Brain tumor evaluation and segmentation by in vivo ... - Springer Link

MAGMA (2005) 18: 316–331 DOI 10.1007/s10334-005-0020-0

Miguel Mart´ın-Landrove Finita Mayobre Igor Bautista Raúl Villalta

Received: 25 April 2005 Accepted: 23 November 2005 Published online: 30 December 2005 © ESMRMB 2005

Brain tumor evaluation and segmentation by 1 HMRS and relaxometry M. Mart´ın-Landrove · F. Mayobre Departamento de Espectroscop´ıa y Desarrollo de Aplicaciones, Instituto de Resonancia Magnética, La Florida, San Román M. Mart´ın-Landrove (B) · I. Bautista R. Villalta Universidad Central de Venezuela, Facultad de Ciencias, Escuela de F´ısica, Centro de Resonancia Magnética, Grupo de F´ısica Molecular, A.P. 47586, Caracas 1041-A, Venezuela E-mail: mmartin@fisica.ciens.ucv.ve. Tel.: +58-212-6051194 Fax: +58-212-6051516, +58-212-9928903

RESEARCH ARTICLE

Brain tumor evaluation and segmentation by in vivo proton spectroscopy and relaxometry

Abstract A new methodology has been developed for the evaluation and segmentation of brain tumors using information obtained by different magnetic resonance techniques such as in vivo proton magnetic resonance spectroscopy (1 HMRS) and relaxometry. In vivo 1 HMRS may be used as a preoperative technique that allows noninvasive monitoring of metabolites to identify the different tissue types present in the lesion (active tumor, necrotic tissue, edema, and normal or non-affected tissue). Spatial resolution for treatment consideration may be improved by using 1 HMRS combined or fused with images obtained by relaxometry which exhibit excellent spatial resolution. Some segmentation schemes are presented and discussed. The results show that segmentation

Introduction Evaluation and segmentation of brain tumors can be assessed by proton magnetic resonance spectroscopy (1 HMRS) and relaxometry, two magnetic resonance techniques. 1 HMRS determines metabolic tissue information by analyzing the composition and spatial distribution of cellular metabolites [1]. 1 HMRS distinguishes malignant tumors from normal brain tissue due to significant spectral differences reported between tumor, necrosis and normal brain tissue. Recent in vivo 1 HMRS studies have been used to grade brain tumors [2–6]. The metabolites involved in the differentiation of neoplastic and non-neoplastic tumors are: N-acetyl aspartate (NAA)

performed in this way efficiently determines the spatial localization of the tumor both qualitatively and quantitatively. It provides appropriate information for therapy planning and application of therapies such as radiosurgery or radiotherapy and future control of patient evolution. Keywords Relaxation · in vivo Spectroscopy · Assessment · Segmentation

considered a neuronal marker, choline (Cho) a marker of membrane turnover or higher cellular density, creatine (Cre) a metabolite involved in cell energy metabolism, lactate (Lac) a marker of anaerobic glycolysis and mobile lipids (Lip) visible after membrane breakdown. NAA and Cre decrease and Cho increases in the presence of high grade tumors. 1 HMRS spectra are mainly interpreted on the basis of the relative amplitudes of the above metabolites [1]. Norfray et al. [6] found significant differences in Cho/Cre ratio between tumor and normal brain regions. Vigneron et al. [7] and Nelson et al. [8] reported Cho/NAA ratios greater than 1.3 in spectra of histologically confirmed tumors, the mean value for all tumor types being 3.91 ± 1.52. Other

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Fig. 1 1 H SVS obtained from a patient with histological proven fibrillary astrocytoma grade III (patient 3). Spectrum from the tumor on the right and from the contralateral normal tissue on the left; TE = 30 ms, TR = 1,500 ms, 256 averages

