WO2006099339A2

WO2006099339A2 - A fiber coherence index apparatus and method for imaging and characterizing fibrous structures

Info

Publication number: WO2006099339A2
Application number: PCT/US2006/008973
Authority: WO
Inventors: Xiaohong Joe Zhou
Original assignee: University of Illinois System
Current assignee: University of Illinois System
Priority date: 2005-03-14
Filing date: 2006-03-10
Publication date: 2006-09-21
Anticipated expiration: 2007-09-14
Also published as: WO2006099339A3

Abstract

A method to process a diffusion tensor imaging (DTI) dataset includes the steps of: acquiring a set of diffusion-weighted images with varying diffusion-weighing gradient directions; acquiring an additional image without a diffusion-weighting gradient, or acquiring a second set of diffusion-weighted images with varying diffusion-weighing gradient directions; calculating the diffusion tensor matrix at each and every voxel location based on the images acquired; calculate the principal eigenvector from the said diffusion tensor matrix at each and every pixel location; computing a fiber coherence index (FCI) for a given voxel, based on directional coherence between the said voxel and the vocels close to it; said computing is performed using the principal eigenvector; computing a regional fiber coherence index (r-FCI) by averaging individual FCI within a region of interest.

Description

A FBER COHERENCE INDEX APPARATUS AND METHOD FOR IMAGING AND CHARACTERIZING FIBROUS STRUCTURES

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority to US Provisional Application 60/662,064 filedMarch ll. 2005. BACKROUND OF THE INVENTION FIELD OF THE INVENTION

[0002] This invention is in the field of diagnostic medical imaging using a novel fiber coherence index. RELATED ART

[0003] Gliomas are the most common type of primary brain tumor in adults.

Recent statistics have shown that the incidence of malignant gliomas is increasing, especially among the elderly population. (Wrensch M, Minn Y, Chew T, Bondy M, Berger MS. Epidemiology of primary brain tumors: Current concepts and review of the literature. Neuro- Oncology 2002;4:278-299, incorporated by reference herein.) Despite significant advances in diagnostic imaging, neurosurgery, radiation oncology, and chemotherapy, the prognosis for most patients remains dismal. For example, the median survival for patients with glioblastoma is approximately one year, even after treatment with surgical resection, external beam radiation, and (or) chemotherapy.

[0004] Patients with malignant gliomas are typically treated with surgical resection followed by external beam radiotherapy (or combination of radiation and

chemotherapy). Due to the infiltrating nature of the malignant tumors, most patients experience tumor recurrences within a few centimeters of the original resection site. The inability to determine accurately the extent of tumor infiltration has greatly compromised the efficacy of surgical resection, radiation, and intratumoral chemotherapy. In radiotherapy, for example, a recent study shows that very high doses (up to 90 Gy) can sterilize gliomas, but introduce considerable necrosis in normal brain tissues. (Fitzek MM, Thornton AF, Rabinov JD, Lev MH, Pardo FS, Munzenrider JE, Okunieff P, Bussiere M, Braun I, Hochberg FH, Hedley-Whyte ET, Liebsch NJ, Harsh GR. Accelerated fractionated proton/photon irradiation to 90 cobalt gray equivalent for glioblastoma multiforme: results of a phase II prospective trial. Journal of Neurosurgery 1999;91:251-260, incorporated by reference herein.) Since the extent of tumor infiltration cannot be determined using existing diagnostic imaging techniques, radiation oncologists are facing the dilemma in deciding the proper radiation field; a smaller field than needed will not adequately kill tumor cells, whereas a larger radiation field will damage normal brain tissues and compromise or even disable the patient's neurological functions.

[0005] Despite advances in diagnosis and treatment, the prognosis remains poor partly due to the infiltrating nature of the tumor cells and the inability to detect these cells unambiguously using conventional diagnostic imaging techniques. There is a need in the art to develop and validate a quantitative marker for in vivo assessment of tumor cell infiltration along the white-matter fiber tracts using diffusion tensor (DT) magnetic resonance imaging (MRI). Such a marker should provide higher sensitivity and better specificity over existing imaging techniques in identifying tumor infiltration. This capability will improve radiotherapy and surgical resection to maximally eradicate the tumor cells without unnecessarily compromising neurological functions of the patient. Such a marker would also be advantageously used in studying pathologies in any other fibrous structures or tissues.

[0006] When a brain tumor is clinically suspected, MRI is the most common radiological method to detect and characterize the lesion. Conventional MRI (e.g., pre- and post- contrast Tl-weighted, T2-weighted, and fluid-attenuated inversion recovery imaging), combined with more advanced techniques (e.g., dynamic, perfusion, spectroscopic, and functional imaging), has allowed brain tumors to be evaluated based on not only their morphology but also vascular permeability, metabolism, and function. However, tumor cells can extend far beyond the abnormality observed with existing imaging techniques. MRI, MR spectroscopy (MRS), and other imaging modalities have not been able to reveal a clear margin where tumor cells stop and reactive gliosis, edema, or normal brain parenchyma begins, especially in the case of gliomas. The inability to define the extent of tumor infiltration has limited clinicians' ability to determine the extent of surgical resection, the field of radiation, as well as the strategies for intratumoral local chemotherapy. These limitations have led to compromised treatment efficacy and suboptimal outcome. A non-invasive imaging method that is capable of delineating tumor- infiltrated tissue from healthy brain tissue is needed.

