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Micro-infrared spectroscopy is a method of acquiring infrared images of a sample like visible images of an optical microscope, and is applied in a wide range of fields for the purpose of evaluation of component distribution in the sample. However, it is relatively difficult to classify infrared images. On the other hand, deep learning using images has been dramatically developed in recent years.

Therefore, we considered infrared images as multi-channel image data and examined whether it was possible to construct models and classify uncategorized images by deep learning. We also considered transfer learning by selecting three of the channels.

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1

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8 References

[1] Jian Chen. Discrete Element Method for

Non-spherical Particles in Three Dimen-

sions. PhD thesis.[2] .

. .[3] Dominik Krengel and Hans-Georg Matut-

tis. Implementation of static friction formany-body problems in two dimensions.Journal of the Physical Society of Japan,87(12):124402, 2018.

Visualizing an FEM-Flow-Simulation forOptimal Choice of Basis Functions

Jan Mueller and Hans-Georg Matuttis, Department of Mechanical Engineering and Intel-

ligent systems, The University of Electro-Communications

1 DEM and FEM in MATLAB

Two dimensional MATLAB simulation code [1]:

- Polygonal particles (granular medium) modelledwith Discrete Element Method (DEM)

- Newtonian fluid (isothermal, incompressible)modelled with Finite Element Method (FEM)

⇒ Combination allows realistic representation ofmicroscopic fluid solid interactions

Currently Taylor-Hood Element for FEM [2]

x1, y1 x2, y2

x3, y3

velocity and pressure calculation

velocity calculation only

P2P1: Taylor-Hood Element

→ Basis functions are second order plynomials forvelocities, first order polynomials for pressure)

→ Linear combination of basis functions= elementfunction (FEM-solution for single element)

FEM and DEM use second order Gear-Predictor-Corrector (BDF2) for time integration

FEM uses Newton-Raphson iteration to solveflow field within a timestep

2 Limitations of FEM

High particle densities result in tiny pore space→ needs to be discretized for the FEM

Increasing flow rate in pore space → curvaturein flow cannot be sufficiently approximated bysecond order function anymore

True Flow Field

P0 Finite Element

P1 Finite Element

P2 Finite Element

1. Solution: Increased mesh resolution → muchhigher computational cost

2. Solution: Allowing higher (third) order curva-ture for FEM-polynomials

→ For verification, look at current FEM-solutionfor elements and whole geometry is necessary

3 Creating the Sub-Mesh

Two dimensional element functions best dis-played with MATLAB’s trisurf command (be-cause of triangular finite elements)

- trisurf requires set of coordinates and corre-sponding function values

- Raw FEM solution data provides only 6 valueson the element circumference

→ Higher order functions (velocity is second or-der) require sub-mesh for every finite elementto display curvature with decent quality

For arbitrary sub mesh resloution res, elementscan be subdivided with MATLAB’s linspace

Xl =x3 − x1

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- trisurf also requires Delaunay triangulationbetween points

- Limited numerical accuracy → points not ar-ranged on perfectly straight lines → degenerateDelaunay triangles at element edges

→ Equilateral ”dummy” triangle with slightly con-vex outline: linspace limits are extended by± 0.2*sin(i*pi/res) respectively

- Delaunay triangulation of ”dummy” trianglethen mapped to actual finite element

4 Visualizing Basis Functions

- FEM-solution data of a specific mesh node isthe multiplicator for the basis function corre-sponding to that node (basis function is non-zero at that node)

- First order basis functions correspond tobarycentric coordinate functions of the triangle[1], → also form the Lagrange basis [3] for thetriangle’s corner points in two dimensional space

- Coefficients for those Lagrange polynomials canbe easily acquired with use of MATLAB’s ”\”operator [4]

s = [1 1 1]’

polyCoeff = [s triangle]\ eye(3)⎡⎣A0 B0 C0

Ax Bx Cx

Ay By Cy

⎤⎦ =

⎡⎣1 x1 y11 x2 y21 x3 y3

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⎡⎣1 0 00 1 00 0 1

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- Use anonymous functions to represent the threefirst order (pressure) basis functions with theabove coefficients

LagA = @(x,y) A0+Ax*x+Ay*y;

LagB = @(x,y) B0+Bx*x+By*y;

LagC = @(x,y) C0+Cx*x+Cy*y;

- All six second order (velocity) FEM-basis Func-tions are products of the first order basis func-tions (remaining four are permutations of theones shown)

Lag2A = @(x,y) 2*(LagA(x,y)).^2-LagA(x,y)

Lag2D = @(x,y) 4*LagB(x,y).*LagC(x,y)

- For a single element, each basis function is mul-tiplied with the FEM-solution data of it’s corre-sponding mesh point and all are summed up togive the complete element function

