Presentation on theme: "Connie Gomez, M. Fatih Demirci, Craig Schroeder"— Presentation transcript:
1 Connie Gomez, M. Fatih Demirci, Craig Schroeder Unit Cell Characterization, Representation, and Assembly of 3D Porous ScaffoldsConnie Gomez, M. Fatih Demirci, Craig SchroederDrexel University4/11/05
2 OutlineQuick Summary of ProjectEarth Mover’s Distance (EMD)
3 Problem StatementDevelop a framework to assemble biocompatible unit cell structures that mimic tissue properties to serve as a scaffold.?Unit Cell Structures
4 Design Considerations InformaticsPossible Design Solutions1) Mechanical requirements:scaffold structural integrityinternal architectural stabilityscaffold strength and stiffnessE & EEffG & GEffναρφSdporeAporebiomaterial selectioninternal architectureporosity and pore distributionfabrication method2) Biological requirements:cell loading, distribution, and nutritioncell attachment and growthcell-tissue aggregation and formationdporeAporeθporeφSφFClayoutpore size and interconnectivity;vasculature3) Geometrical requirements:anatomical fittingLwhlφSθporedporeAporescaffold external geometryinterconnectivitypermeability selectionφSφFCAporekPVTμρDRe4) Transport requirements:nutrient and oxygen deliverywaste removaldrug delivery
5 Overview of Approach Preprocessing Initial Assembly Unit Cell CharacterizationApplication RequirementsInitial AssemblyUsing a Given/ReferenceUnit Cell(s)Aligning Current Assembly with the Database Unit CellsAdding to the Assembly+Unit Cell RotationVector UpdateHeterogeneous Scaffold and Implant Design
6 Informatics: Mechanical Scaffold Material PropertiesEffective Young’s Modulus (EEff)Effective Shear Modulus (GEff)Poisson’s Ratio (ν)Coefficient of Expansion (α)Contour/Fluid PropertiesDiffusion Constant (D)Viscosity (μ)Density (ρ)Permeability (k)
8 Informatics: Transport Mass/Fluid Flux normal to surface (m)Velocity (u, v, w)Pressure (P)Geometric Tortuosity (T)
9 Model for Transport Characterization Create model of pore spaceUnit Cell Length (L)Length of pore (l)Height of pore (h)Width of pore (w)Diameter of pore (dpore)Area of pore (Apore)Pore angle (θpore)
10 Transport Characterization Input Define fluid propertiesDensity (ρ)Viscosity (μ)Specific HeatDefine flow parametersVelocity MagnitudeVelocity DirectionTurbulent or LaminarCheck ReDefine boundary conditionsInletsOutletsWalls
11 Results for the given properties and flow parameters CFD AnalysisMesh ModelRun AnalysisNodal InformationNode Coordinate and numberVelocity (u, v, w)PressureSurface Meshing: 2570 shellsVolume Meshing:18442 cellsResults for the given properties and flow parameters
12 Unit Cell Representation Common Engineering RepresentationsCADSTLIGESDisadvantages:Not suitable for computing unit cell connectivityComplexity of optimization increases as the size of the scaffold increasesWe can not associate properties using these representations.Any operations that we do using skeletons cost much less than these common engineering representations. Rotation for example.
13 Skeletonization Skeleton: An intuitive representation of shape and can be easily understood by the user, providing more control in the alignment process.Captures the topology of an object in both two and three dimensions.
20 Modified 2D Skeletonization Set of skeleton pointsCoordinates and the radius of the circle used to find the skeleton point (x, y, z, r)LayeringThree directions
21 Skeleton Point and Nodal Point Superposition Skeletal PointsCoordinatesRadiusNodal PointsProperty Values at nodal pointVelocity (u, v, w)Pressure