[0007] Diffusion tensor imaging (DTI), may be used as a tool for characterizing tissue diffusion in vivo, and may also be used as a basis from which to assess the extent of tumor cell infiltration. Prior art DTI examples include US Patent No. 6,463,315 Bl to Klingberg et al., and US Patent No. 6,642,716 Bl to Hoogenraad et al., which are incorporated by reference herein.

[0008] Diffusion is a stochastic thermal phenomenon characterized by Brownian motion. The behavior of unrestricted molecular diffusion is described by the Einstein equation:

r_rmii = sfwi (1)

[0009] where r_rms is the three-dimensional root-mean-squared (rms) displacement, t is the diffusion time, and D is the diffusion coefficient. Sometimes, Equation 1 can be reduced to its one-dimensional form:

where τ_rmSf i_d represents the one-dimensional rms displacement.

[0010] In biological tissues, diffusion of water molecules is affected by the presence of macromolecules, organelles, cell membrane, and other cellular and sub-cellular structures (Le Bihan D. Diffusion and perfusion magnetic resonance imaging: applications to functional MRI. New York, NY: Raven Press; 1995) incorporated by reference herein. These structures manifest themselves as obstacles to molecular diffusion and can considerably reduce the diffusion coefficient of water. Generally, restrictions on water diffusion imposed by macromolecules and tissue structures do not have spherical symmetry. The restriction in one direction can be considerably greater than that in other directions. This causes a phenomenon known as diffusion anisotropy, which means diffusion varies with spatial directions. For example, white-matter fiber tracts in the central nervous system consist of bundles of myelin- covered axons grouped together along certain pathways. Because of this directional linkage and connectivity, water molecules diffuse more freely along the fiber tracts than in other directions. In addition to white-matter fiber tracts, diffusion anisotropy can also be found in other tissues, such as myocardium.

[0011] Water molecular diffusion in an anisotropic diffusion medium, such as the white matter, may be described by multiple diffusion coefficients to account for the directional dependence. Mathematically, the directional dependence can be characterized by a second rank tensor, which is cast in a 3 x 3 matrix:

[3] [0012] Each of the six independent matrix elements in Eq. [3] represents a unique diffusion coefficient defined in a laboratory reference frame with x, y, and z being the spatial coordinates.

[0013] A matrix element along the diagonal corresponds to diffusion along the axis indicated by the subscript, and an off-diagonal element represents the degree of correlation between diffusion in the two axes denoted by the subscripts. All elements of the diffusion tensor are real, and the matrix is symmetric.

[0014] An intuitive description of the diffusion tensor is that the diffusion boundary at each spatial location is ellipsoidal. The axes of the diffusion ellipsoid correspond to three characteristic diffusion coefficients D], D ₂, and D₃, which are the eigen values of the matrix in Eq. [3]. Each eigen value corresponds to an eigenvector. The eigenvector of the largest eigenvalue is called the primary eigenvector.

[0015] In the presence of a magnetic field gradient G_j molecular diffusion

attenuates signals in MRI. The degree of attenuation depends on a dimensionless product of an effective diffusion coefficient D' (in units of maP/s) and a quantity known as b-factor or b- value (in units of s/mm²):

S=S_oe-^bD' W where S and So are the signal intensities with and without diffusion-induced attenuation, respectively.

[0016] D' in Equation 4 represents an effective diffusion coefficient along the

direction of the diffusion gradient whose direction cosine vector is α , where

α_x OCy, and α_z. are the vector components, and the superscript represents matrix transpose. This

effective diffusion coefficient is related to the diffusion tensor by B'=a^τ - {DJ. χ

[0017] In healthy brain, white-matter fiber tracts consist of bundles of myelin- covered axons grouped together along certain pathways. Because of this directional linkage and connectivity, water molecules diffuse more freely along the fiber tracts than in other directions. The fiber direction, or the principal diffusion direction, can be obtained from the direction of the primary eigenvector. In contrast, diffusion in the other tissues, such as gray matter, is less directionally dependent. By characterizing this diffusion anisotropy at each spatial location, the fiber tracts can be distinguished from the other tissues and the fiber orientations mapped in three dimensions.

