Imaging the Prostate with Quantitative Ultrasound: Implications for Guiding Biopsies, Targeting Focal Treatment, and Monitoring Therapy

Abstract

Improved means of imaging prostate cancer would enable more-effective biopsy and treatment guidance and would provide a noninvasive means of monitoring patients on active surveillance and nonsurgical therapies. Current, commonly used, conventional means of imaging the prostate do not reliably depict cancerous lesions, and as a result, image-guided biopsies sample prostatic tissue in a systematic manner with respect to visible anatomic features of the gland, but blindly with respect to cancerous foci. Treatment tends to involve the entire gland and posttreatment monitoring of therapy is based predominantly on serum PSA levels, supplemented in some cases by periodic biopsies. Similarly, patients on active surveillance for low-volume, low-risk disease are required to undergo repeat prostate biopsies annually or biannually.

Conventional transrectal ultrasound (TRUS) is the most commonly employed imaging modality for guiding prostate biopsies and for planning and delivering treatment, but conventional TRUS has a limited ability to depict features indicative of cancer in the prostate. New methods of tissue-type imaging that are based on quantitative analysis of echo signals and that utilize sophisticated methods for classification offer exciting promise for more reliably distinguishing cancerous from noncancerous tissue in the prostate and therefore, for reliably imaging foci of cancer. Such advanced methods have achieved relatively good accuracy as expressed by an area under the ROC curve that exceeds 0.84 compared to an area of 0.64 for conventional assessments of the same locations in biopsy-guidance TRUS images. This translates to a potential improvement in imaging sensitivity (implied by the ROC curve) of more than 50 %. If ongoing validation studies confirm these encouraging results, then an inexpensive, effective, noninvasive means of imaging prostate cancer foci, and subsequently guiding biopsies, targeting focal treatments, and noninvasively monitoring therapies will be available to urologists and radiation oncologists.

Appendix

The basic theories of scattering in tissue assume that scattering is weak and the Born approximation applies [53]. In essence, this approximation considers scattering behavior to depend solely on the interaction between scatterers and the incident field; i.e., it assumes that the total field, which includes contributions that result from scattering, can be replaced by the incident field alone because the contribution of the scattered field to the total field can be ignored. The theoretical framework first published by Lizzi in 1983 expresses the spectrum of the backscattered echo signals received at the transducer as an integral over three spatial autocorrelation functions: the three-dimensional autocorrelation function of spatial variations in relative acoustic impedance, which defines the acoustic properties of the scatterers themselves; the two-way beam-directivity autocorrelation function, which specifies the behavior of the incident-beam profile in two dimensions transverse to the beam-propagation direction; and the one-dimensional autocorrelation function of the time-domain window used to select backscattered signals for spectral processing [34–37]. The fundamental equation derived by Lizzi et al. for a normalized (system-corrected) spectrum is

$$ \begin{array}{l}S=4{k}^2{\displaystyle \iiint {R}_{\zeta}\left(\varDelta x\right){R}_{\mathrm{D}}\left(\varDelta y,\varDelta z\right)}\\ {}\kern0.84em {R}_{\mathrm{G}}\left(\varDelta x\right){\mathrm{e}}^{j2k\varDelta x}\mathrm{d}\varDelta x\;\mathrm{d}\varDelta y\;\mathrm{d}\varDelta z\end{array} $$

where S is the normalized power spectrum (i.e., the spectrum that is corrected for the acoustical and electronic properties of the system), k is the wave number (2π/λ where λ is the wavelength of the US), R _ζ(Δx) is the spatial autocorrelation function of the distribution of the relative acoustic impedance of the scatterers, R _D(Δy, Δz) is the autocorrelation function of the two-way US beam-directivity function, and R _G(Δx) is the autocorrelation function of the gating function (typically a Hamming or Hanning window, which resembles a squared cosine function) [34].

The power spectrum is computed by digitizing RF echo signals over some or all of a scanned plane or volume; defining an ROI for analysis within that plane or volume; gating a portion the RF signals within the ROI by multiplying a gating function times the selected RF data; computing the squared magnitude of the Fourier transform of the gated RF signals; and converting the result to decibels (dB) (i.e., ten times the log of the squared magnitude of the Fourier transform). Because of the randomness of a typical spectrum derived from tissue echo signals, ample averaging is required and is performed by shifting the gating window, repeating the spectral computation, and averaging the results computed over the entire ROI. Once the average power spectrum is computed, normalization is performed to correct for system properties, and parameters representing the spectrum are calculated and related by theory to tissue properties.

In practice, the Lizzi equation is applied using assumed autocorrelation functions for the scatterer acoustic impedance. For most reasonable functions, such as the autocorrelation function for a sphere or a Gaussian autocorrelation function, the equation predicts a gently curving spectrum when the power spectrum is expressed in dB with respect to a perfectly reflecting calibration target. When approximated by a straight line over the available, effective, noise-limited bandwidth, the linear fit to a calibrated spectrum has two basic, independent defining parameters: (1) a slope value that theoretically depends only on scatter size and on attenuation in the intervening medium, and (2) an intercept value that theoretically depends on scatterer size, concentration, and acoustic impedance relative to the environment of the scatterers. An additional spectral parameter is the midband (or midband fit), which is the value of the straight-line approximation at the center of the effective noise-limited bandwidth, i.e., the average value of the amplitude of the straight-line approximation over the usable frequency band. The midband parameter is equivalent to the integrated-backscatter parameter developed by Miller and his coworkers [54–57].

The theory relating spectral parameters to tissue properties was further developed and published in the 1990s by Insana and Hall who applied the concept of form factors to tissue-property assessment [40, 41]. Form factors, which pertain to the “shape” of the relative acoustic impedance of the scatterer, are the Fourier transform of the autocorrelation functions described by Lizzi. The most commonly used form factor is the Gaussian, and it provides a better approximation to the empirical spectrum and, presumably, more accurately estimates effective scatterer properties than the simpler linear approximation.