Image analysis Biomedical images are analyzed in order to get - - PDF document

Lesson 10 Bioimaging analysis: estimation of diffusion parameters from Diffusion-Weighted Magnetic Resonance Imaging (for the recognition of tumor tissues).

Ettore Lanzarone April 9, 2020

MEDICAL SUPPORT SYSTEMS FOR CHRONIC DISEASES

Engineering and Management for Health University of Bergamo

LESSON 10

Image analysis

Biomedical images are analyzed in order to get information of interest with a non invasive approach:

• Screening of patients
• Pre surgical analysis
• Research studies on healthy subject
• …

Lesson 10

Image analysis

Information can be classified as:

• Anatomic information
• Anatomo-functional information

Information about the geometry of the observed districts (shapes, dimensions, connections, …) Also mechanical (or chemical, electrical, …) information derived from the motion of the image between subsequent acquisition.

Image analysis

Information can be classified as:

• Anatomic information
• Anatomo-functional information

One single image of the district of interest, possible with high resolution to detect boundaries. Several subsequent images acquired on the same patient, to detect the movement of the structure of interest.

• Based on the observed movement, through a proper decision support system (a

mathematical model), the moment information is converted into knowledge of the properties of interest.

Lesson 10

Image analysis

We will analyze two relevant examples in this field: 1. Diffusion-Weighted Magnetic Resonance Images to estimate maps of the diffusion properties in a tissue. Alteration of such properties are considered ad biomarkers, e.g., of tumoral tissues. 2. Computed Tomography Angiography to detect the aortic stiffness. Altered aortic stiffness is at the basis of several systemic pathologies.

DW-MRI and IVIM model

Diffusion-Weighted Magnetic Resonance Imaging (DW-MRI) is the use

• f specific MRI sequences, as well as of software that generates

images from the resulting data, that uses the diffusion of water molecules to generate contrast in MR images. This technique allows to map the diffusion process of molecules (mainly water) in biological tissues, and this mapping is performed in- vivo and non-invasively.

Lesson 10

DW-MRI and IVIM model

Diffusion of water and other molecules in tissues is important because such diffusion is not free, but it reflects interactions with the

• bstacles present in the tissue, e.g., macromolecules, fibers,

and membranes. Water molecule diffusion patterns can therefore reveal microscopic details about tissue architecture, either normal or in a diseased state (e.g. tumors).

DW-MRI and IVIM model

However, in DW-MRI the movement of molecules is only given by diffusion but it reflects also convective movements (e.g., in blood vessels). Thus, the movement is modeled as a diffusion component and a pseudo-diffusion component that accounts for the other sources of movement (e.g., convection).

Lesson 10

DW-MRI and IVIM model

The motion of the molecules is described by the IntraVoxel Incoherent Motion (IVIM) model. Le Bihan, father of modern diffusion imaging, coined the term IVIM in the 1980s to refer to the microscopic translation of water molecules within a voxel during an MR experiment. When gradients are applied during evolution of the MR signal, IVIM causes spin dephasing and signal loss.

• If the gradients are relatively strong, IVIM-induced signal losses

are primarily due to diffusion, i.e., to the Brownian motion of water molecules in and around cells.

• When weaker gradients are used, a second IVIM mechanism also

contributes to signal loss: the convective motion due to the microcirculation of blood in the capillary network.

DW-MRI and IVIM model

If only diffusion effects are considered, MR signal intensity in a voxel (S) is expressed as:

S = So e−bD

where:

• b is a factor reflecting the strength and duration of the pulsed

diffusion gradients for the specific image [s/mm²]

• So is the signal in the voxel at the baseline (the morphologic MRI

without diffusion-sensitizing gradients)

• D is the diffusion coefficient that characterizes the tissue [mm²/s]

Lesson 10

DW-MRI and IVIM model

Under this model, a semi-logarithmic plot of signal attenuation ln(S/So) vs b should be a straight line with slope -D. However, considerable departures from this simplified mono-exponential model are observed when considering real data:

• At b ≤ 300 − 500 s/mm² the signal attenuation is greater

than expected due to increased IVIM loses from microscopic perfusion;

• At b ≥ 1000−1500 s/mm², signal attenuation is often

less than expected due to other secondary effects.

DW-MRI and IVIM model

The effect of perfusion is included in the IVIM model, which becomes the following biexponential model:

S = So [f  e−b(D+D*) + (1-f ) e−bD ]

f is the perfusion fraction, i.e., the percent of a voxel volume occupied by capillaries. Conversely, 1−f reflects the extravascular space where

• nly diffusion effects take place.