[0018] It has been reported that glioma infiltration occurs preferentially along the white-matter fiber tracts. With tumor invasion, the organized structure of a fiber tract can lose its structural integrity, leading to changes in the diffusion properties of water molecules. A common site of infiltration is the corpus callosum where glioma can extend across the midline to spread to other locations of the brain. With tumor invasion, the organized structure of a fiber tract can lose its structural integrity and directional coherence, leading to changes in the diffusion properties of water molecules (i.e., tumor cell infiltration along the white-matter fiber tracts causes fibers to lose structural integrity and directional coherence, resulting in changes in the molecular diffusion properties of water). There is a need in the art to measure the changes in fiber coherence and relate the fiber coherence changes to tissue pathologies. There is a particular need for an index specific to tumor cell infiltration even in the presence of peritumoral vasogenic edema, which typically occurs with high-grade gliomas. [0019] Recently, several groups attempted assessing tumor cell infiltration using diffusion tensor imaging (DTI). DTI, or diffusion tensor magnetic resonance imaging (DT- MRI), is a technique that measures the orientation dependence (i.e., anisotropy) of the diffusion process. (Basser PJ, Mattiello J, Le Bihan D. MR diffusion tenser spectroscopy and imaging. Biophysical Journal 1994;66:259-267, incorporated by reference herein.) This technique relies on diffusion-induced MRI signal loss as a function of diffusion-weighting gradient orientations as described by Eq. [4]. With DTI, the diffusion tensor at each spatial location (i.e., a pixel or a voxel) can be fully characterized, and a series of parameters can be obtained to describe various aspects of the diffusion process in biological tissues. Typical parameters calculated from DTI include apparent diffusion coefficients (ADC), diffusion anisotropy indices, and the principal diffusion direction. These parameters can be used to reveal certain tissue structures, such as white-matter fiber tracts in the brain, and monitor their changes during disease progression and regression. Published studies have primarily focused on measuring changes in a scalar diffusion anisotropy index, such as fractional anisotropy (FA), or relative anisotropy (RA). The essential idea is that tumor invasion can cause the organized structure of the fiber tracts to lose integrity, allowing water molecules to diffuse more isotropically. While this approach can be useful in evaluating low-grade gliomas without peritumoral vasogenic edema, it often fails on patients with high grade gliomas (WHO grade III and IV) due to the presence of peritumoral vasogenic edema, which can also cause a substantial decrease in diffusion anisotropy. Since the edematous regions are not always infiltrated with tumor, a very high false positive rate occurs when using FA or RA to identify tumor infiltration. Sinha et al. recently reported that the mean diffusivity can be used to differentiate normal white matter, edema, and enhancing tumor margins but that FA added no benefit to tissue differentiation. See, Sinha S, Bastin ME₅ Whittle IR, Wardlaw JM. Diffusion tensor MR imaging of high-grade cerebral gliomas. American Journal of Neuroradiology 2002;23:520-527. Studies performed by Sinha and others have suggested that DTI has the potential for studying tumor cell infiltration, but fell short of realizing the potential using the common diffusion anisotropy indices such as RA or FA. Clearly, an alternative index to FA and RA, that is both sensitive and specific to tumor cell infiltration, must be sought.

[0020] There is a need in the art for a new diagnostic tool for in vivo assessment of tumor invasion in malignant gliomas. Neurosurgeons, neuro-oncologists, and radiation oncologists have a need for a more sensitive and specific index to optimize patient treatment and management strategies, and lead to improved outcome patients with gliomas or other white- matter diseases.

SUMMARY OF THE INVENTION

[0021] The present invention is a Fiber Coherence Index (FCI). Unlike the scalar indices such as FA and RA, the FCI is based on fiber directional coherence among a cluster of

voxels within a region of interest in a fiber tract. The fiber orientation ( X_j ) at voxel j can be

approximated by the principal diffusion direction in that voxel, which can be measured using DTI. After the individual fiber orientations are determined for a cluster of voxels in the fiber, the FCI for voxelj can be simply calculated using Eq. [6]:

[6] where i is the index for the voxels in the close proximity of the 7th voxel, λ± is a fiber

orientation of the zth voxel, g(ij) is a weighting function that defines the spatial extent over which the summation is performed, and N is the total number of voxel pairs used for the inner product calculation. To calculate a regional FCI (r-FCI) within a Region of Interest (ROI) containing M voxels, the individual FCI values can be simply averaged according to Eq. [7].

[0022] The mathematical formulae for calculating FCI and r-FCI are not limited to those described by Eqs. [6] and [7]. Alternative formulae are described in the "Detailed Description" section.

[0023] Fig. 1 depicts an FA map of the brain. Figs. 2 and 3 show the principal diffusion directions for a cluster of pixels (white box in Fig. 1), as represented by the arrows.

The λ: arrow at the center shows the principal diffusion direction for the pixel of interest, while

the black arrows show the principal diffusion direction for its neighboring pixels. Without pathology, for example, tumor infiltration, a high degree of vector coherence is illustrated with all vectors pointing to the same direction, as in Fig 2. With pathology such as tumor infiltration (shown by the "explosive" patterns in Fig. 3), the fiber coherence is reduced.

[0024] The definitions given by Eqs. [6] and [7] normalize FCI and r-FCI values between 0 and 1. When FCI=O, the fiber direction for the voxel of interest has no directional coherence with respect to its neighbors. When FCI=I, the fiber direction for all voxels involved in the calculation points along the same direction (Fig. 2); that is the fibers are completely coherent. In a general case, FCI should be between these two extreme values with coherent fibers showing a higher FCI and less coherent fibers showing a lower FCI. These properties equally apply to r-FCI.

