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

Lesson 10 University of Bergamo Engineering and Management for Health FOR CHRONIC DISEASES MEDICAL SUPPORT SYSTEMS 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 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 Information about the geometry of the observed districts (shapes, dimensions, connections, …) • Anatomo-functional information 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 One single image of the district of interest, possible with high resolution to detect boundaries. • Anatomo-functional information 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 of 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 obstacles 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 = S o  e −b  D where: • b is a factor reflecting the strength and duration of the pulsed diffusion gradients for the specific image [s/mm²] • S o 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/S o ) 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 = S o  [ 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 only 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 � of f . and an approximation of 𝑔 The following simplified model is used: (i,j) refers to the coordinates of a voxel in a 2D image (layer of a 3D image) � is discharged The estimation of D is kept while 𝑔

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* . (i,j) refers to the coordinates of a voxel in a 2D image All of the images at the different b are used in this step. (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 of 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 over 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 optimizer module: 1) See how to install the module 2) See the example