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Abstract

Introduction

Ovarian cancer is a major global concern. Due to late detection, it is one of the few malignancies for which the five-year survival rate continues to be low without appreciable improvement in recent decades. Screening methods are needed that non-invasively, without ionizing radiation, detect early-stage ovarian cancer with clear distinction from benign lesions. Magnetic resonance spectroscopy (MRS) could be a key contributor to early ovarian cancer detection, insofar as data analysis and interpretation after appropriate signal processing are implemented.

Methods

The derivative non-parametric and parametric fast Padé transform (dFPT) and the derivative fast Fourier transform (dFFT: optimized, unoptimized) are applied to proton MRS time signals encoded from the ovary. These include in vivo MRS for a borderline cyst, and in vitro MRS for serous cystic adenoma and serous cystic adenocarcinoma.

Results

On a broad chemical shift axis (aliphatic and aromatic), over 300 thin, clearly-delineated peaks are baseline-resolved and displayed in a readily amenable form for clinical interpretation. This is from the in vivo encoding. Clearly quantifiable peaks include cancer biomarkers: total choline components (phosphocholine, glycerophosphocholine, free choline) and the lactate doublet, as well as other diagnostically-relevant metabolites in spectrally-crowded regions. Concordance among three algorithms (parametric and non-parametric dFPT as well as optimized dFFT) provides cross-validation, essential for clinical trustworthiness of derivative MRS.

Conclusion

With these results that help benchmark derivative MRS for clinical applications in oncology, the time is deemed ripe to implement the stated advances. More effective early detection of ovarian cancer should be among the most urgent priorities for this upgrade.

Keywords

ovarian cancer early detection magnetic resonance spectroscopy derivative signal processing optimization fast Fourier transform fast Padé transform

Introduction

Ovarian cancer is a major global concern, associated with approximately 207 000 deaths worldwide among women in 2020 alone.¹ It is one of the few malignancies for which the 5-year survival rate continues to be low and has not appreciably improved in recent decades.² The diagnosis of ovarian cancer is usually made at the late stages associated with advanced disease and poor prognosis.^3,4 Yet, if the cancer is detected at the early stage when confined to the ovary, the prognosis is excellent (90% or even higher 5-year survival).²

The crux of the problem is the lack of accurate early detection methods. The usual screening procedures are transvaginal ultrasound (TVUS) and serum cancer antigen (CA-125). However, large randomized trials indicate that screening with CA-125 and TVUS for ovarian cancer in women without increased familial risk does not significantly reduce mortality due to this malignancy.^5,6 Moreover, screening with TVUS and CA-125 is associated with a large percentage of false positive findings. One of the deleterious consequences is that many women undergo surgical intervention to remove benign ovarian lesions.⁵ The overall conclusion is: “given that screening did not significantly reduce ovarian and tubal cancer deaths, general population screening cannot be recommended” (p. 2182).⁶

Women at high ovarian cancer risk often undergo screening with CA-125 and TVUS, although prospective evidence is lacking regarding successful early detection.⁷ For women at very high ovarian cancer risk, eg carriers of deleterious BRCA mutations, bilateral salpingo-oophorectomy has been recommended. This recommendation was made by the U.S. National Comprehensive Cancer Network for women 35–40 years of age who have completed childbearing.⁸ Although salpingo-oophorectomy does, obviously, protect against ovarian cancer, it is associated with many adverse consequences.⁹ In this light, the need for truly “personalized” assessment has been underscored for patients considered to fall into the high-risk category.¹⁰ Screening methods that non-invasively detect early-stage ovarian cancer on a molecular level with clear distinction from benign lesions would be a welcome advance.⁴

Magnetic Resonance Spectroscopy — Possibilities for Timely Ovarian Cancer Detection

For well over two decades now,¹¹ magnetic resonance spectroscopy (MRS) has been suggested as a candidate for early ovarian cancer detection. The reasons include non-invasiveness, complementarity to anatomic imaging for potentially identifying metabolic features of cancer, and lack of exposure to ionizing radiation. However, the ovary is a small, moving organ, for which it is technically difficult for MRS to encode good quality time signals or free induction decay (FID) data.¹² With conventional processing of FIDs encoded by in vivo MRS, benign and malignant ovarian lesions have not been adequately distinguished.¹³

Fundamental to MRS is signal processing which can respectively provide qualitative and quantitative information by shape and parameter estimations (viewed as two entirely separate categories). Without mathematics, the time domain data encoded in clinical scanners or via laboratory spectrometers are not directly interpretable. The equivalent representation of FIDs is the frequency domain which depicts spectra. The spectra are plotted as intensity versus frequency (chemical shift, expressed in parts per million, ppm). They display peaks or resonances assignable to molecules (called metabolites due to their involvement in cellular metabolism).

In clinical magnetic resonance (MR) scanners, signal processing is mainly done by the fast Fourier transform (FFT), a linear, low-resolution, non-parametric processor without noise suppression. Its spectrum is a single polynomial. It describes only a total shape spectrum or envelope, but not the components. Thus, the FFT, as a shape estimator, cannot autonomously generate the quantitative information needed to ascertain concentrations of cancer biomarkers and other metabolites of diagnostic interest.¹⁴

The fast Padé transform (FPT), an advanced, non-linear signal processor, provides high resolution with good signal to noise ratio (SNR). It can perform both shape and parameter estimations by the non-parametric and parametric FPT, respectively.^14–20 In each version, the envelope spectrum is given by the ratio of two polynomials $P_{K} / Q_{K}$ of common degree K. Being also the total number of resonances, K is reconstructed by the FPT. This is opposed to guessing, as is usually done in post-processing of FFT envelopes.

As a single polynomial, the FFT describes the zeros of the spectrum. To describe poles, the FFT needs much constructive and destructive interference to counter the unattenuated sines and cosines. This requires long total acquisition time (denoted by T). Resolution in the FFT is predetermined by T, irrespective of the structure of the FID. In contrast, the FPT as the ratio of two polynomials describes both the spectral zeros and poles. This, in turn, retrieves the sought structure of the FID. The advantages of the FPT are better resolution and SNR, built-in quantification capabilities, as well as shorter T. The FPT is therefore more suitable than the FFT to describe spectra in MRS. Generally, functions with polar structure, as in the FPT, are the most frequently-employed mathematical models for spectra in inter-disciplinary research.¹⁴

The parametric FPT yields densely-packed and often overlapping component peaks. Therein, prior to plotting, resonances are quantified by providing their parameters (position, widths, heights, phases, areas). These can be of diagnostic value, eg transverse relaxation time (inversely related to peak width) and peak area (proportional to metabolite concentration). These help characterize the tissue. The parametric FPT was established as a reliable and robust signal processor in MRS.^13,14,21 This set the stage for the next steps aimed at clinical implementation.

