Applications of the fractional calculus to study the physical theory of ion motion in a quadrupole ion trap.

In this article, fractional calculus has been applied to study the motion of ions in a three-dimensional radio frequency quadrupole ion trap; we have called this arrangement a fractional quadrupole ion trap. The main purpose of the article is to show that by controlling the fractional parameter of a trapped ion, one can gain a more efficient mass separation. In what follows, we will see that with decreasing the fractional parameter, we can achieve a smaller first stability region. Note that a small stability diagram will result in a good and acceptable mass separation. Various methods can be proposed to obtain a desired ion acceleration with a sufficient accuracy for good mass separation, which is similar to the one obtained by a fractional ion trap. Some of these methods are using the effects of a damping force, a magnetic field or both on the confinement of particles in the quadrupole ion trap. The first stability regions are plotted for all of the aforementioned methods, and simulation results are provided to compare them with those for the fractional case.

Comparison of iodine uptake in tumour and nontumour tissue under thyroid hormone deprivation and with recombinant human thyrotropin in thyroid cancer patients.

AIM: Recombinant human thyrotropin (rhTSH) is a new option for diagnostic follow-up in patients with differentiated thyroid cancer (DTC). Iodine kinetics after administration of rhTSH is controversially discussed. The aim of our study was to compare the time course of radioiodine in tumour and normal tissue during periods of TSH elevation in patients in a hypothyroid state (HS) following hormone withdrawal, with those under euthyroidism (ES) after the administration of rhTSH. PATIENTS AND METHODS: We investigated four patients who had undergone near-total thyroidectomy and were suffering from metastatic disease. Dosimetric calculations were performed using tumour and whole-body uptake, and background measurements from 123-iodine scans performed 0, 4, 24 and 48 h after the application of (123)I. RESULTS: All patients had lesser uptake of (123)I under rhTSH stimulation than after hormone withdrawal. The median maximum TG (thyroglobulin) levels were 733.1 ng/ml with HS and 548.0 ng/ml with ES. The median half-life in tumour tissue was 39.8 h (mean 65.9, range 11.5-194.0) with HS and 21.9 h (mean 38.7, range. 8.7-113.9) with ES. The median uptake dose in per cent in tumour tissue was 0.08 (mean 0.15, range 0.04-0.6) with HS and 0.05 (mean 0.08, range 0.03-0.2) with ES. Furthermore, the cumulative activity in metastatic tissue was lower after rhTSH than during hypothyroidism, with considerable variations between individual lesions. CONCLUSION: In our small group of DTC patients with metastatic disease, the effectiveness of radioiodine therapy following rhTSH was anticipated to be less than that in individuals who were hypothyroid after levothyroxine (L-T(4)) withdrawal. Endogenous TSH stimulation of metastatic thyroid cancer with radioiodine should not be performed without prior target tumour lesion dosimetry with (123)I.

Frequency and relevance of elevated calcitonin levels in patients with neoplastic and nonneoplastic thyroid disease and in healthy subjects.

Routine measurement of serum calcitonin (CT) has been recently proposed for all patients with neoplastic thyroid disease to detect clinically occult medullary thyroid carcinoma (MTC). Data on the prevalence of elevated CT levels in nonneoplastic thyroid disease or in healthy subjects have not been reported to date. Four hundred and fourteen consecutive patients with suspected thyroid disease and 362 healthy controls underwent thyroid examination with measurement of basal serum CT. Whenever serum CT was 10 pg/ml or more, a pentagastrin (PG) stimulation test was performed. Twenty-eight of 414 patients (6.8%) showed elevated basal serum CT levels, 15 of them with nonneoplastic thyroid disease, and the remaining 13 subjects with neoplastic thyroid disease. Four patients with abnormal PG testing (stimulated CT, > or = 100 pg/ml) were identified. Three of them had biochemical and sonographical evidence of thyroiditis. Elevated basal CT levels were significantly more frequent in patients with Hashimoto's thyroiditis (HT; P < 0.05). One female patient with HT had a 5-mm nodule, which was classified as MTC. None of the 6 out of 362 healthy controls with elevated basal CT (1.7%) presented an abnormal PG test. Our data suggest that basal CT measurements can be of use in the detection/screening of MTC not only in subjects with neoplastic thyroid disorders, but also in patients with immunological evidence of HT. They also confirm earlier reports on the essential value of PG stimulation testing, even when basal plasma CT levels are only modestly elevated, with regard to establishing the diagnosis of MTC or its premalignant associated conditions (micro-MTC and neoplastic C cell hyperplasia).