Reducing the influence of b-value selection on diffusion-weighted imaging of the prostate: evaluation of a revised monoexponential model within a clinical setting

Abstract

Purpose

To compare the accuracy of standard and revised monoexponential models of diffusion-weighted MR imaging (DW-MRI) data for differentiating malignant from benign prostate tissue, using surgical pathology as the reference standard.

Materials and Methods

The institutional review board waived informed consent for this HIPAA-compliant, retrospective study of 46 patients (median age=61 years; range: 42–85 years) who underwent DW-MRI between May and December 2008 before radical prostatectomy for biopsy-proven prostate cancer, had no prior treatment, and had whole-mount step-section pathology maps available showing at least one peripheral zone (PZ) lesion >0.1 cm³. DW-MRI data were obtained for b-values of 0, 400, and 700 s/mm². Apparent diffusion coefficients (ADCs) were estimated from PZ regions of interest (ROIs) on b=0, 700 and b=0, 400 s/mm² images, using a standard monoexponential model. The true diffusion coefficent (D) and perfusion fraction (f) were measured using a revised monoexponential model incorporating all three b-values. Areas under receiver operating characteristic curves (AUCs) were calculated to assess the accuracy of individual parameters and a logistic regression model combining D and f (D+f) in distinguishing malignant ROIs; P<0.05 denoted significance.

Results

ADC₄₀₀ (AUC=0.81, p<0.0001), ADC₇₀₀ (AUC=0.79, p<0.0001), D (AUC=0.71, p=0.0001) and D+f distinguished malignant from benign ROIs (AUC=0.82, p<0.0001), but f did not (AUC=0.56, p=0.28); D+f was significantly more accurate than D (p=0.016) but not more accurate than ADC₄₀₀ (p=0.26) or ADC₇₀₀ (p=0.12).

Conclusion

The true diffusion coefficient provides an additional DW-MRI parameter for distinguishing prostate cancer that is less influenced than the ADC by b-value selection.

INTRODUCTION

Diffusion-weighted magnetic resonance imaging (DW-MRI) is a non-invasive technique that is sensitive to the structure of biological tissue at the microscopic level. Preliminary studies at both 1.5 Tesla (T) and 3.0 T have suggested that apparent diffusion coefficient (ADC) values calculated from monoexponential analysis of DW-MR images may have clinical utility in prostate cancer detection (1-4) and tumor volume measurement (5) and may also help differentiate between Gleason scores (6,7).

In biological tissues, microscopic motion detected by DW-MRI includes both diffusion of water molecules, influenced by the structural components of the tissue, and microcirculation of blood in the capillary network (perfusion). The standard monoexponential diffusion model requires at least two acquisitions (one with a b-value of 0 and one with a higher b-value) to generate ADC maps. Although straightforward, this model ignores the rapid signal decay caused by microperfusion at low b-values and yields ADCs that are influenced by the choice of the second b-value. To compare results from different centers using this model would require selection of the same second b-value by all centers.

To separate perfusion effects from pure diffusion in DW-MRI studies, Le Bihan proposed the intravoxel incoherent motion (IVIM) bi-exponential model (8-10). To estimate diffusion parameters with this model, diffusion signal was measured for a large number of b-values, ranging from very low to high. Although it is more detailed than the monoexponential model, the biexponential model makes assumptions regarding the microcirculation and provides estimates that are not sufficiently reproducible to make it a reliable measurement tool (11-13). Furthermore, acquiring images at a large number of b-values is impractical in the clinical setting, firstly because the advanced software needed to process the data is not always available, and secondly because it is important to minimize the duration of the examination for patient comfort.

We sought to develop a model appropriate for use in the clinical setting that would reduce the influence of b-value selection on DW-MRI while producing images of adequate quality. Therefore, based on the pioneering work of LeBihan, et al., we applied a revised monoexponential model that provides estimates of true diffusion (D) and perfusion fraction (f) with a minimum of just three b-values. The purpose of our study was to retrospectively compare the accuracy of the standard and revised monoexponential models of DW-MRI data for differentiating benign from malignant prostate tissue, using whole-mount step-section histopathology as the reference standard.