authors reported similar values for high grade tumors [9– 11]. Adamson et al. [12] reported Cho/NAA ratio lower than the reported above (over 1 for confirmed neoplastic tumors). Presence of Lac or Lip with elevated Cho is evidence of relatively high grade tumors [12]. Low levels of Cho, Cre, and NAA correspond to necrosis. Relaxation studies were used in the past for the localization and evaluation of tumors, being the T2 -map of a tissue often used as a basis for interpreting clinical images [13]. Studies of multiexponential T2 decay have previously been performed in both non living material [14–16] and biological systems [17–19]. Among the different imaging techniques that generates T2 -weighted images are spin echo, fast spin-echo, and GRASE (gradient spin echo), being the first two the most accurate for anatomical detail and relaxation time determination [20]. Sometimes spinecho techniques are combined with the application of contrast agents [21,22] to evaluate perfusion. Regardless of its diagnostic power, in vivo 1 HMRS could be benefit by being combined with images of appropriate spatial resolution in order to obtain improved information for treatment considerations. Some approaches for the solution to this problem have been proposed introducing the concept of nosologic image, i.e., an image where the pixels are classified according to the presence of disease [23]. The image is obtained either with spectroscopic information alone or combining it with T1 - and T2 -weighted

images [24, 25]. Unfortunately, nosologic images obtained in this way still lack of appropriate spatial resolution usually limited to the spectroscopic voxel size. The aim of this work is to combine or fuse in vivo 1 HMRS information with images obtained by MR relaxometry and to obtain nosologic maps of appropriate spatial resolution for the evaluation and segmentation of brain tumors.

Methods Ten patients with different brain tumor types were analyzed in the present work. Data obtained from measurements on two healthy volunteers served as controls. All the patients and volunteers were informed about the experimental procedures to be performed and signed informed consent forms in compliance with ethical guidelines. All the measurements were carried out in a Siemens Magnetom Sonata, with a magnetic field strength of 1.5 T. MR images were obtained before 1 HMRS for voxel localization. 1 HMRS studies were assessed by single voxel spectroscopy (SVS) or by chemical shift imaging (CSI) techniques. Single voxel spectroscopy was performed by a PRESS sequence with CHESS for water suppression, TR of 1,500 ms, 256 averages and TE = 30 ms. Voxel sizes covered a range between 4.1 and 5.4 cm3 and a reference voxel was used for control (Fig. 1). In some cases, when contrast with Gd-DTPA was necessary, unimportant changes in the spectrum were observed. Chemical shift imaging provides a spectral array which maps tumor heterogeneity and determines the spatial extent of the metabolite abnormality. CSI was performed with a PRESS sequence to obtain spatial distributions of metabolite relative concentration across the lesion, using a TE = 135 ms, TR = 1,500 ms,

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Fig. 2 Some of the CSI grids used in this work; the red colored insert correspond to those voxels where the spectroscopic evaluation was performed

and VOI of 96 cm3 (80 × 80 × 15 mm). At TE = 135 ms, Lac signal appears as an inverted doublet in the spectrum which allows the differentiation from the Lip signal. No lipid saturation pulses were used. The CSI grids included the region of the lesion as well as neighboring tissues as depicted in Fig. 2. VOI consisted of an 8 × 8 cm region placed within a 16 × 16 cm field of view on a 1.5–2 cm transverse section. A 16 × 16 phase-encoding matrix was used to obtain an 8 × 8 array for spectra in the VOI, with an in-plane resolution of 1 × 1 cm and a voxel size of 1 × 1 × 1 cm3 . The spectroscopy data analysis was performed only in voxels within an 8 × 8 matrix centered on the lesion, avoiding those on non neurological structures and discarding others on the basis of poor spectral quality, i.e., low signal to noise ratio or bad phase and base line adjustment. The quantification of the spectroscopic information was based on relative values: each spectrum was fitted for NAA at 2.02 ppm, Cre at 3.04 ppm, Cho at 3.21 ppm, Lac at 1.3 ppm and Lip at 0.9 and 1.4 ppm using the fitting software in the equipment. Peak integrals and integral ratios were calculated for the metabolite markers Cho, Cre, and NAA. Cho/NAA ratio was used as the main criterion in this study and the Cho/Cre ratio as a secondary criterion. The criterion for malignancy in any voxel was a Cho/NAA ratio over 1.3. This value was used for both SVS and CSI. The voxel was considered atypical if the Cho/NAA ratio had a value between 0.9 and 1.29. No quantification of other metabolites was performed. Relaxometry studies were performed after the 1 HMRS studies and prior to additional 1 HMRS studies performed with GdDTPA when they were necessary to fully assess the tumoral lesion. A standard multiecho sequence (CPMG) was used with 16 echoes, at echo times given by a base TE = 22 ms and eight 5 mm thick planes centered on the tumor. The slice parameters were the same for those used for the CSI grids. This procedure allowed for the inclusion of two relaxometry planes in the same spatial region of the CSI grid, facilitating the information matching between the two types of measurements. The multiecho sequence

