The Challenge of Ovarian Cancer: Steps Toward Early Detection Through Advanced Signal Processing in Magnetic Resonance Spectroscopy.

BACKGROUND: Ovarian cancer is a major cause of cancer death among women worldwide, and particularly in Israel. Although the disease at stage IA has 5 year survival rates of over 90%, early detection methods are not sufficiently accurate. Consequently, ovarian cancer is typically diagnosed late, which results in high fatality rates. An excellent candidate for early ovarian cancer detection would be in vivo magnetic resonance spectroscopy (MRS) because it is non-invasive and free of ionizing radiation. In addition, it potentially identifies metabolic features of cancer. Detecting these metabolic features depends on adequate processing of encoded MRS time signals for reconstructing interpretable information. The conventional Fourier-based method currently used in all clinical scanners is inadequate for this task. Thus, cancerous and benign ovarian lesions are not well distinguished. Advanced signal processing, such as the fast Padé transform (FPT) with high-resolution and clinically reliable quantification, is needed. The effectiveness of the FPT was demonstrated in proof-of-concept studies on noise-controlled MRS data associated with benign and cancerous ovaries. The FPT has now been successfully applied to MRS time signals encoded in vivo from a borderline serous cystic ovarian tumor. Noise was effectively separated out to identify and quantify genuine spectral constituents that are densely packed and often overlapping. Among these spectral constituents are recognized and possible cancer biomarkers including phosphocholine, choline, isoleucine, valine, lactate, threonine, alanine, and myoinositol. Most of these resonances remain undetected with Fourier-based in vivo MRS of the ovary. With Padé optimization, in vivo MRS could become a key method for assessing ovarian lesions, more effectively detecting ovarian cancer early, thereby improving survival for women afflicted with this malignancy.

Molecular imaging in the framework of personalized cancer medicine.

With our increased understanding of cancer cell biology, molecular imaging offers a strategic bridge to oncology. This complements anatomic imaging, particularly magnetic resonance (MR) imaging, which is sensitive but not specific. Among the potential harms of false positive findings is lowered adherence to recommended surveillance post-therapy and by persons at increased cancer risk. Positron emission tomography (PET) plus computerized tomography (CT) is the molecular imaging modality most widely used in oncology. In up to 40% of cases, PET-CT leads to changes in therapeutic management. Newer PET tracers can detect tumor hypoxia, bone metastases in androgen-sensitive prostate cancer, and human epidermal growth factor receptor type 2 (HER2)-expressive tumors. Magnetic resonance spectroscopy provides insight into several metabolites at the same time. Combined with MRI, this yields magnetic resonance spectroscopic imaging (MRSI), which does not entail ionizing radiation and is thus suitable for repeated monitoring. Using advanced signal processing, quantitative information can be gleaned about molecular markers of brain, breast, prostate and other cancers. Radiation oncology has benefited from molecular imaging via PET-CT and MRSI. Advanced mathematical approaches can improve dose planning in stereotactic radiosurgery, stereotactic body radiotherapy and high dose-rate brachytherapy. Molecular imaging will likely impact profoundly on clinical decision making in oncology. Molecular imaging via MR could facilitate early detection especially in persons at high risk for specific cancers.

Possibilities for improved early breast cancer detection by Padé-optimized magnetic resonance spectroscopy.

