Design of a system for rapid three-dimensional digital                
                 rendering of living endothelial cells for computational
                 flow and stress analyses
 
                               Brian Patterson
 
                      Sponsor: Peter J. Butler, PhD, Cell and Tissue Mechanotransduction Laboratory,                    
                                      Department of Bioengineering, The Pennsylvania State University, University Park, PA 16802
 

 

 

                                           

      

 

 

 

                        The Primary Goal:  Creating Finite Element Models of Cell Topography from Widefield Microscopy Images

 

Executive Summary:

Endothelial cells (ECs) convert mechanical cues from blood flow into intracellular biochemical signals, a process known as mechanotransduction. Since these cues are spatially varying, subcellular analysis of surface and internal forces in endothelial cells will provide insight into how, when, and where mechanotransduction occurs. The goal of this project was to design a rapid method for 3-D volume and surface rendering of confocal and widefield images of endothelial cells to provide input into a novel partial differential equation solver, FEMLAB. FEMLAB is a MATLAB-based programming environment which supports modeling of flow fields and their effects, including viscoelastic deformation of bodies under flow and provides numerical solutions to arbitrary partial differential equations. Rapid volume rendering and stress analysis provides spatial assay points for optical interrogation of mechanotransduction events.

The program was capable of accurately modeling endothelial cells both singly and in confluent monolayers. The program’s accuracy was verified by creating models from stacks taken of 6µm beads. Models created were both spherical and of the correct diameter. Faithful reproductions of cellular topography are critical for accurate stress calculations. Common distortions in 3D rendering include axial stretch and enlargement due to inclusion of out of focus light. Axial stretch was eliminated in the program by accounting for the difference in refractive index between the sample and immersion oil using a constant scaling factor. Out of focus light was reduced with both commercial deconvolution software and careful filtering of the images within the program.

The program is capable of rapidly producing cell topography data, and can process an average stack on images in less than one minute. This allows nearly real – time analysis of cell morphology and stresses during flow experiments. The ability to access this data in rapid time will allow future experiments to be performed accurately by accurately coordinating actual stress felt by the cells to specific mechanotransduction events.

Design Criteria:

The system will consists of three related components:  a method for dyeing cultured cells for observation, a microscope system for obtaining images of the cultures, and a software system for digital reconstruction of the images.  The original design constraints were:

Dyeing Method:

 

  • Uniform staining without damage
Microscope System:
  • *Rapid and Accurate Image Acquisition
Software Program:
  • *Faithful rendering of topography, usable output format
 

 

 

 

Final Design:

The final design utilized two membrane dyes, DiIC16 and Calcein AM.  The design incorporated a piezoelectric stage for microscopic sectioning of dyed cells.

 

Cellular Image Stacks:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Text Box:   Text Box:   Text Box: Initial TIFF stack of images are read into MATLAB Text Box: A 3D Array representing the volume is created by combining the 2D images. The array consists of a set of pixel intensity values corresponding to points in space. Text Box: The array is divided into slices along its vertical axis. Each slice is median filtered with a selectable window to remove "salt and pepper" type noise, then the slices are recombined. Text Box: The entire array is smoothed with a 3D Gaussian lowpass filter of selectable depth and window. This passes only larger characteristics to simplify the rendering process Text Box: The binary volume is converted back to a series of 2D slices, which are saved along with the original images for border comparison Text Box: The array is now "padded" with layers of zero valued elements on each of its 6 faces. This effectively borders all features which continue outside the image plane, ensuring a closed surface for the solid model. Text Box: The padded array is converted to a binary volume with a user selected dual threshold ("sliced"). This assigns a uniform white value to all pixels within a certain intensity range, and sets all other pixel values to zero. Text Box: An arbitrary 3D function of the form z = f(x,y) is fitted to these surfaces using the MATLAB command griddata. This function is interpolated on a grid of points in the XY plane, forming a smooth surface which can be exported to FEMLAB. Text Box: An algorithm finds the thickest slice in the binary array, and creates a surface by mapping the height of the highest point above and below the reference slice. In practice, this can be thought of as dropping a blanket over the 3D surface. This creates two surfaces, the top and bottom of the cells. Text Box: The top and bottom surfaces are joined in FEMLAB to create a solid model of the cell which can be used in further computations. Text Box: The array is scaled in three dimensions to account for the spacing in the X, Y, and Z directions. This process utilizes a "squash factor" that accounts for Z axis stretching due to differences in the samples refractive index. Text Box: A stack of endothelial cell images, from the base at left to the cells’ apexes at right. (this particular stack was obtained using a confocal microscope) Text Box: An original image and corresponding binary image used for creating the surface Text Box: The original outputs of the program (top and bottom of an endothelial layer) Text Box: Interpolated surfaces fitted to the above results Text Box:   Text Box: A plot of calculated surface stress over the monolayer under flow. Text Box: The surface imported into FEMLAB and divided into finite elements for analysis Text Box: A diagram illustrating one origin of axial stretch due to differences in refractive index, Dobjective > Dfocal plane Text Box: Dobjective Text Box: Dfocal plane Text Box: Oil, n ≈ 1.5 Text Box: Glass, n ≈ 1.5 Text Box: Objective Text Box: Sample, n ≈ 1.3