22 Property Calculation r=6.7 The nodal points can be associated with different cross sections.
23 Property Assignment Expansion of the skeleton representation Original Skeleton PointUnit Cell 1: [ x, y, z, r]Layered in three directions for rotationExpanded Skeleton Point of the Pore MaterialUnit Cell 1: [x, y, z, r, p1, p2, …pn]Properties (normal to the surface)P1: DensityP2: Velocity MagnitudeP3: Positive/Negative DirectionP4: PressureP5: Flow RateP6: Permeability
24 Overview of Approach Preprocessing Preprocessing Initial Assembly Unit Cell CharacterizationApplication RequirementsPreprocessingUnit Cell CharacterizationApplication RequirementsInitial AssemblyUsing a Given/ReferenceUnit Cell(s)Aligning Current Assembly with the Database Unit CellsAdding to the Assembly+Unit Cell RotationUpdate VectorsHeterogeneous Scaffold and Implant Design
25 Unit Cell Assembly (Alignment) Framework to provide a structural and/or contour connectivity between unit cellsThe goal :To develop an approach that will assemble characterized unit cell structures into a larger heterogeneous scaffold
26 Assembly Given the volume (anatomical geometry) Bottom Up Approach Starts from a unit cell at a given location within the volume with only a primary directionTop Down ApproachStarts with two unit cells and a path to optimize.Goal is to provide transport connectivity for one of the parameters on this path.
27 Bottom-Up Approach Assemble a scaffold given constraints A reference unit cellOuter scaffold geometryDirection for flowThree step assemblyAssemble the unit cells along the primary directionGrow the line of unit cells in a second direction to form plane, starting from the reference unit cellGrow plane of unit cells in the third direction, starting from the reference unit cell
30 Top-down Approach Assemble a scaffold given constraints A path along which optimal flow is desiredFixed connections at either end of the pathOuter scaffold geometryTwo step assemblyConstruct the path, filling in cells along the path so as to minimize total discontinuity between cellsFill in the rest of the scaffold, choosing cells that minimize discontinuity
31 Top-down: Path Filling Choose cubes and orientations for each cell in the pathMinimize total discontinuity between adjacent cells along the pathIllustration: filled path as part of a scaffold
32 Top-down: Scaffold Filling Choose cubes and orientations for each remaining cellFill from the path outwardsChoose best fitIllustration: filled scaffold with path highlighted
36 SummaryUnit cell informatics, necessary for unit cell alignment, have been set forth.Unit cell characterization approaches have been outlined.The unit cell’s geometry has been reduced to a skeletal representation to reduce complexity.Top-down and bottom-up approaches have been used to create an assembly inside a 3D volume.
37 Earth Mover’s Distance (EMD) Measure of dissimilarity between two sets of elementsHow much “work” is required to turn the first set into the second set
38 Earth Mover’s Distance (EMD) GivenTwo sets of elementsSome way to determining how dissimilar two elements areResultA measure of how dissimilar the two sets are
39 EMD Usage EMD takes two sets of elements The elements are the skeleton pointsThe elements include the properties attached to the skeleton pointsThe sets of elements are the skeletons
40 EMD UsageEMD needs some way to determine how dissimilar two elements areSkeleton points differ by positionApos, BposDissimilarity(A, B) = Distance(Apos, Bpos)Attributes are taken into account laterThis is called Ground Distance; EMD uses this
41 EMD Usage A match between two skeleton points A dissimilarity: Distance(Apos, Bpos)An amount of attribute being matched: aCost of match: Distance(Apos, Bpos) * aA match between two skeletonsA set of matches between skeleton pointsAll of the attribute of skeleton has been associated with skeleton points from the other skeletonTotal cost of all matches is minimal
48 Attributes and Work All matches Attribute of each node spread across the arrowsCost of each arrow is the length of the arrow times the amount of attribute assigned to it“Force” required to move that much attributeThis distance times “force” is where the notion of “work” comes fromTotal “work” is minimized
49 Not One-to-OneNote that some skeleton points have no arrows touching themThere is more of this attribute in the red skeletonNot all of the red points have room to match with greenAll of green points match with one or more red pointsNote that others have multiple arrows touching themGreen or red nodesThese nodes have more of the attribute than what they are paired withMultiple arrows, total, contain the full amount of the attribute of that node
50 Why EMD? Known to be suitable in other domains Object RecognitionWho else uses this?Allows partial matches in a natural wayTwo skeletons might not match up exactlyPartial matches make the comparison more flexibleWhat else goes here?
51 Simple ExampleDo we need some sort of illustration(s) that show a small example of EMD step by step?Better idea of what is going onEMD process hard to visualize – linear programming problemSimplex method?ExampleHow many nodes?Should they be complete scaffolds?Should they be labeled with attributes?Should they be labeled with coordinates?Should costs be computed and shown per edge?Should the cost be computed and shown for the whole thing?Should the optimal and a suboptimal match be shown for comparison?Does he need to see this example through all stages of the pipeline?Probably a lot of work!He seems to be okay with the other parts of the processQuestionable benefit in understanding EMD