Difficulties in MRS Impeding Fulfillment of the Main Diagnostic Expectations

The work of diagnosticians within oncology and radiology would be greatly facilitated if all the peaks in the given spectrum were visualized and quantified. Yet, the most vital clinical need is the trustworthiness of such information. Until recently, these two requisites seemed incompatible within MRS, especially for in vivo encoding at clinical magnetic field strengths (1.5, 3.0T). Shape estimators are not trustworthy. They yield only envelopes that do not accurately reflect the genuine presence and concentration of metabolites when the peaks are congested. Lineshapes from parametric estimation can be difficult to interpret visually when the reconstructed spectra are plotted. Namely, for FIDs encoded by MRS from eg the ovary, these resonances are very densely packed and overlapping. Clinical interpretation then becomes difficult.

A robust mathematical solution to this conundrum was developed by means of derivative signal processing. It was initially achieved through the derivative fast Padé transform (dFPT),^22–24 and more recently via an optimized derivative fast Fourier transform (dFFT).²⁵ When derivative signal processing is used within MRS, this modality is termed derivative MRS.

Derivative MRS can Address Diagnosticians’ Needs

Slope changes in a spectral lineshape may point to hidden structures. Derivatives probe and then describe the slopes of lineshapes. The higher the derivative order, the more structure is revealed. By applying the derivative operator $D_{m} = (d / d ν)^{m}$ of order m (positive integer) with respect to linear frequency $ν$ , each peak in the spectrum should become thinner and taller. With non-derivative shape estimators, a single peak in the envelope may be wide and asymmetric (shouldered). When the $D_{m}$ operator is applied, two or more components might emerge. These could have been masked within a singlet-appearing peak in the non-derivative envelope.

The dFPT processes the originally encoded FID data points ${c_{n}}$ with no derivative-induced noise. In fact, the dFPT simultaneously suppresses noise and improves resolution. Resolution is improved by separating overlapping peaks. Noise is reduced by lowering the peak tails. Derivatives are made directly on the spectrum $P_{K} / Q_{K}$ , ie $dFPT = D_{m} P_{K} / Q_{K}$ . Importantly, this avoids ill-conditioned numerical derivatives. Noise from the FID is transferred to the spectrum via $P_{K}$ as well as $Q_{K},$ and subsequently cancelled out in the ratio $P_{K} / Q_{K}$ .

The dFPT has passed rigorous benchmarking,^22–24 including cross-checking between the parametric and non-parametric estimations with their full agreement. The magnitude mode for derivative lineshapes was found to best facilitate clinical interpretation. With non-derivative envelopes, the peaks are broadened in the magnitude mode compared to the absorption mode. However, as the derivative order $m$ in the dFPT is increased, the resonances become progressively narrower in the magnitude mode. The magnitude-mode derivative resonances are then better resolved than the non-derivative absorptive peaks. In the derivative absorption modes, the resonances are surrounded by several artificial lobes.²² Such lobes are suppressed in the derivative magnitude mode. Thus, the magnitude-mode is recommended for derivative spectra, as applied throughout this study.

The question was raised as to whether the FFT could also yield further insights by its derivative version, ie $dFFT = (d / d ν)^{m} FFT$ . This would be of practical importance since the FFT is built into MR scanners with automatic application of the computationally expedient Cooley-Tukey algorithm.²⁶ However, the unoptimized version of the dFFT markedly worsens the spectra, even compared to its non-derivative predecessor, the FFT.^22–24 The reason is that the unoptimized dFFT multiplies the processed FID by a weight function (proportional to the time variable raised to power $m$ ). This emphasizes the FID tail, ie the end of the acquired data dominated by noise. Consequently, the unoptimized dFFT adds further noise, so that both resolution and SNR of the spectrum are deteriorated compared to the FFT.

An optimized version of the dFFT was recently introduced by judiciously apodizing the FID. This is done by an attenuating exponential (or Gaussian) filter which must be adapted to the derivative order m and to the SNR of the encoded FID. By such a derivative-adapted optimization, quantitatively interpretable component spectra are generated with improved resolution and SNR.²⁵ This is achieved exclusively by shape estimation, and yet the sought quantitative information (parametrized component spectra) is provided. The mentioned sharp border between shape and parameter estimators is thereby erased.

Aim of the Present Study

Our goal is to offer a detailed, comprehensive view of how the dFPT and the optimized dFFT can be applied in the clinical setting within MRS to aid in diagnosing ovarian lesions. The particular focus is on conveying the results in such a way that physicians would be able to utilize derivative MRS in efforts to achieve timely and accurate detection of ovarian cancer.

Methods

The STARD checklist for reporting diagnostic accuracy studies has been thoroughly reviewed²⁷ together with the complementary presentation.²⁸ The pertinent STARD items are addressed herein.

Signal Processing

Non-Derivative Estimations

We use the Padé and Fourier estimations based on the non-derivative (FPT, FFT) and derivative (dFPT, dFFT) spectra. The FPT and FFT spectra are:

Non - parametric FPT = \sum_{n = 0}^{N - 1} c_{n} u^{n} = \frac{P_{K} (u)}{Q_{K} (u)},

(1a)

Parametric FPT = \sum_{k = 1}^{K} \frac{d_{k}}{u - u_{k}},

(1b)

FFT = \sum_{n = 0}^{N - 1} c_{n} e^{- 2 π i n k / N}, 0 \leq k \leq N - 1,

(2)

where

u = e^{- 2 π i ν τ}

is the complex harmonic variable and

τ

is the equidistant sampling rate of time

t

in the FID,

{c_{n}} (t = t_{n} = n τ, 0 \leq n \leq N - 1)

. The actual total signal length N can be extended by zero-filling

(c_{n} = 0, n > N),

amounting to trigonometric interpolation in the FFT. Note, Eq. (1a) is the definition of the well-known Padé approximant (PA), equivalently called the FPT in MRS. Therein, the sum is the MacLaurin polynomial in powers of u with the FID points

{c_{n}}

as the expansion coefficients. If we expand

P_{K} (u) / Q_{K} (u)

also in powers of u, the ensuing truncated series will generate twice more expansion coefficients than in the MacLaurin polynomial. This extrapolation means that the FPT is predictive. It provides the FID data points at

t > T

. Thus, the same resolution in the FPT and FFT can be obtained when the former employs merely half of the input time signal points.¹⁴