There are major dilemmas regarding the optimal modalities for breast cancer screening. This is of particular relevance to Israel because of its high-risk population. It was suggested that an avenue for further research would be to incorporate advances in signal processing through the fast Padé transform (FPT) to magnetic resonance spectroscopy (MRS). We have now applied the FPT to time signals that were generated according to in vitro MRS data as encoded from extracted breast specimens from normal, non-infiltrated breast tissue, fibroadenoma and cancerous breast tissue. The FPT is shown to resolve and precisely quantify the physical resonances as encountered in normal versus benign versus malignant breast. The FPT unambiguously delineated and quantified diagnostically important metabolites such as lactate, as well as phosphocholine, which very closely overlaps with glycerophosphocholine and phosphoethanolamine, and may represent a magnetic resonance-visible molecular marker of breast cancer. These advantages of the FPT could clearly be of benefit for breast cancer diagnostics via MRS. This line of investigation should continue with encoded data from benign and malignant breast tissue, in vitro and in vivo. We anticipate that Padé-optimized MRS will reduce the false positive rates of MR-based modalities and further improve their sensitivity. Once this is achieved, and given that MR entails no exposure to ionizing radiation, new possibilities for screening and early detection emerge, especially for risk groups. For example, Padé-optimized MRS together with MR imaging could be used with greater surveillance frequency among younger women with high risk of breast cancer.

Single charge exchange in collisions of energetic nuclei with biomolecules of interest to ion therapy.

This study is on the theory of single electron capture by fast nuclei from a variety of molecular targets of biological significance with high relevance to ion therapy of deep-seated tumors. The adopted theoretical framework is that of the first principles of quantum physics. As such, no free, adjustable parameters are used. This is in sharp contrast to the associated existing cross section input data to Monte Carlo simulations that all abound with empirical/phenomenological formulae. The present theory has the well-established track of its predictive power. This means that the computed cross sections can confidently be used in the cases for which no experimental data exist. These cross sections are from the full continuum distorted wave method (CDW). We first compute atomic cross sections in the independent electron model and then generate the corresponding molecular cross sections. The latter follow from the former within the independent atom model accompanied by the Bragg additivity rule. The investigated atomic targets are from the backbone of DNA and/or RNA molecules. These are atomic hydrogen, carbon, nitrogen and oxygen (H, C, N, O). Neon is also added to this sequence of targets as an isoelectronic atomic counterpart of water vapor, methane and ammonia molecules. The studied molecular targets are H2O (water vapor), CO (carbon-monoxide), CO2 (carbon-dioxide), CH4 (methane), C2H4 (ethylene), C2H6 (ethane), C4H10 (butane) as well as the DNA/RNA nucleobases C4H4N2O2 (uracil), C5H5N5 (adenine), C5H5N5O (guanine), C5H6N2O2 (thymine) and C4H5N3O (cytosine). The obtained total cross sections for any electronic target shell are compared with the available experimental data and overall favorable agreement is recorded at intermediate and high impact energies, which is the validity domain of the CDW method.

Exact quantification of time signals in Padé-based magnetic resonance spectroscopy.

This study reports on the fast Padé transform (FPT) for parametric signal processing of realistically synthesized free induction decay curves whose main spectral features are similar to those encoded clinically from a healthy human brain by means of magnetic resonance spectroscopy (MRS). Here, for the purpose of diagnostics, it is of paramount importance to be able to perform accurate and robust quantification of the investigated time signals. This amounts to solving the challenging harmonic inversion problem as a spectral decomposition of the given time signal by means of reconstruction of the unknown total number of resonances, their complex frequencies and amplitudes yielding the peak positions, widths, heights and phases. On theoretical grounds, the FPT solves exactly this mathematically ill-conditioned inverse problem for any noiseless synthesized time signal comprised of an arbitrarily large (finite or infinite) number of damped complex exponentials with stationary and non-stationary polynomial-type amplitudes leading to Lorentzian (non-degenerate) and non-Lorentzian (degenerate) spectra. Convergent validation for this fact is given via the proof-of-principle which is thoroughly demonstrated by the exact numerical solution of a typical quantification problem from MRS. The presently designed study is a paradigm shift for signal processing in MRS with particular relevance to clinical oncology, due to the unprecedented capability of the fast Padé transform to unequivocally resolve and quantify isolated, tightly overlapped and nearly coincident resonances.

Exponential convergence rate (the spectral convergence) of the fast Padé transform for exact quantification in magnetic resonance spectroscopy.

