Rahul Lung Ctsim Report

Project Report 3D Lung Model & CT Simulator Under Supervision of~ Prof.Benjamin B. Kimia

By: Rahul Gautam

How this began… • The NIH Proposal 2003~ Model-based Tomographic Reconstruction of Vessel Networks

Aims of the Proposal~ •

Develop algorithms for the direct tomographic reconstruction of pulmonary vessel networks based on a 3-d representation of vessels and junctions

•

Demonstrate the accuracy of the reconstructed network for x-ray CT using manual segmentation as ground truth.

Preparing the way~ • A search for good 3D Lung model... Options? ....Many Chose… One of the best available…

Our Choice… ‘A three-dimensional model of the human airway tree’ By~ Prof. Hiroko Kitaoka, Ryuji Takaki, and Béla Suki

The Reason… • This algorithm generates geometric data of a three-dimensional human airway tree whose morphometric characteristics are in good agreement with those reported in the literature

The basic Principle • generation of the dimensions and directionality of two daughter branches is governed by the properties of the parent branch and the region the parent supplies • The terminal branches of the tree are homogeneously arranged within the organ

The Rules • The algorithm is composed of nine basic rules and four complementary rules.

Rules… • ~ Branching is dichotomous. • ~ The parent branch and its two daughter branches lie in the same plane, called the branching plane. • ~ The volumetric flow rate through the parent branch is conserved after branching; that is, the sum of the flows in the daughter branches is equal to the flow in the parent branch.

Rules…Continued • ~The region supplied by a parent branch is divided into two daughter regions by a plane called the "space-dividing plane." The space-dividing plane is perpendicular to the branching plane and extends out to the border of the parent region • ~ The flow-dividing ratio is set to be equal to the volume-dividing ratio, defined as the ratio of the volume of the smaller daughter region to that of its parent.

Rules … few more • ~The length of each daughter branch is assigned a value that is three times its diameter • If branching continues in a given direction, the daughter branch becomes the new parent branch, and the associated branching plane is set perpendicular to the branching plane of the old parent

Just a few more… • The branching process in a given direction stops whenever the flow rate becomes less than a specified threshold or the branch extends beyond its own region. THAT’S IT

So the first step… • Applied the algorithm to generate 3D Lung data

The Result…

Oops…A Problem • Rough edges , abrupt at branching points…. Unrealistic if used to model a lung

The Solution… Generate a Volumetric model,

…apply Gaussian Smoothing to it,

Use Marching cubes to extract surface..

The Outcome…

Breaking News… • Brown Eyes now has… 3D Lung Model Generator…

Mission 3D Lung Model…

… Accomplished

The Next Step… Step ...Mission CT

• To obtain a CT Simulator… that performs CT scan on virtual 3D models and generate projection data

CT…????

CT~ Computed Tomography

(From Siemens) (From Picker)

CT is ~ the general process of transmitting X-rays and creating cross-sectional or tomographic images from projections of the object at multiple angles and using a computer for image reconstruction

Projection measurement…

Exponential attenuation of Xrays − µ∆x Ni

No = Nie

No

Ni: input intensity of X-ray No: output intensity of X-ray µ: linear X-ray attenuation

µ ∆x Ni

µ

µ

µ

1

2

3

X-rays

No

No = Nie

− ( µ1 + µ 2 + µ 3 ) ∆ x

x

Attenuated more

Ray-Sum of X-ray Attenuation Ni

No

µ κ

∆x

Ray-sum

Ni ∑ µ k ∆ x = ln k No

Line integral ∞

Ni ∫− ∞ µ ( x)dx = ln N o

Projection & Sinogram Projection: All ray-sums in a direction P(θ,t)

y

Sinogram: All θ projections

t π θ

x

f(x,y) X-rays

Sinogram

t

Scanning modes

First Generation One detector Translation-rotation Parallel-beam

Second Generation Multiple detectors Translation-rotation Small fan-beam

Third Generation Multiple detectors Translation-rotation Large fan-beam

Fourth Generation Detector ring Source-rotation Large fan-beam

Spiral/Helical Scanning Simultaneous

•Source rotation •Table translation •Data acquisition

Cone-Beam Geometry Z

Y

X

Back to the Problem…

..Mission CT

Our Requirements... • Cone Beam CT • Should scan 3D phantom objects • Close to a real CT scanner

Here we go again…

Event: .. Birth of CTSim • Specifications Resolution ….Variable Magnification ….Variable Spot size detector…. As desired Spot size source…..point No beam hardening No Quantum noise

The Outcome….

The Result…

Too good to be Real

Keeping it Real…. Accounting for factors like… ~Photon statistics/quantum noise ~Spot size ~Beam Hardening

Quantum noise

The Outcome… • Background Noise Comparison…

Spot Size…Source

Outcome…

Sinograms…

Finally what we have… • CTSim has found its new home in Brown eyes

CTSim In action…

The Road ahead… Making CTSim more realistic by including effects like beam hardening.

Special thanks to these great guys… Amir

Vishal

Ming

Ozge

Last but not the least… Prof. Benjamin B. Kimia for guiding me all the way.

Easy questions Plz…

Thank You