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I’m trying to get an MRI to do a PET scan. bioRXiv LinkWhy would I do such a thing? Aberrant glucose metabolism occupies a central role in cancer and other pathologies. The rapid uncontrolled growth of cancer cells requires a different metabolism than the steady, controlled growth of normal cells. The breakdown of glucose, one of the primary energy sources of cells, is normally under tight regulation by the cell. In many types of cancer this control is lost and the cell overexpress glucose transporters to import as much glucose as possible to feed tumor growth.[1][1][1][1][2][2][2][2] PET scans detect tumors through the gamma rays emitted by a radio-labeled analog of glucose, Fludeoxyglucose (18F) or FDG. A tumor is likely to be present wherever FDG accumulates as the 18F radioactive label persists as the glucose is further broken down the glycolytic cycle.[3][3][3][3]Going beyond PET by measuring the tumor microenvironment by MRI: The persistence of the 18F radioactive label does cause one problem, or technically a loss of opportunity. One of the most important metabolic signals in cancer is the Warburg effect, the non-oxidative breakdown of glucose to lactate. The Warburg effect is correlated with hypoxia; the lack of oxygen in regions of the tumor due to insufficient blood vessel formation. As early as 1904, it has been known that hypoxic tumors are resistant to radiation due to short lifetime of the radicals produced by radiation in the absence of oxygen.[4][4][4][4] The presence of hypoxia can therefore guide the choice between radiation treatment and chemotherapy, among other options.[5][5][5][5] Unfortunately, techniques that can detect hypoxia in vivo are very limited.[6][6][6][6]SNR limits MRI metabolite imaging: In theory, it is possible to take an NMR spectrum in each region voxel of an MRI scan. In practice, limited signal to noise limits this technique to static measurements of metabolite concentration. This is a problem since we need to inject a tracer to follow the metabolic process to follow the activities of individual enzymes. To overcome this a technique called DNP was invented that involves cooling the sample to near absolute zero and transferring the much stronger polarization of one molecule to the tracer.[7][7][7][7] The problem with DNP is that it is:Very expensive, more so even than PETWon’t work for all molecules including glucoseMath to the rescue: We can make two weak assumptions:1. Only a few metabolites are present2. The signal varies smoothly with time and spaceThis implies that the signal matrix is what mathematicians call low rank, it can be reconstructed as the linear combination of simpler structures. A low rank approximation like Singular Value Decomposition uses the fact the most highly weighted vectors in the approximation correspond to signal while the others likely correspond to noise. Throw these away and you can get a greatly cleaned up signal.An example of one of the spectra. Every glucose peak is in the right place and resolved even though it is completely absent in the raw data:A singular value decomposition on each voxel would take care of the correlation in time. But what about the correlation in space? It turns out it is much more efficient to work with each voxel simultaneously and construct a global model using matrices that correspond to images as a basis rather than vectors by using Tensor Factorization. Using this technique, we were able to increase the SNR >15 times and directly detect glucose metabolism without DNP, which as recently as 2014 was considered impossible.[8][8][8][8]The red grid on bottom is the raw data from one of the experiments from a mouse with a leg tumor xenograft. The white line represents the outline of the tumor. Voxels are 1.5 x 1.5 x 16 mmOne image is taken every 12 seconds which allows the kinetics of the breakdown of glucose into lactate to be measured.Footnotes[1] GLUT1 expression in malignant tumors and its use as an immunodiagnostic marker[1] GLUT1 expression in malignant tumors and its use as an immunodiagnostic marker[1] GLUT1 expression in malignant tumors and its use as an immunodiagnostic marker[1] GLUT1 expression in malignant tumors and its use as an immunodiagnostic marker[2] Glucose transporters in cancer metabolism.[2] Glucose transporters in cancer metabolism.[2] Glucose transporters in cancer metabolism.[2] Glucose transporters in cancer metabolism.[3] http://www.snm.org/docs/PET_E-Library/Use%20of%20PET%20in%20Oncology.pdf[3] http://www.snm.org/docs/PET_E-Library/Use%20of%20PET%20in%20Oncology.pdf[3] http://www.snm.org/docs/PET_E-Library/Use%20of%20PET%20in%20Oncology.pdf[3] http://www.snm.org/docs/PET_E-Library/Use%20of%20PET%20in%20Oncology.pdf[4] https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2752413/[4] https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2752413/[4] https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2752413/[4] https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2752413/[5] Hypoxic radiosensitization: adored and ignored.[5] Hypoxic radiosensitization: adored and ignored.[5] Hypoxic radiosensitization: adored and ignored.[5] Hypoxic radiosensitization: adored and ignored.[6] Jeffrey Brender's answer to Could magnetic resonance imaging be performed with electrons instead of nuclear spins?[6] Jeffrey Brender's answer to Could magnetic resonance imaging be performed with electrons instead of nuclear spins?[6] Jeffrey Brender's answer to Could magnetic resonance imaging be performed with electrons instead of nuclear spins?[6] Jeffrey Brender's answer to Could magnetic resonance imaging be performed with electrons instead of nuclear spins?[7] Jeffrey Brender's answer to How can one increase the ratio of spin up states to spin down states of polarizable nuclei in a magnetic field, beyond the thermal average, without changing the temperature?[7] Jeffrey Brender's answer to How can one increase the ratio of spin up states to spin down states of polarizable nuclei in a magnetic field, beyond the thermal average, without changing the temperature?[7] Jeffrey Brender's answer to How can one increase the ratio of spin up states to spin down states of polarizable nuclei in a magnetic field, beyond the thermal average, without changing the temperature?[7] Jeffrey Brender's answer to How can one increase the ratio of spin up states to spin down states of polarizable nuclei in a magnetic field, beyond the thermal average, without changing the temperature?[8] Magnetic resonance imaging of tumor glycolysis using hyperpolarized 13C-labeled glucose[8] Magnetic resonance imaging of tumor glycolysis using hyperpolarized 13C-labeled glucose[8] Magnetic resonance imaging of tumor glycolysis using hyperpolarized 13C-labeled glucose[8] Magnetic resonance imaging of tumor glycolysis using hyperpolarized 13C-labeled glucose

It's a byproduct of how the "games back" are measured. The formula is:(Team A wins - Team B wins) + (Team B losses - Team A losses)/2If everyone has played the same number of games, the result of the top part will be an even number that washes out to a whole number when divided by two. But if the teams have played a different number of games (rainouts, differences in travel schedule, etc.) you can end up with an odd number on the top of the equation, which leaves a half-game when the number is calculated.To use some real examples...If you're 84-80 and I'm 83-81, I'm said to be 1 game back, even though it would actually take two results (you losing AND me winning) to catch up. If we both play a game on the same day, we will either be:W - W: 85-80 and 84-81, still 1 game backW - L: 85-80 and 83-82, 2 games backL - W: 84-81 and 84-81, evenL - L: 85-81 and 84-81, still 1 game back.However, if I play and you don't, or vice-versa, there's a discrepancy in games remaining. These are accounted for as half-games. In the same examples:W - DNP: 85-80 and 83-81, 1.5 games backL - DNP: 84-81 and 83-81, 0.5 games backDNP - W: 84-80 and 84-81, 0.5 games backDNP - L: 84-80 and 83-82, 1.5 games backAt the end of the season, every team will have played 162 games and the half-games will disappear, but at certain points during the season, they will exist.