The methodology behind correlated diffusion imaging (CDI) is summarized in Figure 1. First, multiple signal acquisitions are conducted at different gradient pulse strengths and timings. Second, the acquired signals are then mixed together to obtain the local correlation of signal attenuation across the acquired signals, which produces a final signal that characterizes the tissue being imaged. A detailed description of the steps involved is presented below.
Imaging protocol
To evaluate the effectiveness of CDI for prostate cancer diagnosis, twenty patient cases with known prostate cancer were used in this study. The patients ranged in age from 58–80 years, with a median age of 69 years. Informed consent was obtained from all patients, and approval for this study was obtained from the ethics review board of Sunnybrook Health Sciences Centre. All results were reviewed by an expert radiologist with 16 years of experience interpreting body MRI and 11 years of experience interpreting prostate MRI.
Examinations using CDI were performed using a Philips Achieva 3.0T machine at Sunnybrook Health Sciences Centre, Toronto, Canada. The axial echo-planar sequence was performed for CDI with the following imaging parameters: TR range from 3336 – 6178 ms with a median of 4890 ms, and TE ranged from 61 – 67 ms with a median of 61 ms. The resolution of the signal acquisitions ranged from 1.36 × 1.36 mm2 to 1.67 × 1.67 mm2, with a median of 1.56 × 1.56 mm2. Slice thickness ranged from 3.0 – 4.0 mm with a median of 3.5 mm. The display field of view (DFOV) ranged from 20 × 20 cm2 to 24 × 24 cm2 with a median of 24 × 24 cm2.
For comparison purposes, apparent diffusion coefficient (ADC) maps were also obtained using the same axial echo-planar sequence with the same imaging parameters and Ω = {0s/m m
2,100s/m m
2,1000s/m m
2}, as it is considered state-of-the-art for prostate cancer analysis in existing diffusion imaging [24]. Finally, axial T2-weighted imaging acquisitions with the same slice locations as the CDI sequence were obtained as a baseline reference of comparison. Examinations using T2-weighted imaging were performed using a Philips Achieva 3.0T machine with the following imaging parameters: TR range from 4688 – 7504 ms with a median of 6481 ms, and TE range from 110 – 120 ms with a median of 120 ms. Slice thickness ranged from 3.0 – 4.0 mm with a median of 3.5 mm. The display field of view (DFOV) ranged from 20 × 20 cm2 to 24 × 24 cm2 with a median of 24 × 24 cm2.
Signal acquisition
As the first step of the CDI imaging process, axial single-shot echo-planar sequences with two gradient pulses of equal magnitude (one pulse in each side of the 180o pulse to dephase and rephrase the spins, respectively), as shown in Figure 2 are used to obtain multiple signal acquisitions using a set of different configurations of gradient pulse strengths and timings, which we will denote as Ω = {q
i
|i = 1,...,N}, where q
i
denotes the i
th sequence.
Imperfect rephasing occurs due to motion of water molecules, leading to attenuation in the acquired signal and thus allowing for the study of water diffusion based on signal attenuation behavior. By varying the configuration of gradient pulse strengths and timings between signal acquisitions, each signal acquisition is sensitive to a different degree of Brownian motion of water molecules in tissues, thus providing unique information with respect to the water diffusion characteristics of the tissue being imaged. The different configurations of gradient pulse strengths and timings can be defined by the following set of parameters [27]:
(1)
where, for the i
th sequence, G
i
denotes the gradient pulse strength, δ
i
denotes the gradient pulse duration, and Δ
i
denotes time between gradient pulses. By grouping the gradient terms, the configuration of gradient pulse strengths and timings used for a particular sequence q
i
can be simplified to [28]
(2)
where γ denotes the proton gyromagnetic ratio.
Signal mixing
As the second step of the CDI imaging process, the multiple signal acquisitions are mixed together to obtain the final signal that characterizes the tissue being imaged. Here, we are interested not in the signal attenuation obtained using the individual configurations of gradient pulse strengths and timings, but in the local correlation of signal attenuation across the different configurations of gradient pulse strengths and timings within a local spatial sub-volume V to provide a better overall characterization of the water diffusion properties of the tissue being imaged. As such, we would like to mix all of the signal acquisitions together into a single quantitative signal characterizing the local signal attenuation correlation.
To achieve this goal, we introduce the following signal mixing function for characterizing local signal attenuation correlation, which is parameterized by diffusion range defined by [q
α
,q
β
] and is defined as
(3)
where denotes spatial location, S denotes the acquired signal, f denotes the conditional joint probability density function, and denotes the local sub-volume around . For this study, [q
α
,q
β
] was set at [0s/m m
2,2000s/m m
2], and V was defined as a 7 mm3 spatial sub-volume for assessment purposes as it was found to provide good tissue delineation.
Image analysis and interpretation
The ADC maps and CDI images were reconstructed using the ProCanVAS (Prostate Cancer Visualization and Analysis System) platform developed at the University of Waterloo Vision and Image Processing research group, and were analyzed such that each modality was analyzed independent of other modalities. All visual assessments were made by an expert radiologist with 16 years of experience interpreting body MRI and 11 years of experience interpreting prostate MRI.
Statistical analysis
Two different analysis strategies were performed to quantify the potential of CDI as a tool for prostate cancer detection and localization. In the first analysis strategy, a receiver operating characteristic (ROC) curve analysis was performed using CDI to quantitatively assess prostate detection and localization. The ROC curves were estimated assuming bivariate normal data. For illustrative purposes, the ROC curves obtained from the pooled data of all patient cases was plotted. To provide a quantitative assessment of diagnostic accuracy, the area under the ROC curve (A
z
) was obtained as a single metric of diagnostic accuracy. For comparison purposes, ROC curve analysis was also performed using ADC map as the baseline reference method for assessing prostate cancer using diffusion imaging.
In the second analysis strategy, we wish to study whether CDI would be a useful imaging modality for building computer-aided clinical decision support systems to assist in the prostate cancer detection and localization process. To quantify the usefulness of CDI for the purpose of building such systems, leave-one-out cross-validation (LOOCV) trials were performed across all patient cases. For each trial, a two-class Maximum Likelihood (ML) classifier model is trained based on the CDI signal intensity statistics of the individual voxels within the prostate gland (one class characterizing cancerous tissue, with the other class characterizing healthy tissue) across the training patient cases. This learned two-class ML classifier model is then used to calculate sensitivity, specificity, and accuracy for the validation patient case. This process is repeated for a number of trials so that each patient case is used once as the validation patient case. The same was performed on ADC for comparative purposes.