Introduction

Tensor-valued diffusion encoding enables a more comprehensive description of tissue microstructure than conventional diffusion encoding¹. Optimized diffusion-encoding waveforms are highly efficient but exhibit different encoding frequencies, i.e., effective diffusion times^2,3. If studied tissue contains restrictions on multiple scales, diffusion time effects may cause erroneous interpretation/quantification of its features^2,4. An excellent example of this is the prostate where time-dependent diffusion has been demonstrated⁵ and exploited to better depict its microstructure⁶. Therefore, in the prostate, the application of tensor-valued diffusion-encoding requires careful attention to diffusion times across different b-tensors.

We demonstrate for the first time an experimental design and analysis that accounts for diffusion time effects when using tensor-valued diffusion-encoding in the human prostate in vivo. To enable this technical challenge, we leveraged efficient diffusion-encoding waveforms^7,8, spiral readout^9,10, advanced image reconstruction^11,12 with field monitoring¹³, and ultra-strong gradients^14,15.

Methods

Study cohort: We scanned one healthy control (35y) and two patients (67 and 73y) with biopsy-confirmed cancers (Gleason grade 3+3, low-grade) with prior ethical approval.

Diffusion-encoding waveforms: The waveforms (Fig.1) were designed to modulate the b-tensor ($$$\textbf{B}$$$)¹⁶ and the “m-tensor” ($$$\textbf{M}$$$)³. $$$\textbf{M}$$$ describes the variance of the encoding frequency spectra; high values correspond to short diffusion time and high frequencies. Across waveforms, we modulate:
1) the diffusion-weighting ($$$b=\mathrm{Tr(\textbf{B})}$$$),
2) the b-tensor “shape”/ “anisotropy” ($$$b_\Delta$$$)¹⁷
3) restriction weighting ($$$m=\mathrm{Tr(\textbf{M})}$$$), and
4) the m-tensor shape ($$$m_\Delta$$$, related to the spectral anisotropy)³.

The waveforms for spherical b-tensor encoding were obtained by numerical optimization¹⁸ with additional constraints that yield an approximately axisymmetric m-tensor⁸. Additional waveforms were derived from the first by selecting subsets from it (Fig.1). Obtained four waveforms provide four unique combinations of $$$b_\Delta$$$, $$$m$$$, and $$$m_\Delta$$$.

MRI data acquisition: Images were acquired on a 3T Connectom research-only scanner (Siemens Healthcare, Erlangen, Germany).

Multi-echo GRE images were used to estimate $$$B_0$$$-maps and coil sensitivities.

Diffusion MRI was performed with a prototype pulse sequence that enables user-defined diffusion- and spatial-encoding waveforms¹⁹ (Fig.1). Diffusion-encoding waveforms were scaled to yield b = [0, 0.1, 0.7, 1.4, 2] ms/μm² in [5, 4, 6, 15, 20] rotations, respectively. The readout was accomplished with spirals²⁰ to yield acceleration factor=2.24, voxel size=1.15×1.15×5 mm³, TE=62 ms, TR=3 s, #slices=18, and a scan time of 10:30 min.

Image reconstruction: Data were reconstructed using an “expanded encoding model”^11,12,21,22 including static $$$B_0$$$ and higher order field^23,24, measured with a field-camera (Skope Magnetic Resonance Technologies)¹³.

Post-processing and parameter estimation: Complex data was denoised^25,26, motion-corrected²⁷ and smoothed (2D-Gaussian, σ=0.7 mm). The signal representation was based on Lundell and Lasic³

$$log⁡\left(\frac{S}{S_0}\right)=-b(D+mD_r)+\frac{b^2}{2}(V_I+m^2 V_{I_r})+\frac{b^2}{2}(b_∆^2V_A+m^2m_Δ^2V_{A_r})$$

where the long-time (zero-frequency) parameters are the apparent mean diffusivity ($$$D$$$), variance of isotropic diffusivities ($$$V_I$$$), and the variance due to microscopic diffusion anisotropy ($$$V_A$$$)^1,28; parameters with subscript $$$“r”$$$ denote how fast each changes with the restriction weighting. We display parameters at zero-frequency (no subscript) and high-frequency (subscript hf, e.g., $$$D_{hf}=D+mD_r$$$), or their difference (prefix $$$\Delta$$$, e.g., $$$\Delta{D}=m_{max}D_r$$$).

Results & Discussion

The signal and estimated parameters could be reconstructed without visible distortions (Fig.2). Higher encoding frequencies (shorter diffusion times) reduce the diffusion-weighted signal and increase the apparent diffusivity. The isotropic diffusional variance is consistently higher than the anisotropic variance ($$$V_I>V_A$$$) in partial agreement with previous works^29,30.

The signal representation accounted well for the dynamics of the signal (Fig.3). It visualizes the hallmarks of time-dependence (initial slope depends on restriction weighting) and diffusional variance (non-monoexponential signal decay). This means that diffusion time effects appear already at low b-values.

Based on descriptive statistics (Fig.4.), the tumours are distinguished by a low diffusivity and strong diffusion time dependence in the apparent diffusivity (low $$$D$$$ and high $$$\Delta{D}$$$) as compared to normal appearing tissue. In patients, the peripheral and transitional zones were dominated by $$$V_I$$$ and $$$V_A$$$, respectively, whereas these parameters were similar across the healthy prostate. This could be explained by the large age difference or a yet unknown pathological effect. The time-dependence of $$$V_I$$$ and $$$V_A$$$, was generally weak (small $$$\Delta{V_I}$$$ and $$$\Delta{V_A}$$$). From theory, we expect the diffusional variance to decrease at higher encoding frequency⁴, but limited signal precision and sensitivity to a positive noise floor bias can counteract this.

Conclusions

We presented a novel approach to measure time-dependent diffusivity and diffusional variance in in vivo prostate. Time-dependence was mainly observed in the apparent diffusivity, and among patients, it was strongest in the tumour.

Our results indicate that diffusion time effects may require consideration when using waveforms adapted for tensor-valued encoding in the prostate. Although our approach uses relatively high frequencies, similar frequencies are achievable at clinical systems at lower b-values, and these effects may thus be visible in more common acquisitions.

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