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Cauchy principal value is a standard method applied in mathematical applications by which an improper, and possibly divergent, integral is measured in a balanced way around singularities or at infinity. On the other hand, entropy prediction of systems behavior from a thermodynamic perspective commonly involves contour integrals. With the aim of facilitating the calculus of such integrals in this entropic scenario, we revisit the generalization of Cauchy principal value to complex contour integral, formalize its definition and-by using residue theory techniques-provide an useful way to evaluate them. [ABSTRACT FROM AUTHOR]

Whole-body 123I-Metaiodobenzylguanidine (mIBG) scintigraphy is used as primary image modality to visualize neuroblastoma tumours and metastases because it is the most sensitive and specific radioactive tracer in staging the disease and evaluating the response to treatment. However, especially in paediatric neuroblastoma, information from mIBG scans is difficult to extract because of acquisition difficulties that produce low definition images, with poor contours, resolution and contrast. These problems limit physician assessment. Current oncological guidelines are based on qualitative observer-dependant analysis. This makes comparing results taken at different moments of therapy, or in different institutions, difficult. In this paper, we present a computerized method that processes an image and calculates a quantitative measurement considered as its entropy, suitable for the identification of abnormal uptake regions, for which there is enough suspicion that they may be a tumour or metastatic site. This measurement can also be compared with future scintigraphies of the same patient. Over 46 scintigraphies of 22 anonymous patients were tested; the procedure identified 96.7% of regions of abnormal uptake and it showed a low overall false negative rate of 3.3%. This method provides assistance to physicians in diagnosing tumours and also allows the monitoring of patients’ evolution. [ABSTRACT FROM AUTHOR]

Cauchy principal value is a standard method applied in mathematical applications by which an improper, and possibly divergent, integral is measured in a balanced way around singularities or at infinity. On the other hand, entropy prediction of systems behavior from a thermodynamic perspective commonly involves contour integrals. With the aim of facilitating the calculus of such integrals in this entropic scenario, we revisit the generalization of Cauchy principal value to complex contour integral, formalize its definition and—by using residue theory techniques—provide an useful way to evaluate them.

Whole-body 123I-Metaiodobenzylguanidine (mIBG) scintigraphy is used as primary image modality to visualize neuroblastoma tumours and metastases because it is the most sensitive and specific radioactive tracer in staging the disease and evaluating the response to treatment. However, especially in paediatric neuroblastoma, information from mIBG scans is difficult to extract because of acquisition difficulties that produce low definition images, with poor contours, resolution and contrast. These problems limit physician assessment. Current oncological guidelines are based on qualitative observer-dependant analysis. This makes comparing results taken at different moments of therapy, or in different institutions, difficult. In this paper, we present a computerized method that processes an image and calculates a quantitative measurement considered as its entropy, suitable for the identification of abnormal uptake regions, for which there is enough suspicion that they may be a tumour or metastatic site. This measurement can also be compared with future scintigraphies of the same patient. Over 46 scintigraphies of 22 anonymous patients were tested; the procedure identified 96.7% of regions of abnormal uptake and it showed a low overall false negative rate of 3.3%. This method provides assistance to physicians in diagnosing tumours and also allows the monitoring of patients’ evolution.