representative, registered, trabecular outlines at slice 5 are shown for the median fractal dimension of individuals with the homozygous major (blue), heterozygous (pink) and homozygous minor (green) genotypes of rs35006907. e, Pearson correlation of global fractal dimension and QRS duration (n = 18,096 individuals). QRS duration phenotype from UKB ID: qrs_duration_f12340_2_0. The Pearson correlation coefficient is indicated in the top right corner.

### Extended Data Fig. 4 Per-slice fractal dimension GWAS and inclusion of additional covariates.

a, b, Manhattan plots (a) and quantile–quantile plots (b) of the independently conducted, nine univariate GWAS on the per-slice fractal dimension measurements for 18,096 UK Biobank individuals passing quality control. a, In the Manhattan plots, the P values (derived from linear association t-statistics) were multiplied by the effective number of independent phenotypic tests Teff = 6.6 and min(Padjust, 1) reported. In the quantile–quantile plots, the unadjusted P values are plotted against equally spaced values in the range of 0–1 of the same sample size (expected P values). The diagonal line starts at the origin and has a slope of one. The genomic control λ values for each quantile–quantile plot are: 1.0557, 1.0436, 1.0496, 1.0557, 1.0649, 1.0679, 1.0679, 1.0618 and 1.0436. λ values were generated with linkage disequilibrium score regression, for details see Supplementary Table 1. c, d, Manhattan plots based on the meta-analysis GWAS (sample size, n = 18,096 individuals) with end-diastolic volume of the left ventricle (c) or myocardial strain (d) as co-variate. e, Manhattan plot based on the meta-analysis GWAS (this panel is the same as Fig. 2a and is shown for comparison). Other co-variates and analysis parameters (as described in the Supplementary Methods) were kept the same in all analyses (ae). P values are meta-analysis P values, not adjusted for multiple testing derived from the transformation of the univariate signed t-statistics (associations on 14,134,301 genetic variants at 16 independent loci from 18,096 individuals) and χ2 distribution with 9 degrees of freedom. In a and ce, the horizontal grey line is drawn at the level of genome-wide significance: P = 5 × 10−8.

### Extended Data Fig. 5 GWAS effect size estimates and replication.

a, Effect size distribution of loci with genetic variant associations of Padjust = 5 × 10−8 in any univariate per-slice fractal dimension GWAS (sample size, n = 18,096 individuals). P were values derived from linear association t-statistics. Distributions are shown for each locus (indicated by chromosomal position and lead genetic variant in the subplot title) across all slices and effect sizes, colour-coded by P value of the association. Variants with no Padjust < 5 × 10−8 in the univariate per-slice fractal dimension GWAS (all blue) were discovered in the multi-trait meta-analyses. b, c, Effect size estimate concordance in discovery and replication cohorts. For each of the nine univariate, per-slice fractal dimension GWAS, the effect size estimates of the genetic variants with the smallest P value for each of the independent loci in the discovery cohort (n = 18,096 individuals) were selected. For some variants, associations that passed the GWAS threshold of Padjust < 5 × 10−8 were discovered in more than one of the nine univariate GWAS fractal dimension slices; for these variants all effect size estimates were selected. Estimates were plotted against the corresponding slice-variant associations in the replication GWAS (b, UK Biobank replication, n = 6,356 individuals; c, UK Digital Heart cohort, n = 1,029 individuals). Non-concordant estimate pairs are depicted in light grey. Effect size estimates that passed the Bonferroni-adjusted validation P-value threshold of P < 0.05/16 = 0.003 are depicted as triangles. r2 for linear model of $${\hat{\beta }}_{{\rm{discovery}}} \sim {\hat{\beta }}_{{\rm{replication}}}$$.

### Extended Data Fig. 6 Annotation of trabeculation associated loci.

a, Gene expression of GTEx-associated genes and tissues. Gene expression is shown as log10-transformed transcripts per million (TPM) for genes for which the expression is associated with trabeculation loci (using GTEx look-up; Supplementary Data 3). Gene expression values and tissues were downloaded from https://www.ebi.ac.uk/gxa/home by querying: gene name AND tissue AND species; that is, GTEx gene AND heart component AND Homo sapiens. Light grey tiles indicate gene expression values for the gene–tissue pair that are not available. b, Enrichment of trabeculation-associated variants in DNase I hypersensitive sites for all available tissues in GARFIELD. GARFIELD was used to compute the functional enrichment (odds ratio (OR)) of genetic variants associated with the trabeculation phenotypes (GWAS: n = 18,096 individuals, P values derived from linear association t-statistics) at P < 10−6 for open chromatin regions. The results across all available studies per tissue are shown as box plots. Lower and upper hinges, 25th and 75th percentiles (IQR); horizontal line, median; lower and upper whiskers extend from the hinge to the smallest and largest value no further than 1.5× the IQR.