MATERIALS AND METHODS

DW-MRI Data Analysis

Standard Monoexponential Model of Diffusion

In the standard monoexponential model of diffusion, the ADC is given by:

$$S\left(b\right)=S\left(0\right)\cdot \exp (-b\cdot \mathrm{ADC})$$ [1]

Where S(b) and S(0) are signal intensities of each voxel with and without diffusion weighing, respectively, and b is the diffusion-sensitizing factor (b-value). ADC maps are constructed according to Eq. [1] with a b-value of 0 and a second non-zero b-value. In our study, we used b-values of 0 and 400 s/mm² to generate ADC₄₀₀, and b-values of 0 and 700 s/mm² to generate ADC_700.

Revised monoexponential Model of Diffusion

LeBihan, et al. presented a model of diffusion in biological tissue, where the effect of perfusion on the total signal was modeled by taking into account the volume fraction f of the tissue water flowing through the microvessels (10). According to their model, the signal attenuation is given by:

$$S\left(b\right)=S\left(0\right)\cdot \exp (-b\cdot D)\cdot \left[\right(1-f)+f\cdot F]$$ [2]

Where S(b) and S(0) are the signal amplitudes at b-values b and zero, respectively, D is the diffusion coefficient, f is the volume fraction of water in perfused capillaries, and F is a quantity due to microcirculation, has a value ≤ 1, and the value of which depends on capillary geometry and blood velocity (10).

In the revised monoexponential model, the effect of perfusion is incorporated. With the assumption: f•F << 1 − f, ADC_b, the apparent diffusion coefficient measured with b-values of b and zero, is expressed as the sum of D, and the contribution due to perfusion:

$${\mathrm{ADC}}_{\mathrm{b}}=\mathrm{D}+\log [1∕(1-f\left)\right]∕b$$ [3]

With the additional assumption of f << 1, Eq. [3] reduces to the linear expression:

$${\mathrm{ADC}}_{\mathrm{b}}\cong \mathrm{D}+\frac{\mathrm{f}}{\mathrm{b}}$$ [4]

ADC_b were first calculated with a b-value of 0 and a second non-zero b-value (Eq. [1]). The ADC_b estimate is then used in Eq. [4] to determine D and f. Figure 1 shows plots of simulated biexponential diffusion signal for benign and malignant prostate tissue based on the values reported by Riches et al (13) and the corresponding values of D and f obtained from modeling the diffusion signal with a linear expression of the logarithmic signal intensity as a function of the b-values (Eq. [4]) to solve for D and f. Assuming that diffusion signal is described by a biexponential model with the parameters based on values reported in the literature for prostate (13), the revised monoexponential model based on Eq. [4], with the acquisition of only three b-values 0, 400, and 700 s/mm² accurately estimates D and f, in both benign and malignant prostate tissue.

Figure 1.

Simulated normalized logarithmic diffusion signal intensity (log(S(b))/S(0)) as a function of b-value based on values reported by Riches et al (13). The plot shows the estimated values of ADC₄₀₀ and ADC₇₀₀ obtained from the standard monoexponential model and D and f obtained from the revised monoexponential model. (A) For benign PZ, the simulated biexponential signal is generated using the following reported parameters (13): D= 1.45×10⁻³ mm²/s, f = 0.20, and D*= 21.20×10⁻³ mm²/s. Estimated ADC values are: ADC = 2.01×10⁻³ 400 mm²/s, ADC = 1.77×10⁻³ mm² 700 /s. Estimated values for the revised monoexponential are: D= 1.45×10⁻³ mm²/s, f = 0.22. (B) For tumor the simulated biexponential signal is generated using the following reported parameters (13): D= 1.10×10⁻³ mm²/s, f= 0.15, and D* = 25.20×10⁻³ mm²/s. Estimated ADC values are: ADC₄₀₀= 1.51×10⁻³ mm²/s, ADC₇₀₀= 1.33×10⁻³ mm²/s. Estimates values for the revised monoexponential are: D= 1.10×10⁻³ mm²/s, f= 0.16.

Patient Population

Our institutional review board waived the requirement for informed consent for this retrospective study, which was compliant with the Health Insurance Portability and Accountability Act. A total of 46 patients were identified (median age = 61 years; range: 42–85 years) who met the inclusion criteria for our study, which were as follows: a) biopsy-proven prostate cancer; b) MRI examination with DW-MRI performed between May and December 2008 before radical prostatectomy; c) no prior hormonal or radiation treatment; d) whole-mount step-section pathology maps available for review; e) at least one PZ lesion with volume > 0.1 cm³ on whole-mount step-section pathology.