- The element function is then handed the coor-dinate vectors of the sub-mesh X, Y to providethe function values via an implicit loop

- Element function can then be plotted viatrisurf

- Loop over sub-mesh generation and building ofthe element function allows for display of mul-tiple elements (even whole geometry)

5 Findings

- FEM-solution for pressure p, horizontal u andvertical velocity v → when particles get closer,first creases appear in the solution function

p u v

- Severe creases and spikes within the FEM-solution of the flow field (here shown for hori-zontal velocity u), when particles get very closeat higher velocitiesat higher velocities

- Flow field should remain smooth, similar to so-lutions for lower speeds

- Finer mesh resolution improves solution qualityfor same state

→ However: same issues arise again, when particledensity or velocity increase further

- Solution quality not affected by particle rotation(locking/unlocking rotatoional degee of free-dom)

6 Outlook

- Enhancing Taylor-Hood Elements with cubic”Bubble” (P+

2P1) will allow them to better fit

curvature of flow field

→ FEM-solution of the flow field should remainsmooth for higher particle densities and veloci-ties

- Visualization already works for finite elementsof up to third order (can be implemented forarbitrary orders)

7 References

[1] Shi Han Ng. Two-Phase Dynamics ofGranular Particles in a Newtonian Fluid.PhD thesis, The University of Electro-Communications, Department of Mechan-ical Engineering and Intelligent Systems,2015.

[2] Philip M. Gresho and Robert L. Sani. In-compressible Flow and the Finite ElementMethod Volume 2: Isothermal LaminarFlow. John Wiley and Sons, Ltd., 2000.

[3] Ionut Danaila, Pascal Joly, Sidi MahmoudKaber, and Marie Postel. An Introduc-tion to Scientific Computing Twelve Com-putational Projects Solved with MATLAB.Springer, 2007.

[4] G. J. Borse. Numerical Methods with MAT-LAB. PWS Publishing Company, 1997.

結果表示 　Motilityを元絵にブレンドした画像（各入力画像ごとに生成） 　Motilityの値をチェックする　　　　輝度勾配の大きさと方向を 　ための3D画像　　　　　　　　　　チェックするための画像

MRI動画像を用いたクローン病活動評価のための解析ツール開発

発表者：　株式会社システムラボラトリ　小澤　泰生　（ozawa@algo-dev.com） （共同研究委託元：　東京医科歯科大学　医学部付属病院　放射線診断科　北詰　良雄先生）　

　MRでクローン病の活動性評価を行う際、高速撮影法を連続撮影することで得られる動画（cine MRI）を用いて評価できることが最近報告されたが、処理が複雑で結果を得るのが困難であった。 　今回、cine MRI動画に、オプティカルフロー・アルゴリズムを適用し、診断で有用なmotility mapを簡易に生成するツールをMATLABを用いて開発した。

Motility mapping 　クローン病活動評価には、motility mapを作成する。これはcine MRI画像に対して前処理を行った後、Horn-Schunck の方法を用いてオプティカルフローを求め、その大きさを用いてmapを作成するものである。

作成ツール 　Motility map作成ツールは、cine MRのDICOM形式の画像を入力として、各相のmotility mapの計算と、すべての相での平均値、最大値、分散を求めて、表示することができる。 　また、計算したmotility mapと、平均値、最大値、分散の結果データを、DICOM形式、およびPNG形式で保存することができる。

必要なMATLABとToolbox 　MATLAB R2017b以降 　Image Processing Toolbox

設定画面 　フォルダ設定 　解析設定 　出力画像設定 　解析前の設定チェック 　解析・出力開始

関心領域（ROI）の設定 　スライスごとに、ROIを設定できる。 　ROIが設定されているスライスに関して、 　オプティカルフローの計算を行う。

　 　計算アルゴリズムは 　右図の通り。　

　説明員によるデモや解説を行っているので、ご覧ください。

References1.  Hahnemann M, Nensa F, Kinner S, Gerken G, Lauenstein T, Motility mapping as evaluation tool for bowel motility: Initial results on the development of an automated color-coding algorithm in cine MRI, J Magn Reson Imaging. 2015;41;354-360.

2.  Odille F, Menys A, Ahmed A, Punwani S, Taylor SA, Atkinson D. Quantitative assessment of small bowel motility by nonrigid registration of dynamic MR images. Magn Reson Med. 2012;68:783‒793.

3.  Horn BK, Shunk BG. Determining optical flow. Artif Intell. 1981; 185-203.

株式会社システムラボラトリ 　小澤　泰生　（ozawa@algo-dev.com） 住所：横浜市中区尾上町５-８０　中小企業センタービル７階インキュベートオフィス Web:　https://www.algo-dev.com/　　（アルゴリズム開発センター）

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