Sinus, Cavernous

On the endocrinological ground, a LH pulse is an increase in LH blood level triggered by the quick release of LH by the pituitary gland. As illustrated in the preceding section, the moderate clearance rate of LH from the blood underlies the specific asymmetric shape of the pulses, which is characterized by a fast increase immediately followed by a slower decrease. This property has been highlighted in dedicated studies using high frequency sampling (for instance [10] : horse, 2 samples per minute) of LH level during a short interval of time.
However, in long-time experiments, the sampling frequency is usually of the order of one per 10 minutes. Consequently, the precise shape and quantitative properties of the pulses are non longer obvious in the time series. In particular, the theoretical pulse amplitude (theoretical highest level hit during a pulse event) is most of the time not properly reflected by the highest sample obtained during the corresponding event. In the following, we introduce few notions allowing us to differentiate the properties of a theoretical pulse from those of the corresponding pulse obtained from a time series.
The advantages of synthetic time series is that the underlying signal LH(t) of LH release and the theoretical continuously measured blood LH level LHp(t) are available. This corresponds to the ideal experimental situation where one could get high-frequency sampled, variability-free time series retrieved at the same time from the cavernous sinus and jugular blood. With synthetic data, we dispose of reference sets that allow us to identify both LH spikes and pulses without any ambiguity.
Moreover, we can easily test different experimental protocols by changing the value of the parameters Ts, r, f, b controlling the sampling properties and choosing various functions and that determine the time-varying amplitude and frequency of LH spikes released by the pituitary gland.

The pituitary gland releases LH into the blood as successive spikes characterized by a quasi-instantaneous increase followed by slower (yet quite fast) decrease (see [4] ). Hence, in our model, the LH release along a spike is approximated by a discontinuous function of time: the jump accounting for the instantaneous increase in the LH release is followed by a fast exponential decrease. The interspike interval is controlled by a function of time accounting for the varying release frequency. The spike amplitude is also subject to an inter-spike variability as well as to long-term changes partly due to the time variations in the stock of LH available for release. In our model, the amplitude is controlled by another function of time . Hence, the instantaneous release of LH (expressed in ng/ml/min) in the blood by the pituitary gland is given by: where ⌊x⌋refers to the greatest integer smaller than x (integer part). The exponential decay rate is directly linked to the spike half-life, , (i.e. the time taken for the instantaneous released LH quantity to drop from the maximal spike value to half this value) through:
We based our choice of parameter values on the few experiments that have investigated the LH release by the pituitary gland in the ewe from synchronous sampling in the jugular blood and cavernous sinus [4] . Accordingly, we chose a spike half-life
We represent the continuously measured LH blood level (expressed in ng/ml) as the solution of: where the LH release rate LH(t) is given by equation (1). Parameter a represents the instantaneous LH clearance rate from the blood. To be consistent with the one hour half-life of LH pulses (i.e. the time taken for the blood LH level to drop from the maximal pulse value to half this value) in the jugular blood, we have fixed .

The total number of 109 specimens including, 79 pituitary adenomas and 30 cadaveric healthy pituitary tissues were included in this study with local ethical approval and informed consent. Following the ethical standards in Declaration of Helsinki, the project was ethically approved by the ethics committee of Vice president of research of Iran University of Medical Sciences. All specimens of pituitary adenomas obtained from patients whom were diagnosed for pituitary adenoma and subjected to the endoscopic transnasal transphenoidal surgery (ETSS) at the neurosurgery department of our institute from January 2017 to June 2020 and patients with a known history of any malignancy were excluded from the study. Notably, patients who received no treatments before surgery were included in this study to avoid any possible effect of medication on necroptosis mediators. The imaging, post-surgery pathology, the patient’s history and clinical signs and laboratory findings helped diagnose the adenoma. The total number of 30 normal pituitary autopsies was collected from cases with no pathological pituitary problems from the Legal Medicine Organization (LMO), Tehran, Iran from January 2017 to June 2020. The anterior epithelial lobe of pituitary with no pathological evidence was collected and normal cases were matched to the patients as a matter of age and gender. The tumor and normal pituitary sample collection and processing was followed as our previous study [24 (link), 25 (link)]. The equal number of male and female donors participated in the study with the age range of 44.94 ± 1.17. Notably, both invasive and non-invasive pituitary tumors were collected based on the Knosp classification system where tumor extension to the adjacent sphenoid sinus and cavernous sinus accounts as invasive feature. Also, during the endoscopic surgery, neurosurgeon confirmed tumor invasion. In addition, patients were classified based on the size of their pituitary tumors and the tumor size greater than 10 mm was defined as macro adenomas and the tumor size less than 10 mm was defined as micro adenomas. Following surgical resection, the pituitary fresh tumor tissues were divided into two sections, one transferred to the pathology department for further histological evaluations and the other part was taken away and kept in RNA latter (Qiagen, Germany) immediately and stored in − 80 °C until usage. Notably, we followed the methods of Tavakoli-Yaraki et al. 2019 regarding the pituitary samples collection [24 (link)]. The clinic- pathological features of patients with pituitary adenoma are summarized in Table 1.
Table 1