MRI Data Acquisition

MRI examinations were performed on a 1.5-T whole-body MRI unit (GE Medical Systems, Milwaukee, WI). A body coil was used for excitation, and a pelvic four-channel phased-array coil combined with a commercially available balloon-covered expandable endorectal coil (Medrad, Pittsburgh, PA) was used for signal reception. Our institution’s standard clinical prostate MRI examination was used to obtain transverse T1-weighted images (TR/TE = 400–700/10–14 ms, 5-mm slice thickness, 0-mm inter-slice gap, 24-26–cm field of view [FOV], matrix, 256×192) and transverse, coronal, and sagittal T2-weighted (T2W) fast spin-echo images (TR/effective TE, 4000–6000/96–120 ms, echo train length, 12–16, 3-mm slice thickness, no inter-slice gap, 12-14–cm FOV, matrix 256×192) of the prostate and seminal vesicles.

DW-MR images were obtained using a spin-echo echo-planar imaging (SE-EPI) sequence with a pair of rectangular-shaped gradient pulses along three orthogonal axes. Imaging parameters were TR = 4000–5475 ms, TE = 77.6–110.3 ms, FOV = 14×14 cm², 3-mm slice thickness, no inter-slice gap; b-values were 0, 400, and 700 s/mm². The orientation and location prescribed were identical to those prescribed for the transverse T2W images of the prostate. Four to eight averages were obtained and the scan duration of the DW-MRI component was approximately four minutes.

Histopathological Analysis and Image Correlation

For each patient, the prostatectomy specimen was serially sectioned from apex to base at 3-mm axial intervals and submitted in its entirety for paraffin embedding as whole mounts. After paraffin embedding, microsections were placed on glass slides and stained with hematoxylin and eosin. The cancer foci were outlined in ink on whole-mount step-section pathologic slices of the prostate so as to be grossly visible and were subsequently photographed (14).

Image Analysis

A radiologist matched the whole-mount step-section pathologic slices with the corresponding DW-MR images with b=0 s/mm² (i.e., no diffusion weighting). At the time of the study, reader 1 (H.A.V.) was a body imaging fellow with a special interest and 2 years experience in prostate MR imaging. Anatomical landmarks that were used as the basis for pairing the most closely corresponding axial DW images and pathologic step-section slices included the presence of urinary bladder and seminal vesicle tissue in superior slices, the slice with the largest diameter and progressive changes in the diameter of the slices, the thickness of the peripheral zone, the position of the pseudocapsule, and the presence, size, and shape of the transition zone. DW-MR images rather than T2-weighted images were used so as to reduce error associated with patient motion and distortions caused by susceptibility-related artifacts. With both the pathology maps and the DW-MR images displayed, the largest possible elliptically shaped region of interest (ROI) was placed on the PZ tumor. A corresponding ROI of the same size as the tumor ROI was drawn on the opposite side of the prostate where there was no indication of prostate cancer on the pathology slides. If cancer existed on both sides of the sextant, only an ROI outlining the cancer was drawn. ROIs were not drawn in areas containing post-biopsy hemorrhage or prostate capsule. The average signal intensity from each ROI was extracted for the DW data analysis.

Statistical Analysis

Analyses were performed with StataSE 11.0 for Windows (Stata Corporation, College Station, TX, 2005) and with PASW statistics software for Windows (SPSS Inc. Chicago, IL). The mean ADC values and mean D and f values of the malignant ROIs were compared to those of the benign ROIs using paired t-tests. Receiver operating characteristic (ROC) curves and the corresponding areas under the curves (AUCs) were estimated non-parametrically for the detection of cancer for each parameter. In all statistical methods, a p-value of less than 0.05 was considered to indicate a significant difference. Because lower values of diffusion parameters (i.e., ADC₄₀₀, ADC₇₀₀, and D) are associated with cancer, for the ROC analysis we multiplied the values by -1 so that the calculated AUCs correspond to detection of cancer. To adjust for the correlated data, the standard errors and comparisons between AUCs were calculated using the methods of Obuchowski (15).