This study deals with the most challenging numerical aspect for solving the quantification problem in magnetic resonance spectroscopy (MRS). The primary goal is to investigate whether it could be feasible to carry out a rigorous computation within finite arithmetics to reconstruct exactly all the machine accurate input spectral parameters of every resonance from a synthesized noiseless time signal. We also consider simulated time signals embedded in random Gaussian distributed noise of the level comparable to the weakest resonances in the corresponding spectrum. The present choice for this high-resolution task in MRS is the fast Padé transform (FPT). All the sought spectral parameters (complex frequencies and amplitudes) can unequivocally be reconstructed from a given input time signal by using the FPT. Moreover, the present computations demonstrate that the FPT can achieve the spectral convergence, which represents the exponential convergence rate as a function of the signal length for a fixed bandwidth. Such an extraordinary feature equips the FPT with the exemplary high-resolution capabilities that are, in fact, theoretically unlimited. This is illustrated in the present study by the exact reconstruction (within machine accuracy) of all the spectral parameters from an input time signal comprised of 25 harmonics, i.e. complex damped exponentials, including those for tightly overlapped and nearly degenerate resonances whose chemical shifts differ by an exceedingly small fraction of only 10(-11) ppm. Moreover, without exhausting even a quarter of the full signal length, the FPT is shown to retrieve exactly all the input spectral parameters defined with 12 digits of accuracy. Specifically, we demonstrate that when the FPT is close to the convergence region, an unprecedented phase transition occurs, since literally a few additional signal points are sufficient to reach the full 12 digit accuracy with the exponentially fast rate of convergence. This is the critical proof-of-principle for the high-resolution power of the FPT for machine accurate input data. Furthermore, it is proven that the FPT is also a highly reliable method for quantifying noise-corrupted time signals reminiscent of those encoded via MRS in clinical neuro-diagnostics.

In vivo magnetic resonance spectroscopy by the fast Padé transform.

The fast Padé transform (FPT) is thoroughly illustrated on two in vivo time signals encoded at 4 T and 7 T via magnetic resonance spectroscopy (MRS). The exact quantum-mechanical spectrum as the Green function series truncated at any partial sum reduces to the unique quotient of two polynomials, which is the FPT. In this Green function as a Maclaurin series in powers of the harmonic variable, the expansion coefficients are the time signal values as damped complex-exponentials with stationary and non-stationary amplitudes for non-degenerate (Lorentzian) and degenerate (non-Lorentzian) spectra. This is automatically shared by the FPT to represent an enormous advantage over the Hankel-Lanczos singular value decomposition (HLSVD) which works only for Lorentzian spectra. Moreover, the resonance amplitudes in the FPT are obtained analytically, rather than solving a system of linear equations as done in the HLSVD. We use two variants of the FPT, initially defined inside and outside the unit circle, but extended automatically to the whole complex frequency plane by the Cauchy analytical continuation. The converged spectra from these two variants of the FPT are found to give the same results, within the experimental background noise level, and this represents an intrinsic cross-validation of the findings and the error analysis.

The fast Padé transform in magnetic resonance spectroscopy for potential improvements in early cancer diagnostics.

The convergence rates of the fast Padé transform (FPT) and the fast Fourier transform (FFT) are compared. These two estimators are used to process a time-signal encoded at 4 T by means of one-dimensional magnetic resonance spectroscopy (MRS) for healthy human brain. It is found systematically that at any level of truncation of the full signal length, the clinically relevant resonances that determine concentrations of metabolites in the investigated tissue are significantly better resolved in the FPT than in the FFT. In particular, the FPT has a better resolution than the FFT for the same signal length. Moreover, the FPT can achieve the same resolution as the FFT by using twice shorter signals. Implications of these findings for two-dimensional magnetic resonance spectroscopy as well as for two- and three-dimensional magnetic resonance spectroscopic imaging are highlighted. Self-contained cross-validation of all the results from the FPT is secured by using two conceptually different, equivalent algorithms (inside and outside the unit-circle), that are both valid in the entire complex frequency plane. The difference between the results from these two variants of the FPT is indistinguishable from the background noise. This constitutes robust error analysis of proven validity. The FPT shows promise in applications of MRS for early cancer detection.