The demographic data of the patients with different pituitary adenomas

Variable		Age			Gender			Tumor size
Patient	Group	≤40	> 40	P-Value	Male	Female	P-Value	Micro	Macro	P-Value
Invasive NFPA (n = 18)		4 (22.22%)	14 (77.77%)	0.442	12 (66.66%)	6 (33.33%)	0.1370	0	18 (100%)
Non-invasive NFPA (n = 21)		7 (33.33%)	14 (66.66%)		9 (42.85%)	12 (57.14%)		0	21 (100%)
Invasive GHPPA (n = 14)		6 (42.85%)	8 (57.14%)	0.973	6 (42.85%)	8 (57.14%)	0.8416	3 (21.42%)	11 (78.57%)	0.3854
Non-invasive GHPPA (n = 26)		11 (42.30%)	15 (57.69%)		12 (46.15%)	14 (53.14%)		9 (34.61%)	17 (65.38%)

CD was diagnosed based on the criteria outlined by Zada in 2013^{2 (link)}. Shortly summarized, patients with clinical suspicion of CS were evaluated by at least two of the established hypercortisolism screening tests (i.e. 24-h urinary cortisol, midnight salivary cortisol, low-dose dexamethasone suppression test) to confirm the diagnosis of CS. The screening tests and their respective evidence are described in detail by Nieman et al.^{11 (link)} in a dedicated Endocrine Society clinical practice guideline. Subsequent serum ACTH level differentiated ACTH-dependent from ACTH-independent hypercortisolemia. In case of an ACTH-dependent CS, the presence of CD was verified by pituitary magnetic resonance imaging (supplemented, if necessary, by dynamic coronal contrast enhanced sequences to increase sensitivity and specificity^{12 (link)}) and high-dose dexamethasone suppression test (+/− corticotropin-releasing hormone stimulation test). In doubtful cases cavernous sinus ACTH sampling was performed by our neuroradiological colleagues to identify an elevated central-peripheral ACTH ratio, which allows differentiation of CD from ectopic ACTH secretion, as well as an intercavernous gradient for the correct lateralization of the adenoma^{13 (link),14 (link)}. Early postoperative biochemical remission was defined as subnormal morning cortisol level (≤ 50 μg/l) on the first or second postoperative day without glucocorticoid replacement according to Esposito and colleagues^{15 (link)}. For patients with a postoperative cortisol nadir below this threshold, a good long-term remission rate of almost 90% has been documented^{16 (link)}.

Data were analyzed using IBM SPSS statistical software Version 24.0 (IBM Corp., New York, NY, USA) and GraphPad Prism (V7.04 software, San Diego, CA, USA). Continuous variables were examined for homogeneity of variance and are expressed as mean ± SD unless otherwise noted. Serum PRL levels are presented as median values and interquartile range (IQR, 25th to 75th percentile). Categorical variables are given as numbers and percentages. For comparisons of means between groups (i.e., patients with AO and EO), Student's t-test was used for normally distributed data, and the Mann–Whitney test for nonparametric data. The Wilcoxon signed-rank test was used to evaluate paired differences in PRL and BMI levels before and after treatment. Categorical variables were compared using Pearson's chi-square test or Fisher's exact test, as appropriate. The Spearman rank-order correlation coefficient was calculated to check for the strength of association between different variables (i.e., PRL, age, patients' BMI, DA dependency). We assessed the proportion of patients with long-term dependence on DAs and performed time-dependent multivariable regression analysis to calculate hazard ratios (HR) for potential risk factors. The variables tested were: age at diagnosis, initial PRL levels, BMI (kg/m²), hypopituitarism at diagnosis, baseline gonadotropin deficiency, prevalence of headache at diagnosis, adenoma size, and cavernous sinus invasion. The multivariable regression analysis included all dependent risk factors in the univariable regression with a p value ≤ 0.05. Baseline PRL values were log transformed before being imputed in the regression and correlation analysis analysis, as data showed a positively skewed distribution. Significance level was set at p ≤ 5%.

MRI was performed on a 1.5- or 3-Tesla system including a Proton/T2-weighted whole-brain study with unenhanced, contrast-enhanced, dynamic contrast-enhanced and post contrast-enhanced overlapping studies over the sellar region (17 (link)–20 (link)). A tumor with a diameter of 1–10 mm was defined as a microadenoma, and >10 mm as a macroadenoma. Infiltration of the cavernous sinus was noted (i.e., Knosp grade ≥1) (21 (link), 22 (link)).