In Eq. (1b), the sum is the Heaviside partial fraction decomposition of $P_{K} (u) / Q_{K} (u) .$ Therein, $u_{k} = e^{- 2 π i ν_{k} τ}$ is the root of the denominator polynomial $Q_{K} (u) = 0$ and $d_{k}$ is the FID amplitude, $d_{k} = {Q_{K} (u) / [(d / d u) Q_{K} (u)]}_{u = u_{k}}$ . Here, $ν_{k}$ is the complex fundamental frequency yielding the position and the width of the k th peak $(1 \leq k \leq K),$ where $I_{m} (ν_{k}) < 0$ . Parameters $u_{k}$ and $d_{k}$ are the results of explicit quantification. They provide the sought four parameters of each peak (position, width, height, phase). The k th component spectrum in the parametric FPT is $d_{k} / (u - u_{k})$ which is contained in the sum over k from Eq. (1b). The parametric FPT performs quantification straightforwardly with only one numerical step added to the non-parametric FPT. This is finding the roots of the characteristic equation $Q_{K} (u) = 0$ .²³

Once the peak parameters ${u_{k}, d_{k}} (1 \leq k \leq K)$ are determined (with no post-processing, nor fitting), the FID is retrieved thereby as $c_{n} = \sum_{k = 1}^{K} d_{k} u_{k}^{n}$ . Here, each FID data point $c_{n}$ is a linear combination of complex damped harmonics $u_{k}^{n}$ of amplitude $d_{k}$ . Thus, the same resonance pair of complex attenuated exponentials and their amplitudes ${u_{k}, d_{k}}$ reconstructs both the spectrum and the structure of the FID.²³

The total number K reconstructed by the FPT contains both genuine $(K_{G})$ and spurious $(K_{S})$ resonances, $K = K_{G} + K_{S}$ . These are distinguished by the fact that the former and the latter are stable and unstable, respectively, against increased K. Spurious resonances, present in $P_{K}$ and $Q_{K},$ are washed out from $P_{K} / Q_{K}$ (pole-zero cancellation), amounting to noise suppression. As a result, the stabilized spectrum $P_{K_{G}} / Q_{K_{G}}$ contains only $K_{G}$ genuine resonances. In the parametric FPT, all spurious resonances $K_{S}$ disappear due to their zero-valued amplitudes, $d_{k} = 0$ .^14,23 In practice, K is at most half of the full signal length N. The spectrum $P_{K} / Q_{K}$ is computed for K varying around $N / 2$ , and monitored for convergence.

Derivative Estimations

To proceed further, we turn to derivative signal processing. The spectra in the dFPT and dFFT are:

Non - parametric dFPT = D_{m} FPT = {(\frac{d}{d ν})}^{m} \frac{P_{K} (u)}{Q_{K} (u)},

(3a)

Parametric dFPT = D_{m} FPT = {(\frac{d}{d ν})}^{m} \sum_{k = 1}^{K} \frac{d_{k}}{u - u_{k}},

(3b)

Unoptimized dFFT = D_{m} FFT = \sum_{n = 0}^{N - 1} {(- 2 π i n τ)}^{m} c_{n} u^{n} .

(4)

In the dFPT from Eqs. (3a) and (3b), the unweighted input FID is processed, as in the FPT from Eqs. (1a) and (1b). Both variants of the dFPT, the non-parametric (3a) and parametric (3b), possess their analytical expressions for D _m FPT, as per Ref.²³

The peak positions, widths, heights, areas and metabolite concentrations retreived by the non-parametric dFPT are corroborated by the corresponding numerical data from the parametric dFPT. The latter is based on the exact solution of the quantification problem by the parametric FPT. In other words, the non-parametric dFPT resolves the FPT envelope into its genuine components. After the peak parameters are extracted from the derivative lineshape, they are mapped to their non-derivative counterparts $(m = 0)$ by the known conversion formulae.^23,24 Thus, by sole reliance upon shape estimations, this amounts to quantification, the ultimate goal of data analysis in MRS.

In the unoptimized dFFT from Eq. (4), the FID is weighted by the time power function $(- 2 π i n τ)^{m}$ . The latter function can separate any overlapped peaks for noiseless FIDs. However, for noisy FIDs (such as those that are encoded) the same function deteriorates SNR. It weights heavily the noisy tails of the encoded FIDs. As a result, with increased m, the unoptimized dFFT spectra have poorer resolution and SNR than their FFT counterparts from Eq. (2).

The resolution-SNR problem in the unoptimized dFFT is solved through apodizing the function $(- 2 π i n τ)^{m} c_{n}$ by eg the time-dependent, derivative-adaptive exponential attenuating filter. The ensuing estimator is called the optimized dFFT:

Optimized dFFT = \sum_{n = 0}^{N - 1} c_{n} [{(- 2 π i n τ)}^{m} e^{- m λ n τ}],

(5)

λ = \frac{1}{T} \ln (T e^{α}), T = N τ .

(6)

Parameter $α > 0$ is a measure of the approach of the FID to zero at the end of encoding $(t = T)$ . For example, $α = 3$ (as presently used in the results section, Figure 4) signifies that at $t = T$ , the intensity of the FID is merely ∼5% of its strength at the onset of encoding $(t = 0)$ . In such a case, the FID is viewed as being almost fully relaxed.²⁵ This is how the time-domain exponential filter $(- 2 π i n τ)^{m} e^{- m λ n τ}$ from Eq. (5) is tailored to the SNR of the encoded FID. The attenuation (apodization) of the FID changes with the derivative order $m$ , ie $e^{- m λ n τ}$ is used in Eq. (5). Had the static counterpart $e^{- λ n τ}$ been used, the noise induced by $(- 2 π i n τ)^{m}$ in Eq. (5) would overwhelm the apodization for increasing m. Crucially, $e^{- m λ n τ}$ suppresses the noise-enhancing feature of $(- 2 π i n τ)^{m}$ and thus retrieves the intrinsic resolving power of this time power function. It is this counterbalancing in the ensuing “adaptive power exponential filter” (APEF) $, (- 2 π i n τ)^{m} e^{- m λ n τ}$ , that is essential for the simultaneous improvement of resolution and SNR in the optimized dFFT.²⁵

Both the dFPT and optimized dFFT can be obtained for any derivative order m by comparable computer time. Stability of the derivative lineshapes for succesively increased derivative order $m$ represents the stopping criterion for determining the optimal value of m. In practice, the dFPT stabilizes for low values of $m,$ since it encounters no derivative-induced noise (it processes the unweighted FIDs). The optimized dFFT, while processing the weighted FIDs, requires somewhat higher derivative orders, particularly for spectrally-congested regions. In the dFFT, the weight function of the FID is the noise-producing time monomial generated by the derivative operator $D_{m}$ .

The results for the optimized dFFT can come straight from every MR clinical scanner and laboratory spectrometer. The time-domain filters of the exponential and Gaussian damping forms are already present in the software of these MR instruments. Thus, all that is needed is to raise these filters (with the damping mechanistically specified in (6)) to the power m and to multiply the outcomes by the time monomial $(- 2 π i n τ)^{m}$ .

