For decades, oxygenation status of tumors has been known to have important prognostic implications . Low oxygen concentration (pO2), or hypoxia, imbues cancer cells with resistance to radiation therapy [2, 3] and strong correlation has been found between electrode measurements of low pO2 and radiotherapy treatment failure in humans . Hypoxic tumors are more resistant to chemotherapy as well . Hypoxia also leads to a more malignant state for cancers, e.g., faster tumor growth due to abnormal proliferation , and plays an integral role in increasing the potential for metastatic progression .
These implications have led to increased interest in methods for probing and, a fortiori, imaging pO2 deep in tissues. The advances in methods to investigate/image tissue pO2 are detailed in the literature [8-11]. In particular, electron paramagnetic resonance imaging (EPRI) has proven to be a useful modality for measuring tissue pO2. EPRI noninvasively acquires highly-resolved, both spatially (∼1 mm3 voxels) and in pO2 (1–3 torr), 3D images of in vivo pO2 [12-16]. The low electromagnetic wave excitation frequencies used in EPRI, comparable to 6 T MRI, penetrate deep in tissue (>7 cm). EPR pO2 images use an intravenously injected, nontoxic spin probe, which distributes in the extracellular compartment of tumors, to report local pO2 .
There are two forms of hypoxia in tumors, resulting from different physiological processes: diffusion limited hypoxia, creating chronically hypoxic regions, too far removed from viable vasculature to receive enough oxygen , and perfusion limited hypoxia, creating acutely hypoxic regions. For many years, the former was believed to be the only type of hypoxia present in tumors and the most clinically relevant pO2 parameter. More recent studies have found that perfusion limited hypoxia is also present [19-22] and may even be the major cause of hypoxia in tumors [22, 23]. Studies suggest acute hypoxia (sometimes referred to as cycling or transient hypoxia) may be as important a determinant of cancer progression and patient prognosis as chronic hypoxia, although specific correlation of a quantitative measure of cycling hypoxia with treatment outcome is limited. It has been postulated that acute hypoxia may be even more deleterious than chronic hypoxia and therefore more clinically relevant because periods of reoxygenation prevent hypoxia-related cell death and select cells that can proliferate in hostile environments by abrogating normal check point signaling [23-28].
Traditional measurements of tumor hypoxia in vivo have been directed towards chronic hypoxia. Unlike chronic hypoxia studies, data relating transient hypoxia to treatment outcome are rare because methods for noninvasive quantification of transient hypoxia need further development. Current techniques include recessed-tip oxygen microelectrodes [29-31], OxyliteTM probes , T2*-weighted MRI , 19F MRI [34-36], 18F-FMISO positron emission tomography (PET) , as well as EPRI [38, 39]. Phosphorescence lifetime imaging in window chamber systems  has sensitivity to dynamic oxygenation but is an invasive measurement and not well suited for evaluating the in vivo relationship between oxygen fluctuations and treatment outcome.
Studies have found pO2 fluctuations with periods from minutes to days [22, 28, 40-44]. EPRI, heretofore, has provided a means of determining the chronically hypoxic fraction of a tumor, which has been found to predict tumor curability . Chronic hypoxia as determined from EPRI has also been validated at the molecular level via correlation to known hypoxia response proteins . Notably, EPRI obtained over longer times, i.e., with lower temporal resolution, cannot differentiate chronically hypoxic regions from acutely hypoxic regions with an average hypoxic state during imaging, but improved temporal resolution will enable this distinction. Recent studies have already begun to utilize EPRI as a means for imaging temporal changes in pO2 [38, 39, 47]. However, our standard EPRI pO2 images take 10 min, which may not provide adequate temporal resolution to study higher frequency pO2 fluctuations. Therefore, to investigate spontaneously occurring cycling hypoxia in vivo, our temporal resolution must be improved. Naturally, decreasing imaging time decreases image signal-to-noise ratio (SNR). We have done extensive work to enhance temporal resolution by improving the hardware, data processing, and by using narrower-line deuterated spin probes.
We have investigated improving SNR by post-processing data to reduce noise. A data-processing method that has proven useful as a denoising and/or feature-recognizing technique is principal component analysis (PCA). Sometimes referred to as feature analysis or the Karhunen-Loève transform, PCA has been used for the enhancement and extraction of spatiotemporal features in many different fields, including geoscience , facial recognition , and astrophysics . In particular, PCA has been used to denoise and highlight important temporal features for dynamic medical imaging modalities, e.g., gamma camera studies [51, 52], electro/magneto-encephalography , PET [54-56], SPECT [57, 58], and MRI [59-61].
The focus of this paper is to show, through simulations and experiments, that PCA can be used as a prereconstruction, spatiotemporal filter for projection data from dynamic EPRI studies. PCA filtering produces images with higher SNR and therefore higher temporal, spatial, and pO2 resolution. These PCA enhanced images will allow dynamic EPRI to be used to investigate important aspects of tumor physiology related to cycling hypoxia.
