Jeevan Shah^{1}, Roger Bourne^{2}, Geoffrey Watson^{3}, and Andre Bongers^{1}

This study investigates mapping
of Surface-to-Volume (S/V) ratios from short diffusion time derived ADC maps to
detect and characterize prostate cancer. ADC was mapped using a cos-OGSE DWI (f_{osc}=50-200Hz)
in one unfixed prostate (Gleason 4+4). Using a previously established model, S/V
and free cytosol diffusivity (D_{0}) maps were estimated by fitting the
temporal behaviour of ADC. S/V and D_{0} were able to clearly and
significantly separate the cancer and normal peripheral zone as indicated by a
t-test and ROC curves. The geometrical nature of S/V may provide additional
information to better characterize prostate cancer independent from diffusion
related parameters.

An unfixed specimen from radical prostatectomy, histologically diagnosed with prostate cancer Gleason Score (4+4), was
prepared as described in Bourne et al.^{5} and imaged on a BioSpec Avance III 94/20 system equipped
with BGA-12S HP gradients (G_{max}=660mT/m, dG/dt_{max}=4570Tm/s)
and 72-mm quad-RF-coil. Multiple DWI experiments were performed using an
in-house developed cos-OGSE sequence^{2} at 7 different oscillation
frequencies (50Hz-200Hz, Δf=25Hz) with 3 directions, 4 b-values
(200,400,600)+b0. General imaging parameters: TE=90ms, TR=2200ms, FoV:
4.5×4.5 cm, Matrix: 64×64, resolution: 700×700µm. Slice thickness: 2mm+2mm
gap, 7 slices, 2 averages. T_{acq}=42min. ADC maps were
calculated for each oscillation frequency by mono-exponential fitting S = S_{0}×exp(-ADC×b)
to the geometric mean of the DWIs. The temporal ADC maps were normalized to the
free water diffusion coefficient of a reference
tube that was inserted into the urethra (D_{0}=2.2mm^{2}/ms, at 22°C) and fitted using the following model^{3}:

$$$D_{g}(t)=D_{0}\left(1-\frac{c^{\prime}}{d}\left(\frac{S}{V}\right)\sqrt{D_{0}\Delta_{\mathrm{eff}}}\right)$$$ where $$$c^{\prime}=\frac{4\pi\cdot C\left(2N^{\frac{1}{2}}\right)+3\cdot S\left(2N^{\frac{1}{2}}\right)}{2\sqrt{2}\pi N},\Delta_{\mathrm{eff}}=\frac{9}{64f_{\mathrm{osc}}}$$$

N,f – OGSE number of periods and frequency; C,S – Cosine and Sine Fresnel Functions

In the fits for S/V and D_{0} quantification only frequencies
50Hz-175Hz were included as a small signal drop in the highest frequency was
found, which can likely be attributed to limitations in our gradient system. After imaging and fixation, the prostate sample was
sliced in exact alignment to the MRI for histological region
determination. Mean values were statistically
compared in cancer and peripheral zone ROIs and ROC for cancer detection was
calculated

- Xu J, Does MD, Gore JC. Sensitivity of MR diffusion measurements to variations in intracellular structure: Effects of nuclear size. Magn Reson Med. 2009;61(4):828-833
- Bongers A, Hau E, Shen H. Short diffusion time diffusion-weighted imaging with oscillating gradient preparation as an early magnetic resonance imaging biomarker for radiation therapy response monitoring in glioblastoma: A preclinical feasibility study. Int J Radiation Oncol Biol Phys. 2018;102(4):1014-1023
- Sukstanskii AL. Exact analytical results for ADC with oscillating diffusion sensitizing gradients. J Magn Reson. 2013;234:135-140
- Reynaud O, Winters KV, Hoang DM et al. Surface-to-Volume ratio mapping of tumor microstructure using oscillating gradient diffusion weighted imaging. Magn Reson Med. 2016; 76:237-247
- Bourne RM, Bongers A, Chatterjee A et al. Diffusion anisotropy in fresh and fixed prostate tissue ex vivo. Magn Reson Med. 2016;76(2):626-634

Fig 1 - (a)
Histopathology of prostate. Red region: Gleason 4 tumor. Green region:
Gleason 3 tumor. (b) Segmentation of T2WI of prostate. Blue region: Reference
tube. Red region: Gleason 4 tumor. Yellow region: Normal peripheral zone
tissue. Surface-to-volume (S/V) (c) and free cytosol diffusivity (D_{0})
(d) maps of prostate created from fitting ADC from OGSE sequence from f_{osc}=175Hz to f_{osc}=50Hz

Fig 2 - Mean ADC values from cancer and normal peripheral
zone ROIs versus square-root of effective diffusion time (Δ_{eff}). ADC
values normalized to the diffusion coefficient of free water in the reference
tube (D_{0}=2.2µm^{2}/ms, at 22°C)

Fig 3 - Mean
of (a) surface-to-volume ratio (S/V) and (b) free cytosol diffusivity (D_{0})
from parametric maps. Error bars represent one standard deviation. Statistical
significance for a difference between the two means is indicated by triple
asterisk (P<0.001)

Fig 4 - Receiver
Operator Characteristic (ROC) curves of (a) the parameters from the S/V model
fit and (b) ADC vales from a cos-OGSE 175Hz sequence and PGSE 20ms sequence.