Fig. 3 Flux diagram of the segmentation procedure

was preferred to other sequences, (T2 -weighted), because it provides a set of images from which the relaxation rates or the relaxation rate distributions could be appropriately and quantitatively evaluated. An image processing algorithm was developed to extract the magnetization decays for different ROIs or relaxometry voxels which come from a specific voxel from the CSI grid, providing the relaxation data. Within each ROI or relaxometry voxel, the relaxation data were processed by an inverse laplace transform (ILT) algorithm to obtain the relaxation rate distributions involved. The application of such algorithm

319

Fig. 4 Performance of the ILT algorithm on a Pentium 4 Workstation, 2.27 GHz. a The processing time depends on the number of replicas and exhibits a linear behavior, with an average time of 3.29 s per replica. b Spectrum coming from a single relaxation voxel as a function of the number of replicas used to define it. Notice that for as much as 50 replicas, i.e., about 164 s in processing time, the relaxation spectrum remains stable in its structure

is fully justified since there is a partial volume problem [26–28], i.e., the voxel size is usually big enough to contain several tissue types, and it is expected that the relaxation spectrum should exhibit some structure depending on the proportion on which any of the different tissue types are present in the voxel. Usually, segmentation methods based on T2 -weighted images determine the relaxation rate distribution by calculating the relaxation rate pixel by pixel using a small number of echoes (2 or 4), assuming a single exponential decay. This brings as a consequence that the calculated relaxation rate is some kind of average of the relaxation rates present in the pixel distorting the actual relaxation rate distribution in any selected ROI. The ILT algorithm will be

discussed in detail in the next section. The relaxation spectra obtained in this way were classified according to the spectroscopic information thereby determining the relaxation rates associated to the different tissue types present in the lesion for a particular patient, (i.e., those relaxation spectra coming from a CSI voxel are all associated to the type of tissue present in that voxel as established by the spectroscopic result, which depends on the metabolic ratios). Once the relaxation spectra were obtained and classified, the relaxation rates for the different tissues were determined, and their values were used for the segmentation procedure. The segmentation was made on a pixel by pixel basis by a linear regression algorithm to determine the proportion in which

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Table 1 Proton magnetic resonance spectroscopy (1 HMRS) and histopathological results of ten patients with brain tumor

Patient number

Age

1H

1 2 3 4 5 6 7 8 9 10

50 46 19 16 37 28 37 7 37 10

15.75 X 3.18 2.66 1.79 3.13 1.10 0.26 1.88 0.85

MRS (Cho/NAA)

1H

MRS (Cho/Cre)

6.10 X 3.46 1.64 1.22 1.89 1.42 1.83 1.72 1.33

1H

MRS (NAA/Cre)

0.39 X 1.09 0.62 0.68 0.60 1.30 6.99 0.92 1.57

Biopsy Glioblastoma multiforme Glioblastoma multiforme Fibrillary astrocytoma grade III Oligodendroglioma grade II Fibrillary astrocytoma grade II Fibrillary astrocytoma grade II Non-Hodgkin’s lymphoma Not performed Meningioma Meningioma

Cho/NAA, Cho/Cre, and NAA/Cre ratios are calculated from single voxel spectroscopy (1 H SVS) spectra. NAA signal was not detected in tumor no. 2 spectrum; for this reason ratios were not calculated (X)

Table 2 Chemical shift imaging (CSI) results of the ten brain tumors studied. number of voxels analyzed, number and percentage of spectra suggesting malignancy (Cho/NAA = 1.3 or over) and number and percentage of atypical spectra (Cho/NAA between 0.9 and 1.29)

Tumor number

Number of voxels analyzed

Malignant spectra number (%)

Atypical spectra number (%)

1 2 3 4 5 6 7 8 9 10

26 6 20 Not performed 10 6 10 Not performed 6 6

20 (77%) 5 (83%) 7 (35%) – 3 (30%) 5 (83%) 2 (20%) – 3 (50%) (*) 2 (33%) (*)

4 (5%) 1 (17%) 6 (30%) – 2 (20%) 0 1 (10%) – 2 (33%) 0

In the case of meningiomas (*), it was obtained a high Cho/NAA ratio, not necessarily associated to malignancy

the different tissue types are present in the pixel. The complete segmentation procedure can be seen as a flux diagram in Fig. 3. Control slices, i.e., those not affected by the lesion in the same patient, and control cases were used to test the segmentation procedures.