[0025] For healthy intact fiber tracts, a high degree of fiber coherence is expected within a small localized region (Fig. 2). With tumor cell infiltration, the fiber coherence can be compromised, leading to a reduced FCI value (Fig. 3).

[0026] The r-FCI exhibits marked differences between fibers infiltrated with tumor and fibers presumably affected by vasogenic edema. This is most likely because edema does not affect the fiber orientations as much as aggressive tumor invasions. In contrast, the FA (or RA) values of the fibers with both pathologies were essentially the same. The invention differentiates edema effect from tumor infiltration, thereby providing new insights into glioma diagnosis and patient management. Diseases affecting any fibrous tissues may be advantageously studied using the Fiber Coherence Index. Diseases of the central nervous system that may be studied with the present invention, without limitation, include in addition to tumors, multiple sclerosis, arteriovenous malformations, stroke and other neurological diseases.

[0027] Further areas of applicability of the present invention will become apparent from the detailed description provided hereinafter. It should be understood that the detailed description and specific examples, while indicating the preferred embodiment of the invention, are intended for purposes of illustration only and are not intended to limit the scope of the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

[0028] The present invention will become more fully understood from the detailed description and the accompanying drawings, wherein:

[0029] Fig. 1 is a FA map of the brain,

[0030] Fig. 2 shows coherent principal diffusion directions for a cluster of pixels,

[0031] Fig. 3 shows incoherent principal diffusion directions for another cluster of pixels,

[0032] Fig. 4 is a graphic depiction of an edge detection technique.

DETAILED DESCRIPTION

[0033] The following description of the preferred embodiment(s) is merely exemplary in nature and is in no way intended to limit the invention, its application, or uses.

[0034] In DTI data acquisition, a diffusion- weighting gradient G _d (t) with an amplitude G^ is applied to the imaged subject. The diffusion-weighting gradient changes its

direction in 3D along N non-collinear and non-coplanar directions; G _di, G _d2,... G _dN- At each orientation, a diffusion-weighted MR image is obtained, typically using a fast pulse sequence, such as a single-shot echo planar imaging (EPI) pulse sequence. The intensities of these images, denoted by S₁, S₂, S₃, ..., SM can be mathematically expressed as where j is the index of the diffusion gradient orientation (j = 1, 2, 3, ..., N), and the other variables have been defined in Eqs. [4] and [5]. Note that index j in Eq. [8] should be distinguished from the index j in Eqs. [6] and [7] for FCI calculations.

[0035] In Equation 8, b-value and ά are user-selectable acquisition parameters. So can be acquired by setting the diffusion gradient amplitude to zero while keeping all other acquisition parameters identical to those used to acquire S_j. This image, together with the diffusion-weighted images Sy, S^, S3,...,S_N, is sufficient to calculate the diffusion tensor from Equation 8, provided that N is no less than six because there are six independent elements in the diffusion tensor matrix (Equation 3).

[0036] The diffusion gradient direction is controlled by varying its vector components (i.e., the direction cosines) along the three orthogonal axes. The number of diffusion gradient directions (N), together with the spatial distribution of these directions, is collectively known as the diffusion gradient scheme. In practice, more than six directions are frequently needed to improve the accuracy in diffusion tensor calculation. Since the actual orientation of the anisotropic structures (e.g., the white-matter fiber tracts) is not known a priori, uniform distribution of the gradient vectors is highly desirable in many design methods.

[0037] For clinical studies of the human brain, the typical b-value ranges between

750 and 1500s/mm ². Single-shot, echo planar imaging (EPI) is the most prevalent sequence for DTI due to its fast acquisition speed, motion insensitivity, and low RF power deposition per unit time. However, the present invention may be practiced with any DTI pulse sequences.

[0038] In one embodiment, MRI examination may be performed on a 3.0 T scanner using an eight-channel head coil. A DTI scan may be added to the patient's brain MRI examination. The axial DTI scan may be performed immediately before contrast injection using the protocol given below. TR = 5000 ms, TE = 72 ms;

Single-shot EPI sequence, matrix size = 256²; FOV = 20-24 cm, slice thickness: 5mm; b-value: 750 s/mm², diffusion direction = 13, NEX=2.

[0039] The initial step of DTI data processing is to calculate the diffusion tensor elements at each voxel location. This step can be accomplished by solving the following equation on a voxel-by- voxel basis:

-b[a_x a. a. ],

[0040] Since there are a total of N measurements (i.e., j =1, 2, 3, ..., N), Equation

9 represents N linear equations with the diffusion tensor elements being the unknowns. When N - 6, the six tensor elements can be uniquely determined, provided that the diffusion gradients are non-colinear and non-coplanar. When N > 6, the tensor elements can be obtained using a least- squares fitting algorithm, such as singular value decomposition, as described by Press WH, et al. in "Numerical recipes in C : the art of scientific computing" (Cambridge University Press; New York, 1992), incorporated by reference herein.