In the dFPT, the polynomial ratio $P_{K} / Q_{K}$ is computed by the fast Euclid algorithm,²⁹ which is of expedience comparable to that of the FFT and dFFT.²⁶ The ratio $P_{K} / Q_{K}$ can also be obtained by applying the standard software from Numerical Recipes³⁰ or Matlab.³¹

Time Signals Encoded by Proton MRS

Herein, the results are presented by applying derivative estimations to MRS data for a borderline serous cystic ovarian tumor from in vivo encoding on a 3T Magnetom Tim Trio scanner. Also presented are the results for benign (serous cystadenoma), and malignant (serous cystadenocarcinoma) ovarian fluid samples from in vitro encoding on a 600 MHz (14.1T) Bruker spectrometer. All diagnoses were histopathologically confirmed. The Regional Ethics Committee stated that they found no ethical issues to preclude implementation of this research.

For 3T, the in vivo encoded FIDs contained 1024 complex-valued data points with bandwidth (BW) of 1200 Hz and sampling time τ = 1/BW ≈ 0.833 ms. The voxel of interest was 3 cm × 3 cm × 3 cm in the inferior cystic portion of the borderline ovarian tumor. A point-resolved spectroscopy sequence (PRESS) for single-voxel MRS was applied using repetition time (TR) of 2000 ms, echo time (TE) of 30 ms using WET (water suppression through enhanced T₁ effects). Sixty-four encoded FIDs were averaged to improve SNR.³²

For 14.1T in vitro encoding, two excised samples from the serous cystadenoma and from the serous cystadenocarcinoma were bathed in D₂0 solvent. The acquisition parameters were: TR = 1200 ms, BW = 6667 Hz, TE = 30 ms and τ ≈ 0.15 ms. Improved SNR resulted from averaging 128 encoded FIDs. Trimethylsilyl-2-2-3-3 tetradeuteropropionic acid (TSP: sodium salt), as an internal reference substance, was added to each sample for calibrating chemical shifts and metabolite concentrations. The averaged FIDs were zero-filled once prior to Fourier and Padé signal processing for both the in vivo and in vitro encodings. The in vitro data were a part of a series of ovarian cyst fluid samples obtained from 40 patients with a primary ovarian tumor (12 malignant and 28 benign).³³ The encoded FIDs were from Refs..^32,33 The signal processing presented herein was performed independently from the histopathology.

Results

The Padé spectra to be presented are computed from the stabilized values of $K$ and m, that are the degree of the quotient $P_{K} / Q_{K}$ and the derivative order, respectively. For the in vivo and vitro FIDs, we used $K = 550$ and 1500, respectively.

In Vivo Encoding from Borderline Ovarian Cyst: the dFPT Delineates Myriads of Peaks in the Full Nyquist Range

Figure 1 is based on the in vivo encoded MRS data from the borderline serous cystic ovarian tumor. The top panel (a) displays the results in the aliphatic and aromatic spectral regions for the FPT. Therein, on the upper trace for the non-parametric FPT, the water residual dominates. It masks all the other metabolites that appear as minuscule irregular structures embedded in the background baseline comprised of broad macromolecular resonances. In the aliphatic region, four unresolved bands are marked containing: total choline (tCho) at ∼3.2 ppm, total creatine (tCr) at ∼3.0 ppm, N-acetylaspartate (NAA) complex at ∼2.0 ppm and lactate (Lac) at ∼1.3 ppm.

Figure 1.

In Vivo MRS (3T) for Ovarian Borderline Cyst: Spectra Covering Almost the Entire Nyquist Frequency, with Aliphatic and Aromatic Regions. FPT (a:m = 0) Versus Derivatives in the dFPT (b-e: m = 3) Estimations. The Non-Parametric and Parametric dFPT Display a Plethora of Well-Delineated Peaks Amenable to Retrieving Concentrations of Cancer Biomarkers and Other Diagnostically-Relevant Metabolites. The dFPT Spectra in (b,c) Coincide, as Do those in (d,e). Note, the Non-Parametric dFPT Maps the Crude, Uninformative Top Trace in (a) to Separated, Sharp Resonances in (b,d). Spectral Intensities (Ordinates) in Arbitrary Units (au); Chemical Shifts (Abscissae) in Parts Per Million (ppm). In (b), Just Above the Abscissa, Illustrative Peak Parameters (Extracted for m = 3 and Mapped to m = 0^23,24) are Displayed for NAA and acNeu: Real and Imaginary Parts of Complex Resonance Frequency $ν_{k}$ (Position, Width) in ppm, $| d_{k} |$ (Intensity) in au and Area $a_{k} = | d_{k} | / 2$ in au (for Details, See Text).

On the lower trace of (a) for the parametric FPT several sub-peaks underlying the water residual are revealed. Elsewhere, on the bottom trace, an enormous number of overlapping peaks appear, whose separate lineshapes are difficult to distinguish, even when enlarged and inspected window-by-window. The envelope for the non-parametric FPT is a single curve which represents the combined contribution of all the individual peaks (Depending on the relative effects of constructive and/or destructive interference, overlaps among the components can have varied influence on the envelope). From this single curve, it is impossible to surmise what the actual contributory sub-peaks are. Not only would that be entirely speculative, but also non-unique, ie many different combinations are possible.

With application of the third derivative in the dFPT, the situation changes completely in the aliphatic (b,c) and the aromatic (d,e) regions. In the non-parametric dFPT (b), many sharp resonances emerge as a direct consequence of the mechanism of derivative signal processing. Namely, this additional transform simultaneously narrows and intensifies all the peaks, lowering their tails and separating overlaps. This is most markedly manifested in the water residual, which collapses to a single sharp peak surrounded by two well-delineated doublets. The mentioned four chemical-shift bands are seen to be baseline-resolved into their quantifiable components. These are tCho: free choline (Cho), phosphocholine (PC) and glycerophosphocholine (GPC), tCr: creatine (Cr) and phosphocreatine (PCr), NAA complex: NAA and N-acetylneuraminic acid (acNeu) and Lac: lactate doublet. In the parametric dFPT (c), the results fully coincide with those for the non-parametric dFPT (b). For illustrative purposes, numerical data for peak areas of some derivative lineshapes are presented in panel (b), after mapping to their corresponding non-derivative counterparts.^23,24

Likewise, in the aromatic region (d,e), a plethora of well-delineated, sharp peaks appear, descending to the flattened baseline in the dFPT ( $m = 3$ ). These include eg histidine (His), tyrosine (Tyr), lipid (Lip), α- and β-glucose (Glc). Here too, as was the case for the aliphatic region, the results from the dFPT in the non-parametric (d) and parametric (e) estimations are entirely coincident.