The ILT algorithm There are a wide variety of different approaches [29, 30] to solve numerically the ILT problem, and some of them are of standard use in many laboratories around the world. Such is the case with the DISCRETE and CONTIN programs [29], which are applicable in many situations. Most of these approaches make use of assumptions about the mathematical properties of the function to be obtained by the inversion procedure and rely on these properties in the general development of the algorithm, while others introduce regularization parameters or a fixed number of components in the relaxation spectrum. The algorithm

developed for this and other investigations [31,32] was shown to be adequate for precise line shape determination. Nevertheless, there are always some drawbacks: a long processing time due to the optimization procedure based on simulated annealing as well as the requirements of appropriate and complete data acquisition; i.e., improper sampling of the decay introduces artifacts in the relaxation rate spectrum, which sometimes may be easily detected and eliminated from the relaxation spectrum. The ILT algorithm used in this work is described below. Since the signal is known in a finite number of points on the real axis, the numerical solution of the problem corresponds to a very ill-posed first-kind Fredholm integral equation of the form ∞ M(t) =

dλ e−λt P (λ),

(1)

0

where M(t) corresponds to the transversal magnetization, and λ is the relaxation rate. Equation (1) represents a very

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Fig. 5 Average probability distribution function or relaxation rate spectra for different malignant lesions, a, b correspond to gliobastoma multiforme, d corresponds to an oligodendroglioma grade II and c–f correspond to fibrillary astrocytomas

general way of expressing the transversal relaxation decay depending on the particular relaxation rate distribution P (λ) [31–33]. This distribution can be represented by a histogram or collection of bars of variable width, which is given by P (λ) =

N k=1

Pk (λ),

(2)

where N is the number of components, and Pk (λ) is the kth elementary component given by Pk (λ) = Pk (λ − λk ) (λk + λk − λ).

(3)

This representation can be used for the description of discrete and continuous distributions as well. In the particular case of a discrete distribution, a set of very localized functions with a small width can be obtained, and it is indistinguishable from a very narrow and continuous distribution. This width is a function of relevant physical effects, noise, and loss of information due to the use of a number of finite points. In practice it is very difficult to separate each contribution, although in the case of noise, previous filtering procedures can be considered.

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Table 3 Relaxation rates, 1/T2 (s−1 ), for edema or necrosis, tumor, and normal gray/white matter in the different pathologies studied in this work

Tumor type

1/T2 (s−1 ) Edema or Necrosis

1/T2 (s−1 ) Tumor

1/T2 (s−1 ) Gray/white Matter

Glioblastoma multiforme Glioblastoma multiforme Fibrillary astrocytoma grade III Oligodendroglioma grade II Fibrillary astrocytoma grade II Fibrillary astrocytoma grade II Non-Hodgkin’s lymphoma Craniopharyngioma Meningioma Meningioma

1.88 2.22 1.74 2.67 1.89 3.43 2.20 2.12 0.65 1.77

6.61 6.69 6.26 5.52 7.43 5.05 5.18 6.67 6.67 7.47

11.02 11.47 9.34 8.67 14.48 11.91 12.52 9.80 25.26 13.70

The rates were obtained by analysis of the relaxation spectra shown in Fig. 5

The problem to be solved can be stated as an optimization procedure where a set of distribution components, which provide the best fit for the M(t) function, has to be found. For this purpose simulated annealing and Metropolis algorithms [34–37] were used. The configuration to be tested in each Metropolis algorithm cycle is given by a finite number of elementary components that are sampled in the relaxation rate position λk and width λk for the kth element. At the same time, the total number of components N for the configuration is also changed, which is a new feature in an optimization procedure of this kind. This sampling in the total number of components is performed by considering two options with the same probability within the Metropolis algorithm cycle:

form probability distribution. This probability distribution provides a practical boundary for the domain to be sampled, and it should vanish for large relaxation rates. The simplest choice corresponds to an exponential distribution, but other distributions can be considered as well. In the present implementation of the algorithm, the exponential distribution was chosen. The cost function was chosen from results of robust statistics to noise filtering, and it is known in the literature as the least absolute deviation (LAD) optimization (38). For nP , points it is given by nP Mexp (ti ) − Mop (ti ) 1 (4) = Mexp (ti ) nP

