GeomCellDesign of Cell Geometry

Július Parulek1,2, Miloš Šrámek2,3 and Ivan Zahradník1

(1) Institute of Molecular Physiology and Genetics, Slovak Academy of Sciences, Slovakia(2) Faculty of Mathematics, Physics and Informatics, Comenius University, Bratislava, Slovakia(3) Austrian Academy of Sciences, Austria

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Overview

Introduction to GeomCell Previous work on geometrical

modeling of muscle cells Representation of mitochondrial

shape GeomCell Implementation Conclusions and future work

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GeomCell - Intro An environment for virtual cell modeling

based on a precise geometric background possibilities of modern computer graphics

and computer hardware to represent a virtual micro-world of cells

first building blocks for representation of a static cell geometry

models of skeletal muscle tissues idealized models rather than exact

reconstruction

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Muscle Cell Organelles

(Courtesy of Dr. Novotová)

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Muscle Cell Organelles

Laon

git

ud

inal axis

Transversal axis

(Courtesy of Dr. Novotová)

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Input Data - EM images

(Courtesy of Dr. Novotová)

Volume and surface density (stereology)

Volume and surface density (stereology)

Sizes(morphometry)

Sizes(morphometry)

Shape(morphology)

Shape(morphology)

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Cell Model Organelles

Desired subset of cell organelles:1) Myofibrils2) Sarcolemma3) Sarcoplasmic reticulum4) Mitochondria5) T-tubules

1

3

2

45

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XISL Implicit Objects

XISL – Implicit modeling environment XML based modeling language C++ library, tools (conversion,

rendering, ...)

f(x) > 0

f(x) < 0

f(x) = 0

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Cross-sectional Graphs Produce carrier

skeletons for all virtual organelles

Directly used in modeling of myofibrils Thin and long cylindrical

objects cross-sectional graphs

(c-graph) in a system of parallel planes

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Cross-sectional Graphs (cont.)

Real EM images c-graph2D implicit shapes

Quadratic interpolation of the 2D shapes

Minimal distance specification

Minimal distance specification

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Extended Interpolation Spatial warp metamorphosis utilized in

sarcoplasmic reticulum (SR) modeling two compartments: terminal cisterns of the

SR (A) and Longitudinal SR (B) skeleton: a set of seed (C) points distributed

in a system of cross-sectional planes

A

B C

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Mitochondrial Shape

Elliptically shaped and prolonged organelles of irregular smooth forms and variable sizes implicit sweep objects

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Components of Sweep Objects

A 2D sweep primitive (template) and a 3D sweep trajectory

2D template2D template 3D trajectory3D trajectory

Sweep objectSweep object

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Template defined as 2D implicit ellipsoid with variable dimensions

Trajectory as quadratic B-spline

Sweep Components for Mitchondria

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Method Overview

Transformation (MS) maps the 2D template along the curve using so-called reference frames (RF)

Rotation of RF around C’(t)

fe

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Method Overview (cont.)

Estimate all curve points NP(x) (parameters si), for which x lies in the template planes

Resultant function

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Problem of Parameter Estimation

Analytical solution (a, param t) of a general curve trajectory is rarely possible

for instance: cubic spline (C(t) is degree 3) - the polynomial (a) is degree 5

Solution in using quadratic curves analytical solution

(a)(a)

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End Caps

Union with two implicit semi-ellipsoids at both ends

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Model Generation

Fully automatic, guided by Model Description Language (MDL) basic cell dimensions c-graph distribution organelle’s geometric parameters

specified in a probabilistic sense Quantification, visualization, …

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GeomCell Implementation Computationally intensive tasks

generation of large number of models evaluation of volume and surface areas of

organelles model visualization

High throughput computing required Utilization of a grid environment

retrieval of cell models using metadata (morphological and stereological data, images, MDL spec.,…)

eased with a GUI portal

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Conclusions and Future Work System for cell model generation,

quantification, visualization and conversion implemented in Grid environment - GeomCell

Organelle’s behavior add physical layer to all objects growth, deformations, cell

contraction, … Pathological cells

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Thank You for Your Attention

Homepage: www.sccg.sk/~parulekCell modeling project: www.sccg.sk/~parulek/cellGrid implementation:http://cvs.ui.sav.sk/twiki/bin/view/EGEE//GeomCellInEGEE-MuscleCellModelingOnTheGrid

Visualization of a volumetric format of a cell model