 

 

 

 

 

 

 

 

 

 

 

Verification:

In order to verify the program’s accuracy, 6 µm beads were rendered with the system.  The initial uncorrected stack displays significant distortion along the Z axis, which is effectively corrected by the program

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Alternative Software Design:

 

A surface production program incorporating MATLAB’s Qhull based Delaunay triangulation functions was also written.  This design is very robust, but was set aside due to the complexity of the output, which hindered further processing.  This program is able to model more than two vertically overlapping surfaces, allowing possible multi channel staining of the cell in order to incorporate the mechanical properties of organelles in later simulations. 

 

 

 

 

 

 

 

 

 

 

 

                                                                    The MATLAB output of the alternative program

 

Project Budget and Timeline:

 

Final Budget:

  Item:                                                                                                   Supplier:                                  Cost:

DiIC16, solid (100 mg)
Molecular Probes, Inc
$197.00 
DMSO (Dimethyl Sulfoxide) (250 mL)
Sigma Aldrich
$35.00
Dulbecco’s phosphate buffered saline,(1L)
Sigma Aldrich
$21.30
1000 uL pipet tips, (100)
VWR
$5.90
50uL pipet tips, (100)
VWR
$5.90
Polypropylene Centrifuge Tubes, 50ml (50)
VWR
$15.50
Polypropylene Centrifuge Tubes, 15ml (50)
VWR
$14.20
DMEM high glucose cell culture medium (1L)
VWR
$6.00
Calcein AM, liquid (1 mg) (An added expense not originally proposed)
Molecular Probes, Inc
$164.00
Total
  
$464.80

List of Equipment Used in the Design Implementation:

 

Software:

MATLAB®  (Mathworks, Inc.)

FEMLAB® (Comsol, Inc.)

Autodeblur®, and Autovisualize® Deconvolution suite (Autoquant, Inc.)

Camware® (Cooke, Inc.)

 

Hardware:

Olympus IX71 research microscope with 60X TIRF objective (Olympus, Inc.)

Microdrive® X-Y stepper motor stage (Mad City Labs, Inc.)

Nanodrive® piezoelectric Z stage (Mad City Labs, Inc.)

High speed microscope shuttering system (Uniblitz, Inc.)

Objective heater (Bioptech, Inc.)

Heated coverglass flow chamber (Bioptech, Inc.)

Sensi-Cam®  remote cooled CCD camera (Cooke, Inc.)

 

Final Project Completion Timeline:

Red lines indicate areas of extended scheduling not included in the original proposal:


 

 

 

 

 

 

 

 

 

 

 

Links:

 

 

A paper published in the Proceedings of the 2004 Asilomar Conference on Signals, Systems and Computers (PDF)

 

Full text of the related Honors Thesis