(1) The total number of components N is unchanged, and in this case one component is taken with equal probability from the current configuration set to change the numerical value of the relaxation rate position and its width. This change is achieved first by adding an increment with uniform probability within the interval [−ε, +ε] and taking the absolute value of the result for the energy position; then the same process is repeated for the corresponding width. The value ε = 1 was taken arbitrarily. The time scale is set by assuming that the maximum measurement time is equal to 1. (2) A new component is created and added to the existing configuration. The creation of this component implies the generation of a relaxation rate position and its corresponding width by means of the following steps: (a) A choice with equal probability is made in order to decide whether the new relaxation rate is going to be within the existing set or, on the contrary, happens to be the maximum of the new configuration set. (b) In the former case the new relaxation rate is placed with equal probability in between two other relaxation rates of the old configuration, while in the latter case, the new relaxation rate is chosen with a non uni-

and it can be seen as an average relative error. In the presence of information loss the absolute value provides better noise filtering than the usual quadratic value since the median is much less sensitive than the mean to the presence of fluctuations of any size. The quantity Mexp (t) corresponds to the measured signal and Mop (t) is the optimized signal given by ∞ dλ e−λt Pk (λ). (5) Mop (t) =

i=1

k

0

In this work a fast simulated annealing approach is used (Cauchy machine) [39], which mean that the temperature parameter is proportional to the inverse of the Monte Carlo iteration number. Up to 300 parallel simulations with different initial conditions were performed in order to avoid the problem of the appearance of metastable states [37–39] which are intrinsic to the metropolis algorithm. For each simulation, 10,000 Monte carlo steps were performed during an annealing cycle. Stability is assumed when there is no change of the parameters during a complete annealing cycle. Once stability is reached, it may be supposed that the

323

Fig. 6 Variation of the image segmentation according to the squared correlation coefficient value in the range from 0.91 (top left) to 0.99 (bottom right). Only pixels shown in color satisfied the correlation coefficient criterion

lowest minimum was obtained in every simulation. The final histogram is taken by averaging the total set of individual histograms, each one of them corresponding to different initial conditions. This procedure is performed in order to avoid the increase in condition number for the matrix used in the least square procedure when the number of components is also increased. The total processing time depends on the number of relaxation voxels, the number of data points for each relaxation data (eight in the present case) and the number of parallel simulations or replicas. In the present work a Pentium 4 Workstation working at 2.27 GHz was used for the calculations. The average processing time for a complete simulation was of 3.29 s, usually comprising two or more

annealing cycles in the optimization procedure. The average time needed for the evaluation of the histogram in a relaxation voxel was of 999.13 ± 195.74 s, for 300 simulations or replicas. Some results of the performance of the ILT algorithm are shown in Fig. 4. By inspection of the figure, it can be seen that the total processing time can be shortened considerably using a smaller number of simulations (instead of 300) and by an appropriate selection of the relaxation voxels in order to reduce its number. Further reduction of the processing time up to a limit close to the processing time per simulation or replica can be achieved by parallel computing. In its present form, the ILT algorithm can be used as a tool to determine precisely the relaxation spectrum within a region of interest but it

324

is impractical for the analysis of relaxation data on a pixel by pixel basis.