Further Elucidation of Total Cho Components by the dFPT: in Vitro MRS for Benign & Cancerous Ovarian Cysts

The focus in Figure 2 is on the in vitro encoded MRS data from the benign (serous cystadenoma: a-d) and malignant ovarian fluid (serous cystadenocarcinoma: e-h) within the chemical shift range 3.17–3.30 ppm. In (a) for the non-parametric FPT, the resonances associated with free Cho, PC and GPC appear as rather wide, small peaks that are difficult to distinguish from the rolling baseline. In (b), the parametric FPT shows several overlapping peaks at 3.21–3.24 ppm. With the third derivative in the dFPT of the non-parametric (c) and parametric (d) spectra, on a fairly flattened baseline, the small peaks associated with PC and GPC are clearly identified. Free Cho at 3.19 ppm appears to be minimal. Taurine (Tau) is the tallest resonance, with an underlying peak which appears as a left shoulder in (c).

Figure 2.

In Vitro MRS (14.1T) for Benign (Left Column) and Malignant (Right Column) Ovarian Cyst Fluid Samples. Cholines are Approximately 4 Times More Abundant in the Latter (e-h) than in the Former (a-d) Cases. In the FPT $(m = 0),$ Free Cho at 3.19 ppm (e, Bottom Trace) is Skewed Due to Overlapping L-acetylated Carnitine, Acn, Which is Separated Out by the dFPT ( $(m = 3)$ in (g: Bottom Trace, Non-Parametric) as Confirmed in (h: Parametric). Ordinates in au, Abscissae in ppm (for Details, See Text).

For the malignant case (e-h), the non-parametric FPT in (e) produces an oscillating baseline on which wide peaks associated with GPC, PC and free Cho are superimposed. Phosphoethanolamine (PE) appears as two peaks at 3.20–3.21 ppm. Inset into (e) with the baseline lifted to 80 au (arbitrary units) is a spectrum from the first derivative non-parametric dFPT. Besides a flattening of the baseline, the most notable finding in this inset is that at ∼3.19 ppm, a conspicuous notch appears on the top of the peak. In contrast, at $m = 0$ on the bottom trace of (e), the peak at ∼3.19 ppm is entirely smooth, albeit slightly asymmetric. Panel (f) for the non-derivative component spectra shows that indeed there are two overlapping peaks at 3.19 ppm: free Cho and L-acetylated carnitine (Acn) of about the same area. Herein, PC and GPC overlap and there are several other resonances that partially underlie these two peaks. In (g) for the non-parametric dFPT, the upper inset for $m = 2$ shows a deeper split between free Cho and Acn. This becomes even deeper for $m = 3$ on the bottom trace in (g). The component spectra in (h) for $m = 3$ from the parametric dFPT concordantly display the two overlapping resonances at 3.19 ppm. At $m = 3,$ the envelope (g) and components (h) in the region 3.17−3.30 ppm are closely coincident on flattened baselines.

Such a coincidence is particularly noteworthy for the ability of the non-parametric dFPT to robustly unravel a completely hidden sub-peak, Acn, in the singlet-appearing free Cho from the bottom trace in (e). Without identifying the splitting, the concentration of free Cho would be underestimated by a factor of 2, thereby compromising the diagnostic accuracy of this cancer biomarker.

High Resolution & SNR with Resilience of dFPT to Derivative-Induced Distortions:

In Vitro MRS Around the Lactate Doublet for Cancerous Ovarian Cyst Fluid

We now focus in Figure 3 on the spectrally dense region (0.9-1.6 ppm) in the vicinity and underlying the Lac doublet (∼1.41 ppm), which is a recognized cancer biomarker. The displayed spectra were obtained using the in vitro encoded FIDs from the malignant sample. Herein, besides Lac, there are many other resonances, whose abundance can be more accurately assessed and displayed by derivative lineshapes. In (a) for the parametric FPT, 6 peaks (2 sharp doublets and 2 wide peaks) are seen beneath the Lac doublet. These 6 resonances must, of course, be excluded to accurately assess the concentration of the Lac doublet from the non-derivative spectrum. The bottom trace in (b) shows the envelope from the non-parametric FPT in the same region as in (a). Most notable here is the elevated baseline upon which lie several adjacent asymmetric peaks. These are doublets of alanine (Ala), threonine (Thr) and β-hydroxybutyric acid (β-HB). Albeit a bit further away from the Lac doublet, in the dense region 0.9–0.97 ppm, the baseline is likewise lifted with asymmetric peaks. In the inset to (b), already the first derivative non-parametric dFPT displays marked baseline flattening. Herein, most of the resonances to the right of the Lac doublet are nearly symmetrical up to ∼1.03 ppm where the first valine doublet appears. Below ∼1.03 ppm, the resonances are a bit better resolved, but the baseline is still visibly elevated. For $m = 3,$ the parametric dFPT in (c) and the non-parametric dFPT in (d) are in agreement. The steadiness of this process is indicated in the upper trace of (d), in which nearly all the resonances above 1.0 ppm have been fully resolved to the baseline already with the second derivative in the dFPT.

Figure 3.

In Vitro MRS (14.1T) for Malignant Ovarian Cyst Fluid Sample. Focusing on Lactate Doublet, Lac, and Its Neighborhood, Including Branched-Chain Amino Acids (Valine Val, Leucine Leu, Isoleucine Iso). The 3^rd Derivative in the dFPT $(m = 3)$ in (d: Non-Parametric, Lower Trace) Resolves All the Resonances Down to the Chemic Shift Axis, as Corroborated in (c: Parametric). Importantly, no Derivative-Induced Lineshape Deformations, as Seen by Passing from m = 1 (b, Top Trace) Through m = 2 (d, Top Trace) to m = 3 (d, Bottom Trace). Ordinates in au, Abscissae in ppm (for Details, See Text).

For the parametric (c) and non-parametric (d, bottom trace) third derivatives in the dFPT, almost all the peaks are resolved down to the chemical shift axis. Each resonance is distinct, isolated and located on the entirely flat baseline. Consequently, all the peaks adjacent to Lac can be accurately quantified. This is noteworthy since small peaks in the vicinity of a large resonance are usually distorted and, as such, non-quantifiable. The Lac doublet also has clear integration limits for finding the peak area and hence the concentration. It is divided by 35 in (c, d) to be displayed as intact on the same ordinate alongside all the other resonances.

Comparing Fourier and Padé Reconstructions in the Region Dominated by the Lactate Doublet

In Figure 4 , the dense region 0.9–1.6 ppm in the vicinity and underlying the Lac doublet is examined again, but therein from several supplementary perspectives. Panels (a, b) and (c-e) are from Padé and Fourier reconstructions, respectively. In (a), the non-parametric FPT is displayed for the benign sample. Therein, the Lac doublet also dominates. Yet, the Lac peak height ratio of the malignant (b) to benign (a) cystic lesions is 18.54. Another notable feature of the non-parametric FPT spectra for both the benign (a) and the malignant (b) ovarian lesions is the asymmetry of the peaks. This is further illustrated in (b) with magnified insets for both the benign (upper inset) and malignant (lower inset) samples. These asymmetries are shared by the FFT, as displayed in (c) for the malignant sample. Herein, skewed and distorted peaks are seen throughout the spectral region. From panels (a), (b) or (c) no trustworthy quantification can be made. Since the baselines are lifted, integration limits cannot be ascertained. In (c) of Figure 4, the envelope from the FFT, aside from showing slightly more pronounced ripples, is similar to (b) of Figure 3 (bottom trace) for the non-parametric FPT.

