A Non-linear Relation for Certain Hypergeometric Functions

Author(s):  
Gerd Schmalz ◽  
Vladimir Ezhov
2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Philippe Thuillier ◽  
David Bourhis ◽  
Jean Philippe Metges ◽  
Romain Le Pennec ◽  
Karim Amrane ◽  
...  

AbstractTo present the feasibility of a dynamic whole-body (DWB) 68Ga-DOTATOC-PET/CT acquisition in patients with well-differentiated neuroendocrine tumors (WD-NETs). Sixty-one patients who underwent a DWB 68Ga-DOTATOC-PET/CT for a histologically proven/highly suspected WD-NET were prospectively included. The acquisition consisted in single-bed dynamic acquisition centered on the heart, followed by the DWB and static acquisitions. For liver, spleen and tumor (1–5/patient), Ki values (in ml/min/100 ml) were calculated according to Patlak's analysis and tumor-to-liver (TLR-Ki) and tumor-to-spleen ratios (TSR-Ki) were recorded. Ki-based parameters were compared to static parameters (SUVmax/SUVmean, TLR/TSRmean, according to liver/spleen SUVmean), in the whole-cohort and according to the PET system (analog/digital). A correlation analysis between SUVmean/Ki was performed using linear and non-linear regressions. Ki-liver was not influenced by the PET system used, unlike SUVmax/SUVmean. The regression analysis showed a non-linear relation between Ki/SUVmean (R2 = 0.55,0.68 and 0.71 for liver, spleen and tumor uptake, respectively) and a linear relation between TLRmean/TLR-Ki (R2 = 0.75). These results were not affected by the PET system, on the contrary of the relation between TSRmean/TSR-Ki (R2 = 0.94 and 0.73 using linear and non-linear regressions in digital and analog systems, respectively). Our study is the first showing the feasibility of a DWB 68Ga-DOTATOC-PET/CT acquisition in WD-NETs.


2000 ◽  
Vol 23 (3) ◽  
pp. 115-129 ◽  
Author(s):  
Pavlo Molchanov ◽  
Arun K. Misra ◽  
Helen Linnik ◽  
Pavlo Mulyar

The simulation principles of monolithic microwave dynamic transistor negatrons (circuits with negative differential active resistance) are introduced. The non-linear model has been developed on the basis of non-linear charge model. The equivalent circuit and Volterra series were used for the calculation of dynamic negatrons' parameters. The expressions were obtained, which give the linear relation between current and voltage charges and allow calculating the transferring characteristics. Experimental oscillators are described, which confirm the theoretical predictions.


Author(s):  
George D. Cashman ◽  
Daniel N. Deli ◽  
Federico Nardari ◽  
Sriram V. Villupuram

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