Results and discussion The histological tumor type found in the patient brains were glioblastoma multiforme(GM) (two patients), fibrillary astrocitoma grade III (one patient), fibrillary astrocytoma grade II (two patients), oligodendroglioma grade II (one patient), non-Hodgkin’s lymphoma (one patient) and meningioma (two patients). No biopsy was obtained from tumor of patient no.8 but MRI suggested a germinoma o craniopharyngioma. This patient did not return to the hospital after the MRI, 1 HMRS, and relaxometry studies. 1 HMRS ratios from control subjects were similar to published normal ratios [1]. 1 HMRS and histopathological results of ten brain tumors are presented in Table 1. All tumors exhibited different MR imaging and 1 HMRS results are expressed as Cho/NAA value. Cho/NAA ratio was used to distinguish between normal, atypical and probably malignant tissue. Vigneron et al. [7] and Nelson et al. [8] found significant Cho levels and a Cho/NAA ratio above 1.3 in patients with histologically confirmed tumors and 1.73 for confirmed cancer. Even though references [16] and [17] represent studies that were performed at long echo times, it can be expected that the threshold ratio Cho/NAA for pathology can be also assumed for short echo times, since the transversal relaxation times for Cho and NAA are very similar [37–42]. For this reason, in the present work any voxel, SVS or CSI, with a ratio Cho/NAA above 1.3 was considered suggestive of malignancy. This assumption turned out to be in good agreement with the histopathological results. Eight patients presented Cho/NAA ratios over 1.3. 1 HMRS results were confirmed later by histological analysis. Low and high grade tumors (grade II, III, and IV astrocytomas as well as non-Hodgkin lymphoma) presented Cho/NAA ratios over 1.3. Meningiomas presented Col/NAA ratios over 1.3. This result agrees with the literature were high Cho signal in meningiomas has been reported [2,42,43]. No alanine was detected. Benign tumor presented a Cho/NAA below 1.3 (patient no. 8). SVS results are showed in Table 1. The highest Cho/NAA and Cho/Cre values were obtained in patient no.1 who presented a GM. No NAA and high Cho signals were detected in patient no.2 who also presented a GM. patient no. 3 who had a grade III astrocytoma presented Cho/NAA and Cho/Cre values slightly elevated if compared with grade II astrocytomas. Even in the small number of patients studied in this work, the 1 H SVS results agree with those of the literature where the higher ratio values correspond to higher tumor grades

Fig. 7 Contour plot for a glioblastoma multiforme. Color scale is related to the value of the AR coefficient: red color indicates maximum value and blue indicates minimum value

Table 4 Values of p, < p >, v, and ρ for patients and controls

Patient number

p

1 2 3 4 5 6 7 8 9 10 C1 C2 C3 C4 C5 C6 C7

0.8415 0.9059 0.7152 0.7838 0.6873 0.7937 0.8393 0.6688 0.8436 0.7586 0.6191 0.5927 0.6149 0.5653 0.5507 0.6863 0.4444

p

0.5819 ± 0.0749

0.7838 ± 0.0766

v

ρ

8155 16030 4394 1947 6046 3095 2849 7793 5954 9914 489 714 316 57 23 878 4

85.52 137.65 53.35 69.42 79.25 86.87 100.41 32.88 133.35 72.82 51.45 37.31 26.04 21.95 20.31 49.48 37.89

Controls C3–C7 correspond to planes unaffected by the lesion. All the quantities represent averages over the complete set of planes (eight in total) except for controls C3–C7. All quantities are adimensional

325

Fig. 8 Segmented images: a and b for glioblastoma multiforme, c and d for meningiomas. Left: segmentation using RGB palette, middle: segmentation with gray palette and right: T2W image for TE = 22 ms

[4,44–46]. NAA/Cre ratios did not discriminate between possibly malignant and normal tissue. The number and percentage of CSI voxels with Cho/NAA above 1.3 (malignant) and between 0.8 and 1.29

(atypical) from the total voxels analyzed are presented in Table 2. Different numbers of voxels were analyzed from each patient. All patients with low and high grade tumors (II, III and IV astrocytoma and non-Hodgkin’s

326

Fig. 9 Segmented image. a for fibrillary astrocytoma grade III, b and c, for fibrillary astrocytomas grade II, c for oligodendroglioma grade II. Left: segmentation using RGB palette, middle: segmentation with gray palette and right: T2W image for TE = 22 ms

lymphoma) presented atypical and possible malignant voxels. Meningiomas also presented voxels with a high Cho/NAA ratio [2,42,43]. For each voxel in the relaxometry grid of a particular case, the relaxation rate spectrum was determined

using the ILT algorithm discussed in the previous section. Each relaxation rate spectrum obtained was correlated with SVS and CSI results and compared with histopathology. This was made taking into account not only the spectroscopic data for that voxel but also the data coming