[0041] The diffusion tensor elements in Equation 9 are patient-orientation dependent. To eliminate this dependence and obtain a set of diffusion tensor parameters inherent to the tissue of interest, the diffusion tensor matrix given by Equation 3 is diagonalized to the following form:

where Di _, D ₂ and D ₃ axe the eigenvalues discussed earlier. Standard methods for matrix diagnolization can be used, such as the one described in "Numerical recipes in C: the art of scientific computing" by Press WH, et al. (Cambridge University Press; New York, 1992) incorporated by reference herein.

[0042] To highlight the location of the fiber tracts, a scalar diffusion anisotropy image can be calculated based on one of the anisotropy parameters, such as relative anisotropy (RA), fractional anisotropy (FA), or volume ratio (VR). These indices are defined in Equations 11-14. Note that the average eigenvalues given by Equation 14 is also referred to as the mean, diffusivity ox apparent diffusion coefficient (ADC).

VR= - pi — <1S)

[0043] Both FA and RA are based on the standard deviation of the eigenvalues, but they are normalized by different denominators and coefficients.

[0044] After the determination of the three eigenvalues Di _, D ₂ and D ₃, the

principal eigenvalue (i.e., the largest eigenvalue) is selected and its eigenvector X is calculated using methods well-known in the arts, such as the one described in "Numerical Recipes in C" by W.H. Press, B.P. Flannery, S.A. Teukolsky, and W.T. Vetterling, (Cambridge University Press, New York, NY, 1988) incorporated by reference herein.

Calculation of r-FCI

[0045] Based on a diffusion anisotropy map, such as an FA, an RA, or a VR map calculated using Eqs. [11-13], respectively, a region of interest (ROI) is selected from a white- matter fiber tract. Selection of an ROI can also be guided by using other MRI images, such as Tl -weighted, T2-eighted, FLAIR, and proton-density-weighted images. For a selected ROI, the r-FCI is evaluated according to Eqs. [6] and [7] or their alternatives. For example, FCI can be alternatively evaluated using the following equation:

where the normalization factor in the denominator of Equation [6] has been replaced by the total number of voxel pairs N. For 2D images, calculations of FCI and r-FCI may be limited to an image plane. For 3D images, the calculations can be extended to all three dimensions.

[0046] Software for data processing may be developed on the FuncTool platform

(GE HealthCare, Milwaukee, WI) with a Linux-based Advantage Window (AW) workstation. The diffusion-weighted images can be easily transferred from the scanner to the AW workstation using a DICOM protocol. Any execution of the algorithms and equations disclosed herein, including without limitation any software, firmware or hardware, is within the scope of the present invention. The Weighting Factor

[0047] The weighting function g(i, j) is adjustable in the r-FCI calculation. A 2D

Gaussian kernel may be used to perform the inner product within the nearest neighbors of the pixel of interest, as diagrammatically shown in Fig. 3 for the specific example involving 3 x 3 pixels. In this example the weighting for the four neighbors sharing a side of the pixel may be assigned 1.0, and the weighting for the other four neighbors sharing a vertex may be determined by the weighting function g(ij). The width of the kernel may be adjusted according to specific applications. For a 3D DTI data set, which can be acquired directly or reformatted from 2D multiple slice interpolation, a 3D Gaussian kernel may be used as the weighting function. For the specific example that involves 3x3x3 voxels, the six voxels sharing a plane with the voxel of interest may be weighted 1.0. The twelve neighboring voxels sharing a line and the eight vertex neighboring voxels may be weighted by the weighting factor determined by the kernel function detailed below. Other functions, such as Lorentzian and Fermi kernels may be used without departing from the scope of the invention.

[0048] To determine the weighting factor for a neighboring pixel i, the center-to- center distance Xy between pixel (or voxel) i and the pixel (or voxel) of interest j is first determined. This parameter is used as an input to the weighting function, such as a Gaussian, to obtain the weighting factor:

where η is a normalization constant, and σ is the adjustable Gaussian kernel width.

[0049] Lorentzian and Fermi kernels may also be used as alternate embodiments.

The Lorentzian kernel would yield a sharper distribution curve and the Fermi kernel would yield a more rectangular curve having a flatter top portion and a steeper transition regions. Use of any of these kernels or other kernels remains within the scope of the present invention. Moreover, use of other weighting factors or separate calculations omitting weighting factors remain within the scope of the present invention. Finally, the size of the kernel may be varied without departing from the scope of the present invention. These size variations may be the resolutions or dimensions of each pixel, and may include the size of the matrix, i.e., 3x3, 5x5, or otherwise. Threshold and Edge Detection

[0050] A potential pitfall in the FCI and r-FCI calculation is that an accurate fiber coherence measure cannot be obtained near the edge of a fiber tract. Such a pixel (or voxel) at or near a fiber edge can be either the pixel (or voxel) of interest, of a neighbor of the pixel (or voxel) of interest. This situation may be prevented by providing a set of safeguards to (a) ensure that the pixel (or voxel) of interest is substantially within a fiber structure, (b) ensure that the neighboring pixels (or voxels) participating in the FCI calculation are substantially within a fiber structure, and (c) FCI calculations do not involve pixels (or voxels) beyond the ROI as shown in Fig. 4. hi Fig. 4, when calculating FCI for the hatched pixel, the neighbors A, B, C₅ and D are excluded from the inner product calculation because they are outside the ROI. This set of safeguards will be referred to as "threshold and edge detection".