Figure 4.

In vitro MRS (14.1T) for Benign and Malignant Ovarian Cyst Fluid Samples: FPT (a,b), FFT (c) and dFFT (d: Optimized, e: Unoptimized). Refocusing on the Lactate Doublet and its Vicinity. Malignant-to-Benign Ratio Levels are Approximately 18 for Lac, 3 to 6 for Ala, Thr, Beta-HB, Val, Leu and Iso, as Seen in (a,b). The Optimized dFFT for m = 4 (d) Generates a Well-Delineated Spectrum from the Rough FFT (c, m = 0). The Unoptimized dFFT (e, m = 4) Loses All Physical Information. Ordinates in au, Abscissae in ppm (for Details, See Text).

For the optimized dFFT at $m = 4$ in (d), numerous well-resolved symmetrical peaks with a flat baseline are observed. In the most crowded region below 1.0 ppm, the upper inset shows that at $m = 10$ the optimized dFFT achieves resolution down to baseline. This makes the peaks readily amenable to quantification.

In sharp contrast, with the unoptimized dFFT, marked deterioration of resolution and SNR occur at $m = 4$ (e), even compared to the FFT (c). In (e), the few recognizable peaks are distorted, and the entire spectral region is dominated by derivative-induced noise. The culprit of this spectral degradation is the time power function $(- 2 π i n τ)^{m}$ from Eq. (4). However, when such a detrimental effect of this time power function is tamed by the filter $e^{- m λ n τ}$ from Eq. (5), the full benefit of optimization in the dFFT becomes evident in panel (d).

Just like in panel (c) of Figure 4, the most congested region below 1 ppm could not be quantified either in Refs.^33,34 by the FFT for in vitro high field ovarian MRS. The same lack of resolution within this diagnostically-relevant region was also reported in a study on ovarian lesions employing MRS with high-resolution magic angle spinning (HRMAS).³⁵

Depletion of Citrate in the Malignant Ovarian Lesion

In Figure 5 , the results of the FPT and dFPT are displayed focusing on citrate (Cit), a quartet centered at ∼2.90 ppm.³³ In panel (a), four pronounced Cit peaks show up, as reconstructed by the non-parametric FPT for the benign sample. The two inner peaks centered at about 2.85 and 2.97 ppm are taller than the two outer peaks. This configuration is predicted by the Pascal rule for J-coupling in the theory of MRS.²³ All four peaks display somewhat widened bottoms, with an asymmetrical descent to the baseline. Therefore, integration limits would not be discernable for computing the Cit area. In (b), the spectra from the parametric FPT for the benign ovarian cyst fluid reveal that unknown metabolites (jointly denoted by U) underlie each of the four Cit peaks.

Figure 5.

In Vitro MRS (14.1T) for Benign and Malignant Ovarian Cyst Fluid Samples. Focusing on the Citrate Quartet. In the FPT (m = 0), the Citrate Abundance is Approximately 5 Times Higher in the Benign (a,b) Relative to Malignant (c,d) Samples. Panels (c-h) Are for the Malignant Sample Alone for Which e.g. the Non-Parametric (g) and Parametric (h) Versions of the dFPT (m = 3) are Identical. Ordinates in au, Abscissae in ppm (for Details, See Text).

The spectra retrieved by the FPT (c,d) using the FID from the malignant sample are yet more complicated. The overall observation is that Cit is several times less abundant for the malignant relative to the benign ovary. Specifically, in (c) from the non-parametric FPT, the outer Cit peak at ∼3.03 ppm appears to be the tallest, and is surrounded by two wide, intense unknown resonances. In that region, the baseline is most lifted. The parametric FPT (d) reveals that in the vicinity of the outer Cit peak at ∼3.03 ppm, there are numerous resonances in addition to the two unknown peaks seen in (c). On the other hand, minuscule resonances underlie the other three Cit peaks. With $m = 1$ , via the non-parametric dFPT in (e), all four Cit peaks are narrowed substantially and the baseline is markedly, albeit not completely flattened. In (f), the parametric dFPT for $m = 1$ likewise shows four narrow Cit peaks with some very small surrounding resonances. Notably, with the malignant sample, in both (e) and (f) for $m = 1$ , the two inner Cit peaks are clearly taller than the two outer ones. This J-coupling pattern is similar to that for the benign case in (a) and (b). In the bottom two panels (g) and (h) at $m = 3$ , the spectra from the non-parametric and parametric dFPT, respectively, are manifestly identical, both exhibiting a completely flattened baseline. Once confirmed in this way, the non-parametric dFPT again emerges as a stand-alone, quantification-equipped shape estimator. This is most evident when comparing the spectra from the non-derivative $(c, m = 0)$ and third derivative $(g, m = 3)$ estimations.

Discussion

To the best of our knowledge, this is the first study in which results for in vivo MRS encoded FIDs from the ovary have been presented for the nearly-entire Nyquist interval. Without derivative processing, the component spectra retrieved by parametric estimations are difficult to interpret visually, due to the numerous overlapping resonances. These overlapping resonances are not even identifiable by any non-derivative shape estimator. Notably, with FFT processing of in vivo encoded MRS time signals from the ovary, overlapping resonances have been a major stumbling block.¹³ In contradistinction, both versions of the dFPT for the third derivative yielded confluent results, with altogether over 300 clearly identifiable, thin, baseline-resolved peaks for the aliphatic plus aromatic regions.

In the aromatic region, among the identified resonances were histidine at ∼7.75 ppm, phenylalanine multiplets centered at ∼7.4 ppm and tyrosine doublets at ∼6.9 and ∼7.2 ppm. These resonances were also observed in the spectrum associated with a serous ovarian carcinoma, as reported by Kyriakides et al³⁴ in their in vitro MRS study of ovarian lesions. With inclusion of the aromatic as well as the aliphatic regions, these authors state: “the respective metabolic profiles contain mechanistic information which could help identify biomarkers and therapeutic targets for ovarian tumours” (p. 7216).

Crucially, for the presently analyzed in vivo MRS data from the borderline ovarian cyst fluid, all three components of tCho in the aliphatic region around 3.2 ppm were quantified by the dFPT ( $m = 3$ ). As such, free Cho, PC and GPC within tCho were visibly delineated. The special challenges surrounding borderline or low-grade serous ovarian cancer have received heightened attention recently.³⁶ There are, however, limited in vivo MRS data from borderline ovarian lesions. In the meta-analysis of in vivo MRS data from 251 ovarian lesions, as reported in Ref.,¹³ only three (1.2%) were of borderline histopathology. A subsequently published study compared large borderline and malignant ovarian tumors using MR spectroscopic imaging (MRSI).³⁷ A significantly lower tCho to tCr ratio was found in the cystic and the solid constituents of the borderline tumors.