### Extended Data Fig. 7 Biomechanical model, genetic correlation and disease associations.

a, Left ventricular pressure–volume loops from finite-element modelling across a range of atrial pressures. Solid and dashed lines indicate smooth and trabeculated ventricles, respectively. b, Mid-short-axis cross-sections of the finite element model of the left ventricle, looking towards the apex, at different trabecular complexities. c, The ventricular model was in series with pre-load (red) and after-load (blue) circuits that define the left atrial pressure (PLA), right atrial pressure (PRA), inflow resistance (R1), aortic resistance (R2), peripheral resistance (R3) and vascular capacitance (c). Initial parameters calibrated to approximate observations from UK Biobank data; the reference model was a trabeculated left ventricle with a PLA of 5 mm Hg. d, Fractal dimension association P values (depicted on −log10 scale, uncorrected for multiple comparisons; estimated by transformation of univariate GWAS signed t-statistics with χ2 distributions with 9 degrees of freedom; univariate GWAS with n = 18,096 individuals) for the GOSR2 locus on chromosome 17; variants associated with mixed aetiology heart failure (n = 47,309 cases, n = 930,014 controls) and DCM (n = 510 cases, n = 1,136 controls) are highlighted in purple. eg, Summary statistics of basal, mid and apical trabeculation GWAS were analysed for genetic correlation with all available summary statistics on LD Hub. e, Additive heritability estimates h2 for regional summary statistics based on 1,208,036 genetic variants. f, Association P values of heart and cardiovascular phenotypes with corresponding estimate of genetic correlation (encoded by size). g, Genetic correlation P values of all available LD Hub traits (x axis, ordered by category) with trabeculation GWAS results (based on linkage disequilibrium score regression correlation of 1,208,036 genetic variants) by region summarized in LD Hub categories (colour-coded). Heart and cardiovascular phenotypes (y axis in f and Supplementary Table 13) are depicted in magenta. g, P values are derived from cross-trait correlation analysis and a block jackknife approach for estimation of the standard error of the genetic correlation (Supplementary Table 13); P values are shown on −log10 scale and are uncorrected for multiple comparisons.

### Extended Data Fig. 8 Mendelian randomization analysis of the effect of trabeculation on heart failure and DCM.

a, Mendelian randomization on heart failure. The effect size estimates for heart failure are based on n = 47,309 cases and n = 930,014 controls in the HERMES study20. b, Mendelian randomization on DCM. The effect size estimates for DCM are based on n = 1,134 cases and n = 510 controls. The fractal dimension effect size estimates from univariate GWAS results on n = 18,096 samples are shown. Scatter plots (top left) depict the genetic variant-exposure effect versus the genetic variant-outcome effect. Centre values show effect size estimates on fractal dimension and DCM, error bars show the standard error of the association test (t-statistic for fractal dimension, logistic regression for heart failure and DCM). Forest plots (top right) show the contribution of each genetic variant to the overall estimate (black; estimated by Wald ratio) and combined as a single genetic instrument (purple; estimated by the indicated method) for the four tested Mendelian randomization methods (these panels are the same as Fig. 4c,d and are shown for convenient comparison). Funnel plots (bottom left) depict the instrument strength against the causal effect of each instrument as a single instrumental variable. Vertical lines indicate the average estimated effect for the tested Mendelian randomization methods. Strong instruments are close to the estimated average effect, while weak instruments spread evenly on both sides. Leave-one-out plots (bottom right) show the results of Mendelian randomization analysis (inverse-variance weighted only), in which each genetic variant is sequentially excluded. This analysis can indicate whether there are any single variants that drive the Mendelian randomization results. In the right panels, centre values mark effect size point estimates, error bars show the 95% confidence intervals.

## Supplementary information

### Supplementary Information

This file contains Supplementary Notes on Mendelian Randomisation, Supplementary Methods, Supplementary References, Supplementary Tables 1-18 and Supplementary Figure 1.

### Supplementary Data

This file contains Supplementary Data files 1-6 and a guide.

### Video 1

: Control-injected medaka embryo at 4 days post fertilisation. Representative video of one control embryo (out of n=87 embryos). Corresponds to Figure 3c, control embryo. LSM was carried out on a 16x multiview selective plane illumination microscope (MuVi-SPIM). Entire heart volumes were acquired with 488 nm illumination, a 525/50 nm bandpass filter, and a z step size of 2 μm. Surface rendering was performed with UCSF Chimera (1.11).

### Video 2

: Moderately affected mtss1 KO embryo at 4 days post fertilisation. Representative video of one mtss1 KO embryo (out of n=13 embryos). Corresponds to Figure 3c, mtss1 KO. It shows abnormal cardiac morphology and reduced amount of intracardiac blood volume. LSM was carried out on a 16x multiview selective plane illumination microscope (MuVi-SPIM). Entire heart volumes were acquired with 488 nm illumination, a 525/50 nm bandpass filter, and a z step size of 2 μm. Surface rendering was performed with UCSF Chimera (1.11).

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Meyer, H.V., Dawes, T.J.W., Serrani, M. et al. Genetic and functional insights into the fractal structure of the heart. Nature 584, 589–594 (2020). https://doi.org/10.1038/s41586-020-2635-8

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