Development of computational mesh models of the hippocampus and ventricles for studies of ageing and disease Maria del C. Valdés Hernández (mvhernan@staffmail.ed.ac.uk)

Background Study that explored the associations between the burden of white matter damage and brain atrophy measurements (Aribisala BS et al. Eur Radiol 2012, e-pub ahead of print) Sample: 672 participants of the LBC1936 (358 male/314 female, age: 73±1 yrs Gender Difference Men > women: BT, CSF, Vent, SSS, CSF+V+M No difference in WMLs (quantitative volume and Fazekas visual rating scores) Associations: P<0.01, P<0.05 ρ = Spearman rho Brain Tissue vol. Vent. vol. Subarach. space (SSS) vol. CSF vol. CSF+veins +meningeal vol. WMLs Volume ρ -0.10 0.11 0.03 0.06 Fazekas Scores -0.12 0.08 0.05 0.13

Background Hippocampal Volume

Are their sizes related ? Proportionally ? Background Are their sizes related ? Proportionally ?

Aims of the project To characterise regional morphological variations of hippocampi and ventricles in relation to: cognitive abilities, vascular risk factors, lifestyle indicators, small vessel disease, brain atrophy and neurodegenerative biomarkers To investigate whether there is a trend or an association between these morphological variations on ageing and disease populations

Complexity in the analysis Surface’s roughness can introduce errors in the inter-subject correspondence Variability in ageing and disease cohorts Five significant shapes of the lateral ventricle from BRIC

Sample selection 1.- Goals -> Shape analysis 2.- Desired Precision of Results -> 5% (This refers to the resultant implications of the sample size, NOT of the measurements) 3.- Confidence level -> 95% 4.- Degree of Variability estimate -> 5% 5.- Response Rate estimate -> N/A or 100% Watson, Jeff (2001). How to Determine a Sample Size: Tipsheet #60, University Park, PA: Penn State Cooperative Extension. Available at: http://www.extension.psu.edu/evaluation/pdf/TS60.pdf 54 participants of the Lothian Birth Cohort 1936 (out from the 672 that had valid imaging information) (mean age: 73 ± 1 years)

Investigating associations of regional differences in hippocampus and 3rd ventricle with different markers We extracted the following parameters for the sample: Score of the Mini Mental State Examination (MMSE), general cognitive ability (g), general processing speed and general memory factors at age 72-73 years old, age 11 IQ, brain tissue volume, and B) Gender (females), self-reported history of hypertension, hypercholesterolaemia, diabetes and cardiovascular disease. Subjects with [param] > or < than SD[param] Subject with/without [param] For the computational image analysis ( e.g., model adjustment and improvement, generation of mean mesh, calculate deformation of each individual mesh) the whole sample was used.

Group-wise shape analysis pipeline Brain Segmentation (Manual / Automatic) Individual Shape Model Construction Model Normalization (Affine Transformation) Mean Surface Construction (Group-wise) Local Surface Deformity & Statistical Analysis 9

Surface modelling Pre-requisites: Smooth surface representing individual shape characteristics Inter-subject point-to-point shape correspondence Robust restoration of individual shape details across large variations of shape and size Surface-based shape analysis is applied to figure out ~. In the shape analysis, the surface modeling is necessary to obtain the shape information from 3D volumetric data as a computational representation The surface modeling satisfies following conditions. First, It needs to generate the smooth surface with correct shape representation And It also parameterizes the surface of target structures with mathematical representation Finally, it needs to build the shape correspondence between subjects Using the individualized surface models obtained through the surface modeling process, we can compare the shape characteristics between control and experimental groups. 10

Coarse-to-fine deformation using a progressive weighting scheme The model rigidity is synchronised to the amount of surface’s deformation: Initially a large value is assigned to the rigidity parameter , which is reduced iteratively using a step function However, the Laplacian This weighting scheme helps to keep the point distribution strongly for the large surface deformation. When the model is not deformed any more, we relax the model rigidity to recover the local shape details. This figure shows how the progressive weighting scheme works in our deformation framework. 11

Advantages of the progressive weighting scheme Robust surface modeling Minimizing the distortion of the point distribution Preventing self-intersection and insufficient deformation The progressive weighting scheme derives a coarse-to-fine surface deformation, This figures shows the advantages of our framework using progressive weighting scheme With large weight for model rigidity, With small ~ These kinds of problems are observed in different surface modeling methods, It can build the shape correspondence between subjects by preservinig the point distribuiton on the template model against shape and size variations. 12

Smooth surface reconstruction Rotation-and-scale invariant transformation (Sorkine, et al 2004) To preserve surface quality while restoring local shape details Vertex Transformation via Laplacian deformation  Rotation, isotropic scale, translation Another feature of our modeling framework is the RSI transformation. When the surface model is fitted to the image boundary locally, the variations of external factors can generate very rough surfaces. This situation is getting severe, when the surface model is deformed at small region. And the unexpected roughness of the surface models can yield the distortion of shape analysis. To Preserve ~, we implemented RSI transformations excluding the anisotropic scale transformation. This transformation help to preserve the surface quality ~.. 13

Evaluation of the inter-subject shape correspondence Results of the landmark placement test :

Alignment and normalisation Surface alignment Rigid transformation Iterative closest point Procrustes method Volume normalization To investigate the shape difference only Isotropic scaling Intra-cranial cavity volume Volume of brain structure

Local surface deformity and statistical analysis Vertex-wise surface deformity Signed Euclidean norm of the displacement vector, projected onto vertex normal Inward/outward difference Statistical analysis Group-wise ANCOVA and false-discovery-rate (FDR) adjustment Vertex-wise Surface Deformity

Regional deformation pattern for general cognitive ability Left H Right H 3rd. ventricle g < SD g > SD

Regional deformation pattern for general memory Left H Right H 3rd. ventricle g_memory > SD g_memory < SD

Regional deformation pattern by gender Left H Right H 3rd. ventricle males females

Regional deformation pattern for brain tissue volume (general atrophy) L H BTV < SD BTV > SD RH Corrected by vol. Corrected by vol. uncorrected uncorrected

Regional deformation pattern for having or not hypertension Differences not significative after correcting for hipp.size LH Do not have hypertension hypertensive RH

Regional deformation pattern for low/high cholesterol levels Differences not significative after correcting for hipp.size LH hypercholesterolaemia normal/low cholesterol RH

Regional deformation pattern for having or not history of cardiovascular disease Differences not significative after correcting for hipp.size No cardiovascular disease Cardiovascular disease

The team: Principal Investigators: Prof. Joanna M Wardlaw (Senior Neuroradiologist, director of BRIC), Prof. Jinah Park (Head of the Computer Graphics and Visualisation Research Lab at KAIST) & Dr. Maria del C Valdés Hernández (Lecturer in Image Analysis at BRIC) Team members: Miss. Natalie A Royle (BRIC), Eng. Jae-il Kim (KAIST), Eng. Hojin Ryoo (KAIST), Dr. Susana Muñoz Maniega (BRIC), Dr. Benjamin Aribisala (BRIC), Dr. Mark E Bastin (BRIC), Prof. Ian J Deary (Director of CCACE), Miss. Catherine Murray (CCACE), Dr. Alan Gow (CCACE, Heriot-Watt University)

Sponsors of the project : Thanks to: The data : Sponsors of the project : Contributors : Radiographers and administrative staff at BRIC, students and staff at CCACE, nurses at the WTCRF and participants of the LBC1936