Altered choline metabolism is considered to represent one of the hallmarks of cancer.³⁸ Phosphocholine, in particular, has been identified as a biomarker for several types of cancer.³⁹ This might be due to loss of tumor suppressor p53 function.⁴⁰ Increased levels of GPC, which comes as a subsequent metabolic step, may also be a biomarker of malignancy, according to Sonkar and colleagues, who highlight the need for more investigation using “innovative” MRS methodologies.⁴¹ However, with FFT processing of in vivo encoded MRS time signals from the ovary, due to overlap, the components of tCho have not been assessed.¹³ Even tCho has not consistently been detected by FFT processing of in vivo encoded data from malignant ovarian lesions.^13,42

Additional insights concerning these diagnostically-important tCho components are gleaned from derivative processing by the dFPT of the in vitro MRS data encoded from benign and patently malignant ovarian fluid samples. Firstly, multifold higher PC and substantially higher GPC levels are observed in the latter specimens. Moreover, free Cho resonating at ∼3.19 ppm is found to closely overlap with L-acetylated carnitine, Acn. The Acn peak is so intense that it must be excluded in order to accurately assess the level of free Cho, and to make an overall assessment of this recognized cancer biomarker.

It is well-known that water is a dominant molecule in human tissues and biofluids. As such, FIDs encoded by MRS from these tissues and biofluids yield spectra dominated by the water peak, which obscures all the other resonances. The water peak is usually fitted with several artificial Lorentzians, as done in eg the Hankel-Lanczos singular valued decomposition.¹⁴ Subsequently, the ensuing lineshapes are subtracted from the total shape spectrum. However, spectral subtraction can wash out some physical resonances. This bottleneck is successfully solved without subtraction of any spectra by the dFPT and the optimized dFFT. These two processors simultaneously narrow the water peak and flatten its tail. Both estimators can give spectra of comparable quality by using the FIDs encoded with and without water suppression.^23,43 The latter acquisition option would reduce the overall examination time for the patient. This would help the patient and hospital management, including the long-sought cost effectiveness of MRS.

It has been generally considered that FIDs encoded by in vitro MRS at high field spectrometers represent the “gold standard”. With in vitro MRS, broad resonances are considerably narrowed, thereby enhancing peak resolution. Nevertheless, more scrupulous assessment of results from in vitro MRS is needed. Namely, in such FFT spectra, there are still many unresolved resonances superimposed on lifted background baselines with uncertain integration limits. This can be seen by examining the spectra extracted from in vitro encoded ovarian data as displayed in Refs..^33–35 Consequently, clinically reliable assessment by non-derivative, non-parametric estimations in MRS is often precluded even with the strongest magnetic fields with or without HRMAS.

Clarification is also needed in the region 1.3–1.4 ppm where Lac and broad Lip overlap. Elevated Lac can be associated with the presence of cancer cells, whose energy source is the glycolytic pathway. This can be due to tissue hypoxia. However, even with normal O₂ levels, cancer cells activate glycolysis⁴⁴ yielding increased Lac, possibly contributing to invasiveness and resistance to immune attack. An in vitro MRS investigation of cells from ovarian cancer and benign ovary revealed significantly higher intracellular Lac in ovarian cancer cells.⁴⁵ High Lip levels at 1.3–1.4 ppm have also been associated with several cancers, particularly necrotic tumors.¹⁴ Thus, this overlap of narrow, longer-lived Lac and broad, short-lived Lip at 1.3–1.4 ppm is troublesome for oncologic diagnostics.

In the meta-analysis of in vivo MRS studies of ovarian lesions (cancerous, borderline and benign), this chemical shift region was of special interest.¹³ On the one hand, the appearance of Lac was significantly associated with malignant ovarian lesions, as opposed to those that were benign. However, data regarding Lac were missing in 75% of cases. Moreover, lipid was more often noted in malignant lesions, although that was not a statistically significant finding.

By sequential quantification,²³ after quantifying Lac, the ordinates for the intensities in the plotted spectrum can be reduced, thus enabling appearance of the broader resonances, including lipids. The latter can be quantified in the same way as done with Lac. Sequential quantification is especially helpful for regions of mixtures of resonances with different widths. It is particularly important at short echo times such as TE = 30 ms,^32,33 for which Lac is otherwise often undetected due to overlap with lipid.²³ Macromolecules impede analysis and interpretation of spectra throughout the Nyquist range. This problem can likewise be solved by sequential quantification without any subtraction of spectra.

Short echo times provide the richest spectra. Frequently, acquisitions are made with long TEs to produce sparse spectra more amenable to interpretation. However, much potentially-important diagnostic information is irretrievably lost thereby. With the dFPT and the optimized dFFT, time signals encoded by MRS at short TEs are fully accessible to estimation, as seen herein.

Another region of interest is 0.91–1.12 ppm where branched-chain amino acids, isoleucine (Iso), leucine (Leu), valine (Val) are interspersed with several other tightly overlapped resonances. Increased levels of Iso, Leu and Val have been viewed as protein breakdown products characterizing malignant ovarian lesions.¹¹ High levels of Val and Leu are reportedly associated with poor survival in patients with epithelial ovarian carcinomas.³⁵ The main obstacle to quantifying the resonances in the band 0.91–1.12 ppm had been attributed to “spectral crowding”.³³ With the third derivative in the dFPT applied to FIDs encoded from ovarian cyst fluid, not only were Iso, Leu and Val resonances fully resolved, but so were several other metabolites residing in that congested region.

Citrate, a quartet centered at ∼2.90 ppm,³³ was seen to be markedly depleted in the serous cystadenocarcinoma compared to the serous cystadenoma. Elevated citrate was also reported in 8 benign ovarian lesions assessed via in vitro MRS.³⁴ A recent metabolomic investigation similarly indicates that Cit is downregulated in ovarian cancer cells.⁴⁶ Moreover, therein, Cit was found to induce ovarian cancer cell death. Together, these findings suggest that lowered Cit may help identify malignant ovarian lesions. It has been established that diminished levels of Cit are a key metabolic marker of prostate cancer as assessed through MRS.⁴⁷

The findings presented in our current study underscore the full agreement between the non-parametric and parametric versions of the dFPT. This agreement also extends to the optimized dFFT. Such a threefold cross-validation helps provide the diagnostic clarity for which clinicians fervently strive. On the other hand, the noise-content of the latter part of the encoded FID completely undermines the unoptimized dFFT.