Next, we developed a model to predict cancer status based on D and f. We applied a binary logistic regression modeling approach using generalized estimating equations (GEE). To produce a bias-corrected estimate of the AUC for the logistic regression model (to compensate for the fact that the model was evaluated using the same data from which it was built), we used the bootstrap resampling method (16). We used a conservative estimate of 500 bootstrap estimations based on the literature.

RESULTS

In the radical prostatectomy specimens of the 46 patients included in the study, a total of 67 PZ tumors had pathological volume > 0.1 cm³. At pathologic examination, thirty-five patients had one lesion each, thirteen patients had two lesions each, and two patients had three lesions each. The mean serum PSA level for the cohort was 5.00 ng/mL (range, 1.19-10.81 ng/mL), with a median value of 4.95 ng/mL. Thirty-seven patients (80%) had a surgical Gleason score of 7 or less (Table 1). In addition, a large majority of patients (76%) had a clinical stage of T1c. The median Gleason score at surgical pathology was 7 (range, 6-9).

Table 1.

Distribution of Pathological Findings and Patient Characteristics

	N	%
Biopsy Gleason Grade
3+3	32	70
3+4	9	20
4+3	2	4
4+4	3	6
4+5	0	0
Clinical stage
T1c	35	76
T2a	4	9
T2b	4	9
T2c	2	4
T3a	1	2
Surgical Gleason Grade
3+3	8	17
3+4	29	63
4+3	4	9
4+4	4	9
4+5	1	2
	Median	Range
Age (years)	61	42–85
PSA (ng/mL)	4.95	1.19 – 10.81

Mean ADC_400, ADC₇₀₀ values (derived from the standard monoexponential model) and mean D values (derived from the revised monoexponential model) for malignant ROIs were significantly lower than those for benign ROIs (Table 2). The mean f value for malignant ROIs was not significantly lower than that for benign ROIs (Table 2). Figures 2 and 3 show representative pathologic maps, T2W-MR images, and parametric maps generated from DW-MRI from a single patient. Comparison of ADC₄₀₀ and ADC₇₀₀ shows that the pseudo-diffusion effects are lower when higher b-values are used and the contribution of perfusion to ADC values decreases as b increases. Using Eq. [4], a linear fit of the logarithmic signal is used to solve for D and f. The tumor is clearly depicted on T2W-MRI and on ADC₄₀₀, ADC₇₀₀, and D maps, but not on the f map. The mean ADC₄₀₀ and ADC₇₀₀, D, and f values from all malignant and benign ROIs in the PZ included in our study are shown in Figure 4.

Table 2.

Descriptive statistics for ADC₄₀₀ and ADC₇₀₀ values derived with the standard monoexponential model and D and f values derived with the revised monoexponential model, in benign and malignant regions of interest in the peripheral zone.

	*Benign PZ	*Tumor PZ	AUC (95% CI)	p-value
ADC400 (× 10−3 mm2/s)	1.96 (1.23 – 3.71)	1.56 (0.98 – 2.33)	0.81 (0.72, 0.89)	< 0.0001
ADC700 (× 10−3 mm2/s)	1.71 (1.04 – 3.61)	1.34 (0.84 – 1.87)	0.79 (0.71, 0.87)	< 0.0001
D (× 10−3 mm2/s)	1.38 (0.68 – 3.47)	1.05 (0.19 – 1.89)	0.71 (0.62, 0.81)	0.0001
f	0.20 (−0.03 – 0.41)	0.20 (−0.10 – 0.60)	0.56 (0.46, 0.67)	0.28

^*Data are mean values (data in parentheses are ranges). PZ = peripheral zone; AUC = area under the receiver operating characteristic curve. The AUC reflects the accuracy of the parameter for distinguishing between benign and tumor tissue in the PZ. The p-value describes the statistical significance of the difference between the mean parameter values for benign and tumor tissue in the PZ.

Figure 2.

Representative data from a 68-year-old patient with prostate cancer, pre-surgical PSA level of 6.29 ng/mL, clinical stage T2a, surgical Gleason score 4+5. (A) Whole-mount step-section histopathologic map shows one of nine slices of the prostate gland. Tumor was present on six slices. (B) Closest transverse T2-weighted image corresponding to the whole-mount step-section pathologic slice in (A). (C) ADC₄₀₀ [mm²/s] and (D) ADC₇₀₀ [mm²/s] maps of the same slice as the T2-weighted image shown in (B). (E) D [mm²/s] map and (F) f [no units] map. DW-MRI acquisition parameters were TR/TE=4000/99.8 ms, field of view=14×14 cm², 3-mm slice thickness, no inter-slice gap, with a 1.9×1.9 mm² in-plane resolution.