[0051] As a safeguard for (a), an FA threshold, FA_sll, can be selected to screen the pixel or (voxel) of interest. FCI is calculated only for those pixels (or voxels) whose FA value (FA_j) satisfies Eq. [17] :

FA_j ≥ FA_sh [17]

Such a threshold is determined empirically. Since FA values are between 0 and 1.0, in one embodiment, the threshold FA_Sh is selected between .25 and .35. As a safeguard for (b), a somewhat relaxed threshold can be chosen for the neighboring pixels (or voxels). In one embodiment, the threshold for the neighboring pixels (or voxels) is selected as 0.6FA_sh. Thus, only the neighbors whose FA values no less than 0.6FA_sh are included in the FCI calculation.

As a safeguard for (c), all pixels (or voxels) which include both the pixel (or voxel) of interest and its neighbors are checked to determine if they are within the ROI (Fig. 4). The pixels (or voxels) lying beyond the ROI are excluded in the inner product in FCI calculations. This safeguard is particularly relevant to the pixels (or voxels) at the boundaries of the ROI.

[0052] It is within the scope of this invention to use any edge detection technique for digital processing of the image data. For example, standard signal processing techniques such as a high pass filter can be used. In the present application, Volume Ratio, the RA value and the FA value can also be used for threshold selection as well as edge detection. Partial Volume Effects

[0053] Another pitfall of using FCI is the partial volume effect due to insufficient spatial resolution. An obvious way to address this problem is to increase the spatial resolution in DTI data acquisition. While this can be difficult using the single-shot EPI pulse sequence, alternative data acquisition techniques, such as multi-shot fast spin echo, interleaved spiral, multi-shot EPI, and PROPELLER, can be employed to achieve a better spatial resolution. When the single-shot EPI pulse sequence is combined with parallel imaging techniques, spatial resolution can also be improved, thereby reducing the partial volume effect.

[0054] Even with the improved spatial resolution, calculation of FCI on specific fiber tracts can be difficult. These situations include, but not limited to, cross fibers within a voxel, branching fibers within a voxel, bent fibers, and small fiber tracts (e.g., 4mm in diameter). Computer simulations have confirmed that even under these challenging conditions, reliable FCI can be obtained from straight and bent fibers whose thickness is approximately two times that of the pixel (or voxel) dimension, and from branching or crossing fibers with branching or crossing angle less than -30°. These results can guide proper use of FCI on specific fibers for clinical applications, when the partial volume effect is a concern

Use of FCI for Identifying Tumor Infiltration

[0055] In one embodiment, use the FCI for identifying tumor infiltration would proceed as follows. FA maps based on a set of diffusion-weighted images are first produced and visually inspected. The white-matter fiber tracts suspected of tumor cell infiltration as judged by the reduced intensity in the FA map, as well as conventional MRI, are identified within a 2-3 cm zone outside the tumor mass as revealed by the Tl, T2, and/or FLAIR images. Values of r-FCI, FA, (or RA or VR) are calculated from the suspected white-matter fiber tracts, as well as the

tracts in the contralateral side to serve as a control. The control value (rFCI_c) will be

subtracted from the suspected tumor value ( rFCI_s ) to obtain the change in r-FCI:

ΔrFCI = rFCI_s - rFCI_c [18]

In this way, the systematic errors and errors due to scan-to-scan and patient-to-patient

variability are partially cancelled. For comparison, the changes in FA (ΔFA) and RA (ΔRA)

may also be calculated in a way analogous to Eq. [18].

[0056] Depending on the tumor location with respect to the fiber tracts, multiple

ROIs (e.g., 2-4) will be selected from a single patient to increase the statistical power of the analyses.

[0057] After the individual fiber orientations are determined for a cluster of voxels in the fiber, the FCI for voxel j can be calculated using Eq. [19]:

where i is the index for the voxels in the close proximity of thejth voxel, Xf is a fiber

orientation of the zth voxel, X_j is a fiber orientation of thejth voxel, g(i,j) is a weighting

function that defines the spatial extent over which the summation is performed, and N is the total number of voxel pairs used for the inner product calculation.

[0058] Alternatively, the FCI for voxel j can be simply calculated using Eq. [6] :

where i is the index for the voxels in the close proximity of theyth voxel, %ι is a fiber orientation

of the zth voxel, X,- is a fiber orientation of theyth voxel, g(ij) is a weighting function that

defines the spatial extent over which the summation is performed, and N is the total number of voxel pairs used for the inner product calculation.

