An isotropic apparent diffusion coefficient (ADC) obtained from diffusion-weighted imaging (DWI) with a monoexponential model may not be able to accurately reflect water molecular diffusion in vivo due to influence by the microcirculation of blood in capillaries¹. The purpose of this study was to quantitatively compare the potential of various diffusion parameters obtained from monoexponential, biexponential, and gamma distribution models in differentiating vertebral lesions in human subjects.

Theoretical Background:

The ADC value was calculated using a monoexponential model as follows:

S(b)/S(0) = exp(-b·ADC),

where S(b) represents the signal intensity in the presence of diffusion sensitization, b, and S(0) represents the signal intensity in the absence of diffusion sensitization.

Three parameters: perfusion fraction (f), pseudo-ADC (ADC_fast), and true ADC (ADC_slow), were calculated using biexponential intravoxel incoherent motion analysis¹:

S(b)/S(0)= [f·exp (-b·ADC_fast)] +[(1 - f )·exp(-b·ADC_slow)].

The GDM assumes a continuous distribution of diffusion coefficients, P(D). The DW signal can be written as follows:

(1) $$S(b)=\int P(D)exp(-bD)dD$$

The gamma distribution function, PG(D) has been suggested recently²:

(2) $$PG(D,\kappa,\theta)=D^{\kappa-1}\frac{exp(-D/\theta)}{Γ(\kappa)\theta^{\kappa}}$$

where Γ is the gamma function, θ is the scale parameter of the same dimensionality as the diffusivity, and κ is the shape parameter. Replacing P(D) in Eq. (1) by PG(D) in Eq. (2), gives the following expression for the DW signal attenuation:

S(b)=(1+bθ)^-κ

The excess kurtosis K of the diffusion probability distribution function (PDF) can be calculated as:

(3) $$K=\frac{\mu_{4}}{\mu_{2}^{2}}-3=\frac{12t^{2}(\kappa^{2}\theta^{2}+\kappa\theta^{2})}{4t^{2}\kappa^{2}\theta^{2}}-3=\frac{3}{\kappa}$$

where μn is n^th moment of the PDF.

MRI examination:

DW images of the 73 subjects’ lumbar spines were categorized as follows: patients with normal bone marrow (n=43), patients with acute spinal fracture (n=11), and patients with malignant spinal tumor (n=19; multiple myeloma, 8; lymphoma, 3; chordoma, 2; acute lymphocytic leukemia, 2; metastatic tumor from lung cancer, 4). MRI examinations were performed on a 3T system (Ingenia; Philips Healthcare) equipped with the anterior coil and the integrated posterior coil. Single-shot DW EPI with 9 values (0, 40, 80, 140, 200, 500, 1000, 1500, 2000) on 3 orthogonal axes were performed with the following acquisition parameters: TR/TE =8000/84 ms, FOV= 35×35 cm², matrix size 192×192, in-plane voxel size 1.8×1.8 mm², slice thickness 4 mm, number of slices 11, slice gap 1 mm, factor of 3 SENSE on the phase direction, and 1 average.

Image data analysis:

Mean signal intensity was calculated by placing operator-determined regions of interest (ROIs) within the malignant spinal lesions or within the bone marrow (BM) of an acute vertebral fracture or within normal BM for each b-value in each subject. Signal intensity values for BM were calculated as the mean value obtained from the L1 to L3 vertebral bodies for normal subjects. For each of subject, ADC, f, ADC_fast, ADC_slow, scale parameter θ, scale parameter κ, the area fraction of D < 1.0mm²/s (frac <1), the area fraction of D > 3.0 mm²/s (frac >3), PG(D) and K, calculated from the GDM, were measured using equations (1-3).

Statistical analysis:

Parameters of the 3 groups (i.e., normal-, fracture-, and malignant groups) were compared by the Kruskal-Wallis test. Multiple regression analysis was performed to identify the potential association of diffusion model parameters for differentiating BM diseases and receiver operating characteristic analyses were then performed.

Table 1 summarizes the MR parameters for the 3 groups. All MR parameters, except for ADC_fast and frac > 3, were significantly different between normal BM and lesions. Perfusion fraction f, scale parameter θ, and PG (D) proved to be useful for the differentiation of malignant lesions from acute spinal fractures.

Multiple regression analysis demonstrated that the perfusion fraction f (P=0.03) and and PG(D) (P=0.02) contributed to the risk for malignant spinal lesions. Areas under the curve (AUCs) were 0.727 for PG(D) (sensitivity: 84.2%, specificity: 63.6%), and 0.703 for perfusion fraction f (sensitivity: 68.4%, specificity: 81.8, Fig. 1).

A meta-analysis in 2008 concluded that the capability of ADC to distinguish benign fractures from pathologic fractures was dependent on signal intensity in a fractured vertebra on DWI³. In this study, perfusion fraction f and PG(D) were shown to be useful for differentiating benign fractures from malignant spinal lesions. They had similar AUCs for differentiation, but these 2 parameters might be regarded as complementary regarding sensitivity and specificity.

Water molecular diffusion parameters may provide additional information and improve the differentiation of spinal lesions compared with conventional diffusion parameters, which would be helpful in improving therapy strategies and prognoses. This also refers to differentiation of malignant lesions from acute spinal fracture, in which both PG (D) calculated from GDM and perfusion fraction f of the biexponential model proved to be useful.