327

Fig. 10 Segmented images for the control cases using the RGB palette. C1 and C2 correspond to healthy volunteers, while C3 through C7 correspond to unaffected slices in patients. Relaxation rates used for the segmentation in control cases C3 through C7 are those obtained from the analysis of the lesions and depicted in Table 3

from other voxels for which single relaxation spectra and interpretable spectroscopic data were available. Once the assignment of relaxation rates to pathology was established, an average relaxation spectrum over the lesion can be obtained to further determine the typical relaxation rates. The average relaxation spectra are shown in Fig. 5 and the results are summarized in Table 3. Inspection of Table 3 and Fig. 5 demonstrate that is not possible to obtain a typical relaxation spectrum or values of the relaxation rate for a particular type of tumor and that it is patient dependent. This is due to the fact that the lesions are of different dimensions and exhibit different

tissue heterogeneity, but nevertheless, a certain range can be establish for each kind of tissue present in the image: from 0.65 to 3.43 s−1 for edema or necrosis, from 5.05 to 7.47 s−1 for tumor and from 8.67 to 25.26 s−1 for normal or unaffected tissue. In order to obtain a segmentation of the lesion, we have selected a color code to indicate the existence of pathology: R (red) corresponds to tumor, G (green) to normal or unaffected tissue and B (blue) that corresponds to edema or necrosis, or in general, to the presence of liquid in the lesion. Instead of using the ILT algorithm for the determination of the relaxation rate or relaxation rate distribution pixel by pixel, i.e., a procedure

328

Fig. 11 Average probability distribution function or relaxation spectrum for a lesion (continuous line) and for non affected tissue (dotted line). Relaxation spectra were determined for the same patient. On the left are shown the relaxometry grids used to calculate the relaxation spectrum

Fig. 12 Single voxel spectrum and segmented images for possible craniopharyngioma

which is time consuming and sensitive to small signal to noise ratios, each pixel was analyzed assuming that it was composed at least of one of the tissue categories given in Table 3. This is equivalent to assuming that the image intensity in each pixel (in a set of multiecho images) is a linear superposition of three different decaying exponential functions, each one of them characterized by a relaxation rate and corresponding to a tissue category I (t) = bl + AR XR (t) + AG XG (t) + AB XB (t),

(6)

where Xi (t) = exp(−λi t)

(7)

with i = R, G or B, λi is the relaxation rate determined by assignment of pathology from the average relaxation spectrum, bl is a parameter introduced to take into account corrections in the baseline of the image intensity (also applied to the ILT algorithm) and the coefficients Ai , which are positive, determine the proportion of each relaxation decay in the image. Particular attention was paid to the correlation coefficient in the linear regression analysis, and in the present work, the coefficients Ai were only accepted for those fittings with a squared correlation coefficient higher than 0.99. This step is necessary because the exponential functions are correlated. For example, two

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exponential functions with relatively different decay exponents could have a squared correlation coefficient close to 1. Figure 6 shows how the image segmentation changes depending on the value of the squared correlation coefficient. Once the Ai s are determined the image can be segmented separately to show edema or necrosis, tumoral, and normal or unaffected tissue. In particular, for therapy purposes, it is important to isolate tumoral tissue and determine contour plots that describe the distribution of tumoral activity in the lesion. This information is depicted in Fig. 7. To further assess the segmentation procedure it is necessary to eliminate false “tumor positive” pixels due to the fact that the exponential functions are correlated. A “tumor density probability”, p, is defined in the following way: for only those pixels with an AR coefficient different from zero, an average is taken over its neighboring pixels including the pixel itself, assigning the value of 1 if the pixel has an AR = 0 and a value of 0 if AR = 0. The average obtained in this way represents the value of p and its maximum value is 1, a situation that occurs if and only if, the central pixel and all the pixels around it have an AR = 0. The pixel is accepted as a true “tumor positive” if and only if p, is greater than 1/3. With this filtering process a more compact segmentation of the tumor is obtained as it eliminates isolated low density pixels and pixel clusters. The segmentation procedure outlined before depends on the particular set of relaxation rates. The combination of the ILT algorithm and the spectroscopic data provides not only the mean relaxation rates but also their dispersions. In order to fully assess the segmentation of the image several set of relaxation rates were used, constructed in the following way: for each relaxation rate value, i.e., the mean value in the relaxation rate spectrum for a particular tissue type, a set of three values are generated, one is the mean value itself and the other two are obtained by adding or subtracting its standard deviation; all 27 combinations were considered in an optimization procedure to maximize the parameter p. Typical values of p covered a range of 0.67–0.96. Control values of p ranged from 0.44 to 0.69. For the calculation of the control parameters not only images obtained from control volunteers were used, but also those planes in patients that were clearly unaffected by the lesion. This is shown in Table 4. Other quantities can be defined to evaluate the tumor, such as the “volume”, v, defined as the number of positive voxels in a particular image, and the “mean tumor image intensity”, ρ, which is the local average image intensity for positive pixels. These additional parameters are also shown in Table 4. Instead of using color code, a gray palette can be used to map the RGB code on a gray scale as follows: AR in 206–255 (light gray), AG in 51–205 (gray), and AB in 0– 50 (dark gray). This procedure is useful when no color display is available, and in general is more familiar to the radiologist, who is trained in analyzing images based on