The present study was carried out for MRS data from three patients. In vivo MRS was from one patient with borderline ovarian cyst. For the other two patients, one with benign and one with malignant ovarian cyst fluid, in vitro MRS was used. The small number of included patients obviously limits statistical analysis as to which metabolites best distinguish these three clinical categories. Rather, the reported findings are intended to be illustrative of the potential for enhanced diagnostics for ovarian lesions through derivative MRS. A key implication of the present feasibility study is that derivative MRS is a viable option for assessing ovarian lesions in the clinical setting. Further rigorously controlled examination will be needed to ascertain the actual readiness of derivative MRS for clinical implementation.

Practical issues should also be considered. Namely, the results for the optimized dFFT can be available from every MR clinical scanner and laboratory spectrometer. The filters of the exponential and Gaussian damping forms are already present in these MR instruments. These just need to be adapted to the derivative order and to the SNR of the encoded time signal, according to Eqs. (5) and (6). Likewise, fast computations in signal processing can enable the dFPT to readily enter the manufacturers’ software for MR devices.

As noted, the ovary is a small, moving organ, such that encoding high-quality FIDs by in vivo MRS is technically difficult, an objective limitation. Moreover, the histopathology of ovarian lesions is diverse,⁴⁸ and includes both cystic as well as solid types, further limiting the generalizability of the reported findings.

Notwithstanding these challenges, it is hoped that the results of the present study will encourage the MR community to give further attention to this problem area of major public health concern.^1,2 Among the next strategic steps would be to apply derivative MRS to FIDs encoded in vivo from various types of ovarian lesions: benign, borderline, as well as cancerous. Potential confounders such as patient age, hormone status and comorbidities, that might affect metabolic profiles would also be important to consider. Blinded validation cohorts will be required in the future to externally evaluate the diagnostic accuracy of derivative MRS for assessing ovarian lesions. Comprehensive multivariable investigation will be needed to identify the metabolite patterns that most accurately distinguish benign, borderline and clearly malignant ovary.

It warrants re-emphasis that MRS examinations do not entail any exposure to ionizing radiation. This consideration is especially salient for ovarian cancer screening, for which women themselves have expressed ardent interest.⁴⁹

Conclusions

We report on furthering molecular imaging by magnetic resonance spectroscopy, MRS, for ovarian tumor diagnostics. This powerful modality could provide quantitative information for trustworthy differentiation between benign and malignant lesions. To achieve this goal, MRS relies heavily upon mathematical analysis and interpretation of encoded FIDs. It is precisely here that trustworthiness is at stake due to customary signal processing. Presently, this gap is bridged by resorting to derivative signal processing.

The ensuing derivative MRS, through data analysis by non-parametric and parametric algorithms, provides the cross-validation essential for clinical trustworthiness. Precisely the lack of trustworthiness has been the reason for which clinicians often decline to use MRS even when readily available, as reported by several European cancer centers.⁵⁰ Notably, in this light, the non-parametric and parametric versions of the dFPT yield identical final results. Since these results stem from two entirely different computational algorithms, they provide the sought cross-validation. Moreover, it is presently shown that the optimized dFFT gives the same results as the dFPT. This accord is all the more important given that the optimized dFFT is yet a third and entirely different computational algorithm.

Both visualization and quantification by the dFPT and the optimized dFFT can be expeditiously implemented in MR clinical scanners. Crucially, then, derivative MRS can provide clinically interpretable findings about cancer biomarkers and other diagnostically-important metabolites to help identify or rule-out ovarian malignancy. With derivative MRS, more accurate non-invasive assessment of ovarian lesions becomes feasible. As stated, malignant lesions confined to the ovary have an excellent prognosis.² Derivative MRS offers the possibility for early detection of ovarian cancer, and could thereby potentially impact on survival.

Footnotes

List of main acronyms

Acknowledgements

This work has been supported by The Marsha Rivkin Center for Ovarian Cancer Research (U.S.), King Gustav the fifth Jubilee Fund, and FoUU through Stockholm County Council to which the authors are grateful. We would like to thank our colleagues, Professors Marinette van der Graaf, Leon Massuger, Ron Wevers, Eva Kolwijck, Udo Engelke, Arend Heerschap, Henk Blom, M’Hamed Hadfoune, and Wim Buurman from Radboud University for kindly making available to us the in vivo and in vitro MRS time signals encoded in the Department of Obstetrics/Gynecology University Medical Centre Nijmegen, the Netherlands. Open Access has been provided by the Karolinska Institute, Stockholm, Sweden.

ORCID iD

Dževad Belkić

Ethical Approval and Informed Consent Statements

The Regional Ethics Committee, Karolinska Institute (Dnr # 2007/708-31/1) June 20, 2007 stated that they found no ethical issues to preclude implementation of this research. No informed consent statements are needed.

Author Contributions

Signal processing and the art work were carried by DžB. Analysis of the obtained spectra was performed by DžB and KB. Both authors cooperatively designed this study. KB drafted the manuscript. Both authors critically read and revised the manuscript and approved the final version submitted for publication.

Funding

This work has been supported by The Marsha Rivkin Center for Ovarian Cancer Research, King Gustav the 5^th Jubilee Fund, and FoUU through Stockholm County Council to which the authors are grateful. Open Access has been provided by the Karolinska Institute, Stockholm, Sweden. The funders had no role in the initiation or design of the study, nor with any other aspect of the study.

Declaration of Conflicting Interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Data Availability Statement

Data from this work can be made available to other researchers upon request to the authors.

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The Potential for Enhanced Ovarian Cancer Diagnostics Through Optimized Derivative Magnetic Resonance Spectroscopy

Abstract

Introduction

Methods

Results

Conclusion

Keywords

Introduction

Magnetic Resonance Spectroscopy — Possibilities for Timely Ovarian Cancer Detection

Difficulties in MRS Impeding Fulfillment of the Main Diagnostic Expectations

Derivative MRS can Address Diagnosticians’ Needs

Aim of the Present Study

Methods

Signal Processing

Non-Derivative Estimations

Derivative Estimations

Time Signals Encoded by Proton MRS

Results

In Vivo Encoding from Borderline Ovarian Cyst: the dFPT Delineates Myriads of Peaks in the Full Nyquist Range

Further Elucidation of Total Cho Components by the dFPT: in Vitro MRS for Benign & Cancerous Ovarian Cysts

High Resolution & SNR with Resilience of dFPT to Derivative-Induced Distortions:

In Vitro MRS Around the Lactate Doublet for Cancerous Ovarian Cyst Fluid

Comparing Fourier and Padé Reconstructions in the Region Dominated by the Lactate Doublet

Depletion of Citrate in the Malignant Ovarian Lesion

Discussion

Conclusions

Footnotes

List of main acronyms

Acknowledgements

ORCID iD

Ethical Approval and Informed Consent Statements

Author Contributions

Funding

Declaration of Conflicting Interests

Data Availability Statement

References