Gregory Lemberskiy^{1,2}, Yousef Mazaheri^{3}, Herbert Alberto Vargas^{3}, Ricardo Otazo^{3}, Els Fieremans^{1}, and Dmitry S Novikov^{1}

^{1}Radiology, New York University School of Medicine, New York, NY, United States, ^{2}Microstructure Imaging INC, New York, NY, United States, ^{3}Memorial Sloan Kettering Cancer Center, New York, NY, United States

For prostate cancer imaging, increasing the echo time selectively suppresses the cellular tissue, and emphasizes luminal water. We study the ADC dependence on echo time and diffusion time in 3 patients with PIRADS≥4 lesions, and propose a modeling strategy to interpret the changes in signal, as lumen diameter and volume fraction shrink during cancer progression. We evaluate cellular and luminal diffusivities, volume fractions, and luminal diameters as cancer biomarkers.

Recently, using low-spatial resolution/high SNR, a non-trivial dependency of DWI on $$$T_E$$$ has been shown in volunteers. It was used to separate cellular (dominating at short $$$T_E$$$) from luminal (visible at long $$$T_E$$$) tissue compartments

Here we use random matrix theory (RMT) reconstruction

By leveraging the large differences in $$$T_2$$$

$$S|_{b=0(T_E)}=S|_{b,T_E=0}\bigg(\underbrace{fe^{-T_E/T_2^{(C)}}}_C+\underbrace{(1-f)e^{-T_E/T_2^{(L)}}}_L\bigg).$$

Here $$$f$$$ is the cellular compartment fraction, $$$T_2^{(C)}$$$ and $$$T_2^{(L)}$$$ represent the fast (cellular) and slow (luminal) $$$T_2$$$ compartments. These values are then used to determine $$$T_E$$$-specific weights that define diffusion compartments of the prostate:$$ADC(T_E,t)=W(T_E)\cdot D^{(C)}(t)+(1-W(T_E))\cdot D^{(L)}(t),\,\,\,\mathrm{where}\,\,W(T_E)=\frac{C}{C+L}$$

To resolve compartment diffusivities, we introduce their time-dependent models. $$$D^{(C)}(t)$$$ is modeled by the short-time limit

We apply this modeling approach to benign and malignant transition zones, thereby evaluating the effect of varying the echo time [Fig.2] on $$$ADC$$$ and $$$T_2w$$$ contrasts. We consider a series of synthesized $$$ADC(T_E,t$$$)-maps as potential new biomarkers [Fig.3], and demonstrate the evolution of ADC contrast with echo time for each compartment [Fig.4]. Area under the curve (AUC) analysis was used to determine the number of true positives versus false-positives between benign and lesion ROIs.

As $$$T_E$$$ increases, $$$ADC$$$ increases in benign, but less so in malignant tissue, which can be explained by selective suppression of cellular water due to increased $$$T_2$$$ weighting [Fig.2,5]. A profound increase in $$$ADC$$$-contrast between benign and malignant tissues is observed with increasing $$$T_E$$$ [Fig.2], in line with high grade lesions having smaller luminal fractions

Furthermore, biophysical modeling provides increased granularity towards diagnosis, as the lesion shows increased $$$f$$$ and decreased (consistent with histology)

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