a gray scale and the particular mapping selected closely resembles gadolinium contrasted images. Additionally, it preserves anatomical details of the image, which are of relevance for image registration or fusion procedures, commonly used in therapy planning. The comparison between color RGB code segmentation and gray scale mapping can be seen in Figs. 8 and 9. Analysis of Figs. 8 and 9 demonstrate that in most cases a segmentation of the lesion can be done. In particular, in Fig. 8a, b and 9a through c, correspond to glioblastoma multiformes and fibrillary astrocytomas, respectively. It is possible to separate the active region of the tumor from its necrotic center and also to quantify the proportion of necrosis to active tumor, a relation that could be very useful in the evaluation of a tumor under therapy. In the case of more benign tumors, such as oligodendrogliomas, Fig. 9d and meningiomas, Fig. 8c, d, it is also possible to define a good segmentation of the lesion and to establish a follow up under therapy. In Fig. 10, the segmented images corresponding to control cases are shown. For control cases C1 and C2, the images were segmented using the relaxation rates coming from the ILT procedure applied to their own set of slices and also using the average relaxation rates obtained from the patients, i.e., these relaxation rates include those corresponding to malignant tissue. For control cases C3 through C7, the relaxation rates used in the segmentation were those obtained by the ILT procedure on the slices that exhibited the pathology. This assumption is justified since the relaxation spectrum within the lesion differs noticeably from the relaxation spectrum obtained from regions of unaffected issue, as depicted in Fig. 11. In either case, the segmentation obtained for control cases did not reveal any significant manifestation of pathology as can be seen in Fig. 10. Finally, in the case of patient no.8, a possible craniopharyngioma, the resulting segmentation is shown in Fig. 12, together with the SVS spectrum. The segmented image is consistent with the 1 HMRS evaluation in the sense that the lesion is not malignant. Nevertheless, since no CSI could be performed on this patient, the segmentation was performed by analyzing the relaxation data and assuming that the relaxation associated with malignant activity was located in the same range as in the other cases studied. This procedure could account for some of the red coloring that is observed on the left of the image.

Conclusions This study combines two non invasive methods 1 HMRS and Relaxation studies, in order to utilize them as complementary methodologies in the assessment of brain tumors. The methodology devloped in this work mixes successfully data coming from 1 HMRS and relaxometry

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to produce appropriate segmentation of tumor images with enough spatial resolution to be used for tumor evaluation and therapy planning. The methodology uses a new algorithm (ILT) to perform the analysis of the relaxation data without making initial assumptions about the characteristics of the tissue. This makes it a powerful tool for the determination of the actual relaxation rate distributions, which is the key factor necessary for the correct segmentation and assessment of the tumor image. This fact opens the possibility to use the relaxation spectra on the same foot as 1 HMRS spectra to determine nosologic images [23–25] with higher spatial resolution, improving the determination of the gross tumor volume (GTV), necessary for treatment planning. Segmentation methodologies and strategies taken from the analysis of nosologic images derived from 1 HMRS spectra alone could also be applied or extended to these new combined images. Also, if a correlation between relaxation rate and spectroscopic data can be established, a task that will be undertaken in the

future, the methodology developed in this work could be used as a tool to improve the spatial resolution of CSI maps by acting in a retrograde manner: the spectroscopic information obtained in a not well defined CSI voxel, (a voxel with atypical metabolite ratios), will be decomposed according to the proportion of its relaxation components, each one associated to each tissue. This will lead to a metabolic map with a higher spatial resolution than the one obtained with the standard CSI sequence. The methodology may also be associated with other imaging techniques, like diffusion or perfusion to further assess the localization of the tumor. Its application can be extended to other organs like breast or prostate. Acknowledgements The authors would like to thank the MRI radiologists and technologists from the Instituto de Resonancia Magnética La Florida-San Roman, Caracas, Venezuela who helped in this pro´ ject. This work was financially supported by Centro de Diagnostico Biomagnetic, C.A.

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