D* is the pseudo-diffusion coefficient and reflects dephasing due to perfusion in semi-randomly organized capillaries.

Lesson 10

DW-MRI and IVIM model

By acquiring DW-MRI images at several b-values and fitting the data to above equation, it is possible to estimate f, D, and D* in each observed voxel and to create maps for each region of interest. Typically, between 6 and 10 images are obtained with b-values ranging from 0 to 1000 s/mm², with at least half of the measurements performed b < 250 s/mm².

DW-MRI and IVIM model

Segmentation

To better identify the parameters, the fitting is usually divided into two steps. At the first step, the initial image at b=0 and the images at 𝑐𝑐 are used to estimate D and an approximation of 𝑔

• f f.

The following simplified model is used: The estimation of D is kept while 𝑔 is discharged

(i,j) refers to the coordinates

• f a voxel in a 2D image

(layer of a 3D image)

Lesson 10

DW-MRI and IVIM model

Segmentation

At the second step, D is known and the complete model is used to estimate f and D*. All of the images at the different b are used in this step.

(i,j) refers to the coordinates

• f a voxel in a 2D image

(layer of a 3D image)

DW-MRI and IVIM model

References

• Le Bihan D, Breton E, Lallemand D, et al. MR imaging of intravoxel incoherent

motions: applications to diffusion and perfusion in neurologic disorders. Radiology 1986; 161:401-407.

• Le Bihan D, Breton E, Lallemand D, et al. Separation of diffusion and perfusion in

intravoxel incoherent motion MR imaging. Radiology 1988; 168:497-505.

• Koh D-M, Collins DJ, Orton MR. Intravoxel incoherent motion in body diffusion-

weighted MRI: reality and challenges. AJR Am J Roentgenol 2011; 196;1351-1361.

• Du J, Li K, Zhang W, et al. Intravoxel incoherent motion MR imaging: comparison
• f diffusion and perfusion characteristics for differential diagnosis of soft tissue
• tumors. Medicine 2015; 94:1-8.
• Iima M, Le Bihan D. Clinical intravoxel incoherent motion and diffusion MR

imaging: past, present and future. Radiology 2016; 278:13-32.

Lesson 10

DW-MRI and IVIM model

Some interesting results of have been reported for tumors of prostate, liver, and soft tissues, where perfusion fractions have been shown to correlate with other methods of assessing vascularity. However, one of the main criticalities is the noise of the obtained maps.

DW-MRI and IVIM model

The simplest approach is to estimate the parameters in a voxel-wise manner, in which the parameters are independently estimated for each voxel (with or without segmentation). How to reduce noise?

Lesson 10

DW-MRI and IVIM model

How to reduce noise?

• Replace the estimated parameters in each voxel with the average value over 9 voxel

(the considered one and the 8 voxels around).

• Clusterize the images (e.g., that at b=0) to divide the image into region, in order to

perfom the average of the estimated parameters over a homogeneous region.

• To include the averaging in the estimation approach. For example, the averaged signal
• ver the 9 voxels can be used.
• More complex approaches to include a spatial structure in the estimation approach (I

will show you a Bayesian approach next time).

Practical lesson

In the simplest case, the voxel-wise minimization of the MSE is not linear (no linear solvers as CPLEX can be used) but it is very simple and can be performed even with the optimizer module contained in EXCEL. Or with the solvers available in MATLAB (e.g., function fmincon).

Example for a single voxel with the EXCEL

• ptimizer module:

1) See how to install the module 2) See the example

Lesson 10

Practical lesson

In the attached material, besides the EXCEL example file, I provide you:

• A simulated dataset (concentric squares) with SNR=20
• A simulated dataset (concentric squares) with SNR=80
• Data from a real patient (head and neck images)

In all cases: b={0;25;50;75;100;150;300;500;800}

Practical lesson

The tasks to perform are: 1. Draw and observe the anatomic MRI for the real patient (image at b=0) 2. Draw a map of the three parameters D, D* and f for both the simulated dataset and the real patient, using a voxel-wise approach (i.e., estimate each voxel independently).

• Create an excel file where the same operations are repated over all matrix
• r create a matlab routine.
• Feel free to use the segmented approach or not.

1. Observe the maps and discuss the noise (variability of the parameters within the concentric squares, for simulated images, or within the same anatomical region, for real images). 2. Try one of the approaches to reduce the noise (see proposals at Slide 20).

Lesson 10

Practical lesson