[0059] Based on the above two equations, there are many other alternative ways that can be used to obtain FCI. For example, rather than making a single calculation with a weighting factor for each pixel of interest, separate calculations can be made and later summed to obtain FCI. In this circumstance, the first calculation would comprise the pixel of interest with the nearest neighbors, i.e., the four pixels sharing a full side, all with the same weighting factor. A second calculation would comprise the pixel of interest with the next nearest neighbors, i.e., the four pixels sharing a corner or vertex with another weighting factor. These two would then be summed to yield the FCI for the pixel of interest. In another alternative

embodiment, the cross product of the λ vectors is taken.

[0060] To calculate a regional FCI (r-FCI) within a Region of Interest (ROI) containing M voxels, the individual FCI values can be simply averaged according to Eq. [7].

₁ M ^rFCI = jfΣ^FCIj rø

It is within the scope of the present invention that r-FCI may alternatively be calculated as a mean or median of the individual FCI values. A geometric mean may be calculated by:

rFCI_gm

Utility

[0061] In addition to accurately isolating the extent tumors, the Fiber Coherence

Index has utility for evaluating any fibrous tissues or structures. Accordingly, muscle fibers and myocardium fibers may be studied with the present invention. Diseases affecting any fibrous tissues may be advantageously studied using the Fiber Coherence Index. Diseases of the central nervous system that may be studied with the present invention, without limitation, include in addition to tumors, multiple sclerosis, arteriovenous malformations, and other neurological diseases.

Studies on tumor cell infiltration - Example 1

[0062] Four patients (2 males and 2 females; age range: 42-65 y.o.) with newly diagnosed glioblastoma multiforme (GBM; WHO grade IV) were studied to investigate using r- FCI for the detection of tumor infiltration into the white-matter fiber tracts. Prior to surgery, the patients underwent MRI scans performed on a 1.5 T GE Signa NV// scanner. The data acquisition protocol included pre-contrast Tl -weighted, T2- weighted, fluid-attenuated inversion recovery (FLAIR), and DTI axial imaging, and post-contrast Tl -weighted axial, coronal, and sagittal 2D imaging and 3D volume gradient echo imaging. Following surgery, MRI scans were repeated approximately at one-month intervals.

[0063] A single-shot EPI pulse sequence to acquire diffusion images at a lower spatial resolution (1.9mm x 1.9mm x 5mm). To avoid the partial volume effect, we limited our analysis only to large fiber tracts, such as the corpus callosum. The key acquisition parameters were: TR = 4000 ms, TE = 72 ms, NEX = 2, FOV = 22 cm, axial slice thickness = 5 mm, image

matrix = 128x128, b-value = 750 s/mm², and number of diffusion gradient directions = 27. The imaging time was ~4 minutes.

[0064] The set of diffusion-weighted images was processed to produce the eigen values and the principal eigenvector of the diffusion tensor on a pixel-by-pixel basis. All data processing was performed using a custom program developed on the FuncTool platform (GE HealthCare, Milwaukee, WI). Regions of interest (ROIs) were drawn in the fiber tracts suspected of tumor infiltration within 2-3 cm zone outside the gadolinium enhancing rings. This zone typically contained peritumoral vasogenic edema as seen in T2 and FLAIR images. FCI was evaluated for each pixel in the ROI by computing the inner product only with the nearest neighbors and by setting g(i,j) in Eq. [6] to 1.0. The average values of FA and r-FCI were then calculated within each ROI. hi order to establish the correlation with follow-up MRI scans, only the ROIs that were not affected by surgical resection were selected.

[0065] Among the four patients, a total of five ROIs were analyzed (Table 1).

Since biopsies were not taken from these ROIs, we relied on follow-up MRI and/or MRS scans, as indirect measures, to correlate with the r-FCI and FA values. The results are shown in Table 1. Reduction in FA values was observed in all white-matter fiber tracts suspected of tumor infiltration, as compared to the normal fiber tracts in the contralateral side without tumor. Only two out of the five regions with reduced FA, however, developed tumor in the follow-up MRI scans. A possible explanation is that the FA changes were predominately caused by peritumoral vasogenic edema which may or may not contain infiltrating tumor cells. This result suggested that a reduced FA value was not specific to tumor cell infiltration.

[0066] The reduction in r-FCI, however, correlated with the follow-up MR results. For patient 2 and patient 3 (ROI 2), the r-FCI did not exhibit significant change, which correlated with the negative follow-up MR results (i.e., absence of tumor). The noticeable decrease in r-FCI in patient 1 and patient 3 (ROI 1), on the other hand, correlated with the presence of tumor as seen by MR. The moderate r-FCI reduction in patient 4 did not follow the correlation established by the other ROIs, after 9 months of follow-up. This result, however, does not exclude the possibility that tumors would be detected in the suspected ROI had the

patients been followed for a longer time.