Figure 3.

Representative data from a 57-year-old patient with prostate cancer, pre-surgical PSA level of 4.99 ng/mL, clinical stage T1c, surgical Gleason score 4+3. (A) Whole-mount step-section histopathologic map shows one of eight slices of the prostate gland. Tumor was present on four slices. The cancer foci were outlined in color inks by a pathologist to denote Gleason score (Gleason grade ≤ 3, green; Gleason grade 4 or 5, black). (B) Closest transverse T2-weighted image corresponding to the whole-mount step-section pathologic slice in (A). (C) ADC₄₀₀ [mm²/s] and (D) ADC₇₀₀ [mm²/s] maps of the same slice as the T2W image shown in (B). (E) D [mm²/s] map and (F) f [no units] map. DW-MRI acquisition parameters were: TR/TE= 4000/99.8 ms, field of view (FOV)= 14×14 cm², 3 mm slice thickness, no inter-slice gap, with a 1.9×1.9 mm² in-plane resolution.

Figure 4.

Box-and-whisker plots of (A) ADC_400, (B) ADC₇₀₀, (C) D, and (D) f of prostate cancer and benign tissue in the peripheral zone.

Based on the results of the logistic regression model combining D and f (Table 3), the following was obtained:

$$\text{Probability of ROI being cancerous}=\mathit{exp}[7.7-4399.7\times D-11.64\times f]∕(1+\mathit{exp}[7.7-4399.7\times D-11.64\times f\left]\right)$$ [5]

Table 3.

Regression model for combining D and f information to estimate the probability of a region of interest being cancerous ^*

	Regression coefficient	95% CI	p-value
Mean D	−4399.7	(−6210.3, −2589.1)	< 0.0001
Mean f	−11.64	(−18.35, −4.93)	0.001

^*Obtained from a logistic regression model with an estimated intercept (95% CI) parameter of 7.7 (4.45, 10.94).

In differentiating malignant from benign ROIs in the PZ, the combination of D and f (AUC=0.82, 95% CI [0.74, 0.90]) was not significantly more accurate than ADC₄₀₀ (AUC=0.81, 95% CI [0.72, 0.89]; p=0.26) or ADC₇₀₀ (AUC=0.79, 95% CI [0.71, 0.87]; p=0.12) but was significantly more accurate than D alone (AUC=0.71, 95% CI [0.62, 0.81]; p=0.016) (Fig. 5). There was no significant difference in accuracy between D alone and ADC_400, but ADC₇₀₀ was significantly more accurate than D alone (Table 4).

Figure 5.

Receiver operating characteristic curves reflecting the abilities of ADC₄₀₀, ADC_700, D and a model combining D and f to differentiate between tumor and benign regions of interest in the peripheral zone. The areas under the curves were 0.81, 95% CI (0.72, 0.89) for ADC₄₀₀, 0.79, 95% CI (0.71, 0.87) for ADC_700, 0.71, 95% CI (0.62, 0.81) for D, and 0.82, 95% CI (0.74, 0.90) for the model combining D and f.

Table 4.

P-values for differences in AUC values of ADC₄₀₀, ADC₇₀₀, D and the model combining D and f

	ADC400	ADC700	D	D +f
ADC400	--	0.47	0.06	0.26
ADC700	0.47	--	0.007	0.12
D	0.06	0.007	--	0.016
D + f	0.26	0.12	0.016	--

DISCUSSION

In this study, we compared the abilities of standard and revised monoexponential models of DW-MRI data to differentiate benign from malignant tissue in the prostate, using whole-mount step-section pathology as the reference standard. To measure ADC values, we used pairs of b-values – first, 0 and 400 s/mm² to measure ADC₄₀₀ and then 0 and 700 s/mm², to measure ADC₇₀₀. We also measured parameters D and f based on a revised monoexponential model of DW-MRI data using three b-values: 0, 400, and 700 s/mm². We found mean ADC₄₀₀, ADC₇₀₀, and D to be significantly different for malignant and benign ROIs in the PZ. However, mean f values did not differ significantly between malignant and benign ROIs. The AUC for the combination of D and f in differentiating prostate cancer was significantly higher than that for D alone but not significantly higher than the AUCs of the ADC values.