Proof-of-the-Concept Study on Mathematically Optimized Magnetic Resonance Spectroscopy for Breast Cancer Diagnostics.

Magnetic resonance (MR)-based modalities aid breast cancer detection without exposure to ionizing radiation. Magnetic resonance imaging is very sensitive but costly and insufficiently specific. Molecular imaging through magnetic resonance spectroscopy (MRS) can provide information about key metabolites. Here, the measured/encoded time signals cannot be interpreted directly, necessitating mathematics for mapping to the more manageable frequency domain. Conventional applications of MRS are hampered by data analysis via the fast Fourier transform (FFT) and postprocessing by fitting techniques. Most in vivo MRS studies on breast cancer rely upon estimations of total choline (tCHO). These have yielded only incremental improvements in diagnostic accuracy. In vitro studies reveal richer metabolic information for identifying breast cancer, particularly in closely overlapping components of tCHO. Among these are phosphocholine (PC), a marker of malignant transformation of the breast. The FFT cannot assess these congested spectral components. This can be done by the fast Padé transform (FPT), a high-resolution, quantification-equipped method, which we presently apply to noisy MRS time signals consistent with those encoded in breast cancer. The FPT unequivocally and robustly extracted the concentrations of all physical metabolites, including PC. In sharp contrast, the FFT produced a rough envelope spectrum with a few distorted peaks and key metabolites absent altogether. As such, the FFT has poor resolution for these typical MRS time signals from breast cancer. Hence, based on Fourier-estimated envelope spectra, tCHO estimates are unreliable. Using even truncated time signals, the FPT clearly distinguishes noise from true metabolites whose concentrations are accurately extracted. The high resolution of the FPT translates directly into shortened examination time of the patient. These capabilities strongly suggest that by applying the FPT to time signals encoded in vivo from the breast, MRS will, at last, fulfill its potential to become a clinically reliable, cost-effective method for breast cancer detection, including screening/surveillance.

Ion beam transport in tissue-like media using the Monte Carlo code SHIELD-HIT.

The development of the Monte Carlo code SHIELD-HIT (heavy ion transport) for the simulation of the transport of protons and heavier ions in tissue-like media is described. The code SHIELD-HIT, a spin-off of SHIELD (available as RSICC CCC-667), extends the transport of hadron cascades from standard targets to that of ions in arbitrary tissue-like materials, taking into account ionization energy-loss straggling and multiple Coulomb scattering effects. The consistency of the results obtained with SHIELD-HIT has been verified against experimental data and other existing Monte Carlo codes (PTRAN, PETRA), as well as with deterministic models for ion transport, comparing depth distributions of energy deposition by protons, 12C and 20Ne ions impinging on water. The SHIELD-HIT code yields distributions consistent with a proper treatment of nuclear inelastic collisions. Energy depositions up to and well beyond the Bragg peak due to nuclear fragmentations are well predicted. Satisfactory agreement is also found with experimental determinations of the number of fragments of a given type, as a function of depth in water, produced by 12C and 14N ions of 670 MeV u(-1), although less favourable agreement is observed for heavier projectiles such as 16O ions of the same energy. The calculated neutron spectra differential in energy and angle produced in a mimic of a Martian rock by irradiation with 12C ions of 290 MeV u(-1) also shows good agreement with experimental data. It is concluded that a careful analysis of stopping power data for different tissues is necessary for radiation therapy applications, since an incorrect estimation of the position of the Bragg peak might lead to a significant deviation from the prescribed dose in small target volumes. The results presented in this study indicate the usefulness of the SHIELD-HIT code for Monte Carlo simulations in the field of light ion radiation therapy.