Table 1. FA, ι»-F£l, and ftolw-vρ MRI Mesttlts of 4 Glioma Fatfaasts

Patient No, FA FA r-FCI ^FCI foϊlow-up tumor side contra-lateral tujrør side αrøtta-iatefal MM*

1 0,23 ±OM 0.76 ± 0.04 045 ± 0,03 0,83 + 0.01 Y

2 0.35 *0Λ8 0,69 ± 0.06 0.79 ± 0.04 N

3a (KUIl) 032 ±0.04 0.74 ± 0.03 0.53 ±0.02 OJ9±0.03 Y

3b (RGΪ2) 0.36 ±044 O.S2 ±aO4 0.86 ±0.04 OJl ±0,02 N

4 O22 ±0Λ7 QM ± 0.04 0.62 ±0.04 0.74 ±0,01 H

* Y and N in the test column represent positive and negative tumor detection, respectively,

[0067] As various modifications could be made to the exemplary embodiments, as described above with reference to the corresponding illustrations, without departing from the scope of the invention, it is intended that all matter contained in the foregoing description and shown in the accompanying drawings shall be interpreted as illustrative rather than limiting. Thus, the breadth and scope of the present invention should not be limited by any of the above- described exemplary embodiments, but should be defined only in accordance with the following claims appended hereto and their equivalents.

Claims

What is claimed:

1. A method to process diffusion tensor imaging (DTI) dataset, the steps comprising:

(a) Acquiring a set of diffusion-weighted images with varying diffusion- weighing gradient directions, where the minimal number of diffusion gradient directions is six;

(b) Acquiring an additional image without a diffusion-weighting gradient, or acquiring a second set of diffusion-weighted images with varying diffusion- weighing gradient directions, where the minimal number of diffusion gradient directions is six, and with a diffusion-weighting factor (i.e., b- value) different from that used in acquiring the first data set in (a);

(c) Calculating the diffusion tensor matrix at each and every voxel location based on the images acquired in (a) and (b);

(d) Calculate the principal eigenvector from the said diffusion tensor matrix at each and every pixel location;

(e) Computing a fiber coherence index (FCI) for a given voxel, based on directional coherence between the said voxel and the voxels close to it; said computing is performed using the principal eigenvector recited in (d).

2. The method as recited in claim 1 further comprising the step of computing a regional fiber coherence index (r-FCI) by averaging individual FCI within a region of interest.

3. The method as recited in claim 1 in which the fiber coherence index for theyth voxel is calculated by:

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where γ,- is the fiber orientation at voxel j, which can be approximated by the direction of the principal eigenvector in that voxel, / is the index of the voxels in the close proximity of the 7th voxel, g(ij) is a weighting function that defines the spatial extent over which the summation is performed, and N is the total number of voxel pairs used for the vector inner product calculation.

4. The method as recited in claim 2 in which the weighting function g(i,j) is a 2D or 3D Gaussian function.

5. The method as recited in claim 2 in which the weighting function g(i,j) is a 2D or 3D Lorentzian function.

6. The method as recited in claim 1 in which the said fiber coherence index (FCI) is calculated by:

where i is the index for the voxels in the close proximity of theyth voxel, \ is a fiber

7. The method as recited in claim 2 in which the said regional fiber coherence index (r-FCI) is calculated by:

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where M is the total number of voxels contained in the region of interest, j is the voxel index.

8. The method as recited in claim 1 in which the calculation is performed on tissues with fibrous structures.

9. The method as recited in claim 6 where the said fibrous tissue include white matter fiber tracts in the brain.

10. A tissue characterization method based on the FCI and/or r-FCI measurement as recited in claim 1.

11. A disease diagnosis method based on the FCI and/or r-FCI as recited in claim 1, comprising steps: a. measuring FCI and/or r-FCI in healthy intact fibrous tissues; b. measuring FCI and/or r-FCI in fibrous tissues suspected of disease; c. detecting the changes in FCI and/or r-FCI by comparing the results obtained from (a) and (b); d. making a diagnosis based on changes in FCI and/or r-FCI.

12. The method of claim 9 where FCI or r-FCI is used to monitor tumor cell infiltration into the white matter fiber tracts, in which the reduced FCI or r-FCI value is related to identify fiber tracts with tumor invasion.

13. Clinical application of the method as recited in Claim 8.

14. Clinical application of the method as recited in Claim 9.

15. The said application in claim 12 includes surgical resection of brain tumors.

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16. The said application in Claim 12 includes determining the radiation field in radiotherapy on patients with brain tumors.

17. A processing apparatus to characterize pathologic disruption of fibrous tissues or structures, said processing apparatus comprising:

a processor, said processor being configured to : determine a first principal eigenvector from a first Diffusion Tensor, said first principal eigenvector corresponding to a first pixel of interest;

determine at least one other principal eigenvector from at least one other Diffusion Tensor, said at least one other principal eigenvector corresponding to at least one other pixel, said at least one other pixel neighboring said pixel of interest;

calculate a dot product of said first principal eigenvector and said at least one other principal eigenvector; and

output a result of said dot product.

18. The processor of claim 17 further comprising a weighting factor.

19. The processor of claim 17 wherein said dot product is a cross product.

20. The processor of claim 17 further comprising a normalizing factor.

21. The processor of claim 17 wherein said principal eigenvectors are received by said processor through operative communication with a second processor.

22. The processor of claim 17 further comprising calculating a regional Fiber Coherence Index from one of an average, a mean or a median of said output.

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