DISCUSSION AND CONCLUSIONS
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- DISCUSSION AND CONCLUSIONS
PCA approximation of projection data from dynamic EPRI studies is presented as a method for noise filtering and enhanced visualization of cycling hypoxia in tumors. Noiseless simulations show that to use PCA filtering effectively without losing important information, N+1 PCs are needed to approximate the data, where N is the number of differently oscillating volumes. After the first PC, each additional PC included allows accurate visualization of the next dominant pattern of temporal fluctuation, with dominance depending on the relative size of the oscillating volume. This is true regardless of which sub-volumes are oscillating, e.g., if only the smallest sub-volume is oscillating two PCs would still accurately approximate the data. Note that, spatially separate regions exhibiting a common temporal fluctuation pattern are considered a single oscillating volume, i.e., commonly fluctuating regions need not be adjacent to increase the dominance of their pattern of fluctuation in the PCA based representation of the data. These results apply for any arbitrary temporal pattern. Any pattern represents a unique direction in the PCA defined n-D space. Therefore, for example, if the majority of an object is undergoing low-frequency oscillations and some portions are undergoing these low-frequency oscillations with high-frequency oscillations superimposed, two PCs will reproduce the low frequency components for both of the oscillating regions, but to reproduce the high frequency oscillations as well, three PCs are required.
Simulated data with random noise approximating that of experimental data showed that incorporating more PCs in the PCA approximation resulted in worse SNR. This is to be expected since noiseless simulations found that using N+1 PCs resulted in an approximation of the data essentially containing the entirety of the signal and therefore, when noise is present, using PCs higher than N+1 should almost solely add noise. This implies that, as N increases and the number of necessary PCs increases, the noise reduction seen from PCA filtering diminishes. However, for the example shown in Figure 6 with a single oscillating volume, two PCs are used and the image SNR is increased by a factor of 3.8. Image SNR is proportional to the square root of the imaging time. Therefore, for this example, using PCA filtering allows for an improvement in temporal resolution by over an order of magnitude while maintaining the image quality of an unfiltered image. PCA filtering provides a means for increasing temporal resolution of dynamic EPRI without decreasing image quality. For the simulations presented here, the noise used was random and uncorrelated. In real EPRI experiments, this may not be the case and the noise may have some correlation. Preprocessing methods that could help whiten the noise and remove correlation could improve the efficacy of PCA filtering.
The usefulness of PCA filtering decreases as the relative sizes of the oscillating volumes decrease (Fig. 7). As less of the volume exhibits a certain pattern, the given pattern begins to be considered noise rather than signal by the PCA filtering and is erroneously discarded.
Simulations showed that PCA filtering, unlike many commonly used filters, did not result in image resolution degradation. This suggests that the apparently higher contrast in the unfiltered images seen in Figures 8a and 9a is an artifact of noise. However, while image resolution is unaffected by PCA filtering in the sense that the modulation transfer function is unaffected, dimension reduction may not always be possible without loss of information. Relatively small volumes with important pO2 fluctuations can be considered noise by PCA filtering and may not be resolved. In this respect, PCA filtering affects spatial resolution. These implications must be considered before applying PCA filtering. For situations with dominant regions of signal amongst less-correlated noise, there is no loss of resolution, but in the case of actual physiology there may be small but real temporal fluctuations (represented in the higher PCs) that are unresolved in PCA filtered images.
Presently, how many oscillating volumes to expect in vivo or how large these volumes might be are not definitively known. However, studies suggest that many tumors contain large regions undergoing cycling hypoxia and that, while the spatial distribution and temporal pattern of these fluctuations vary significantly from tumor to tumor, for a single tumor the acutely hypoxic regions tend to have pO2 fluctuations of a common pattern [40, 66]. Therefore, PCA filtering is particularly suited to enhance dynamic EPRI studies investigating cycling hypoxia, as PCA filtering requires no a priori knowledge of the temporal or spatial pO2 patterns and works well for situations with large portions of the data having similar features and when there are a small number of these features, or in this case, modes of pO2 fluctuation. Preliminary results of PCA filtering applied to dynamic EPRI studies of temporal pO2 fluctuations in murine tumors are promising. PCA filtering works exceptionally well for experiments involving forced fluctuations in pO2 by alternating breathing gas for the mouse between normoxic and hyperoxic (Fig. 8). This experimental paradigm results in pO2 fluctuations in regions with functional vasculature following the periodicity of the controlled FiO2 fluctuations. This is an ideal situation for the application of PCA filtering because there is a single dominant mode of pO2 fluctuation distributed over a large portion of the imaged volume. PCA filtering for the forced pO2 fluctuation experiment appears to be successful in removing noise while preserving the expected pO2 fluctuations.
PCA filtering of dynamic EPRI studies investigating spontaneous cycling hypoxia also has potential. The example presented in this paper (Fig. 9) is an indication that PCA filtering can enhance the visualization of spontaneous temporal pO2 fluctuations using dynamic EPRI, so that cycling hypoxia can be imaged in vivo without perturbing the biologic system being studied. One of the limits to the entire concept of cycling hypoxia has been the limitation of current techniques to quantify the amplitudes of pO2 fluctuations and the volume of the tumor undergoing such fluctuations. This has prevented correlation of these parameters with the effectiveness of anti-cancer therapy. There may even be other pertinent characteristics of cycling hypoxia in addition to amplitude and spatial extent of pO2 fluctuations. The advances presented in this work further enable the evaluation of these characteristics of cycling hypoxia. This evaluation can be obtained noninvasively, allowing for correlation of cycling hypoxia and therapeutic outcome. This, in turn, will begin to disentangle the relationship between chronic and cycling hypoxia, and provide a means for evaluating the role of both forms of hypoxia in therapeutic outcome as well as therapeutic optimization.