A review of published studies revealed considerable discrepancies among the ADC values used to discriminate tumor from benign PZ (17), with lower b-values typically leading to higher ADC values due to the influence of perfusion. Our results were in concordance with this trend, as imaging with a b-value of 400 s/mm² resulted in a higher mean ADC than did imaging with a b-value of 700 s/mm².

A study by Riches, et al. employed a biexponential model, which in addition to D and f, provided estimates for the perfusion coefficient, D* (13). Our results are consistent with those of Riches, et al., who showed that D was significantly lower in malignant prostate tissue than in benign prostate tissue while f was highly variable and could not be used alone to distinguish prostate cancer. In their study, D* did not differ significantly between benign and malignant tissue.

Our findings for D are also similar to those of de Souza, et al., who estimated the “slow component” of ADC based on data over the range of b-values b=100 – 800 s/mm². Our study validated their findings using whole-mount histopathology as the reference standard and, in addition, assessed the value of combining D and f.

We are aware of two additional studies (published as abstracts) on the effects of microcirculation on DW-MRI of prostate cancer (18,19). Dopfert et al reported significantly lower f and D values in cancerous tissue than in healthy tissue (18). In contrast, Pang et al found that the perfusion fraction f was significantly higher in tumor than in normal tissue (19). Given that f is a heterogeneous quantity that varies widely in both normal and cancerous tissue, we hypothesize that a voxel-wise analysis (as opposed to a mean ROI-based analysis) with sufficient signal-to-noise ratio will be required to determine its precise role in distinguishing prostate cancer. Furthermore, incorporating tumor characteristics, such as Gleason grade and volume, could also impact the contribution of f in distinguishing malignant tissue. Differences in the results of the previous studies and our own regarding the perfusion fraction could be related to tissue heterogeneity and patient selection, and the use of this parameter needs to be further studied in a larger cohort.

To model diffusion signal, we used linear fit of the logarithmic signal as a function of the b-value; although this approach is statistically less appropriate than fitting the signals to exponential functions using a least-squares criterion, it is more straightforward and does not require complicated data-fitting. When linear logarithmic fit and exponential fit were compared in another study of the parotid gland, the results were found to be similar (20).

To our knowledge, ours is the first study to use whole-mount step-section histopathology to evaluate a revised monoexponential model of diffusion incorporating true diffusion and perfusion fraction for prostate cancer differentiation. To make it possible to compare ADC measurements from different studies using the standard mono-exponential model, the b-values to be used would need to be agreed upon to ensure consistency and avoid introducing systematic errors. The revised monoexponential model we propose provides a straightforward alternative that can be readily implemented in the clinical setting to provide estimates of both true diffusion and perfusion fraction.

The analysis presented here used the absolute minimum number of b-values (three) required to estimate D and f. This choice was consistent with our objective of maintaining the acquisition within the framework of clinical imaging. However, with the approach presented, the acquisition of images at more b-values is possible and could improve the estimate of the parameters.

A limitation of our study is that our patients were imaged at 1.5 T; the use of a higher-field-strength magnet would have improved the inherently limited signal-to-noise ratio associated with the single-shot EPI acquisition with which we obtained DW-MR images. Our study is also limited by its retrospective design. To establish the clinical utility of the proposed methods, a prospective, preferably multi-institutional study needs to be done with multiple readers that evaluates the probability of cancer as determined by our regression model and uses whole-mount step-section pathological analysis as the reference standard. Our work has supplied the basis for such a study by providing thresholds for parameters with reduced sensitivity to the choice of b-value.

In conclusion, our data and those of previously published studies indicate that ADC values in the prostate are substantially affected by the choice of b-values, limiting the ability to identify absolute ADC threshold values for differentiating benign and malignant tissue. True diffusion, D, which can be obtained easily in the clinical setting using a minimum of three b-values, performs similarly to ADC in differentiating prostate cancer from benign tissue. Because it is less influenced by the choice of b-value, D may be more appropriate than ADC for use in multi-institutional studies of DW-MRI of the prostate.