Dehydroepiandrosterone in adrenal insufficiency and ageing

PURPOSE OF REVIEW

The physiological role of dehydroepiandrosterone remains unclear, and there is continuing controversy on whether dehydroepiandrosterone treatment benefits adrenal-deficient and elderly people with an age-related decline in dehydroepiandrosterone. The objective of this study is to critically review published results and determine whether there is a valid case for dehydroepiandrosterone treatment with advancing age and hypoadrenalism.

RECENT FINDINGS

Oral dehydroepiandrosterone therapy in both elderly and hypoadrenal subjects achieves dehydroepiandrosterone levels comparable to young subjects. Long-term dehydroepiandrosterone replacement in elderly people demonstrated no improvement in body composition, physical performance or any metabolic parameters; however, a modest but inconsistent improvement in bone mineral density occurred at certain sites. Dehydroepiandrosterone replacement in hypoadrenalism modestly improved insulin sensitivity and altered the lipid profile, but it remains uncertain whether these changes improve any patient-important outcomes. Dehydroepiandrosterone replacement in adrenal deficiency inconsistently improves some aspects of mental health.

SUMMARY

Dehydroepiandrosterone replacement increases bone mineral density in elderly subjects; however, the effect is relatively small compared with established therapies for osteoporosis. No additional benefits have been identified for long-term dehydroepiandrosterone replacement, when used in the elderly to prevent or delay ageing. Dehydroepiandrosterone replacement may improve some metabolic variables and measures of psychological well-being in adrenal deficiency, but these benefits are not consistently sustained in long-term therapy. Long-term studies are needed to confirm sustained benefits in adrenal deficiency and establish long-term safety.

Sublabial transseptal vs transnasal combined endoscopic microsurgery in patients with Cushing disease and MRI-depicted microadenomas

OBJECTIVE

To assess whether the type of surgical approach to the sella (sublabial transseptal vs transnasal) affects surgical outcome among patients with Cushing disease.

PARTICIPANTS AND METHODS

Both procedures were performed at our institution from January 1, 1995, through January 31, 2003. From a total of 106 patients with Cushing disease who had had surgery, we identified 42 adults undergoing an initial surgery, with microadenoma (<1 cm) determined by magnetic resonance imaging and a minimal follow-up of 3 months.

RESULTS

We identified 21 patients (4 male, 17 female) for sublabial transseptal transsphenoidal microsurgery. Mean+/-SD age was 45.0+/-12.9 years (range, 27.0-69.0 years); median duration of symptoms was 2.5 years (range, 1.5-7.5 years). Median follow-up was 1.0 year (range, 0.3-11.0 years). We identified another 21 patients (5 male, 16 female) for endoscopic transsphenoidal microsurgery whose mean+/-SD age was 43.8+/-14.1 years (range, 19.0-70.0 years); median duration of symptoms was 2.4 years (range, 0.2-6.0 years). Median follow-up was 2.5 years (range, 0.3-8.7 years). Complications (cerebrospinal fluid leak and transient diabetes insipidus) and cure (86% initial cure; 76% relapse-included cure) were equivalent between the 2 procedures. However, the endoscopic approach was associated with shorter anesthesia time, less blood loss, and shorter hospital stays.

CONCLUSION

The endoscopic transnasal surgical approach led to shorter total anesthesia time, less blood loss, and shorter hospital stay when compared with the sublabial transseptal approach. However, we found no difference between the 2 surgical procedures with respect to cure or complications, suggesting that outcome is more closely related to the experience of the operating team.

Reoperation for sella haematoma after pituitary surgery

OBJECTIVE

Although occasionally discussed as a general complication in large pituitary series, the incidence of reoperation for postoperative sella haematoma is unclear. We retrospectively reviewed a large pituitary surgical series to determine the incidence and associated factors of this complication.

DESIGN

We reviewed all pituitary surgery at Mayo Rochester from January 1987 until January 2007. There were 2312 transsphenoidal procedures during this period.

PATIENTS

All patients had proven pituitary pathology by computed tomography (CT) or magnetic resonance imaging and pituitary function studies.

MEASUREMENTS

Reoperation for sella haematoma and perioperative clinical correlations were the only measurement tools. It is indeterminate how many patients had postoperative sella haematoma without visual loss because routine postoperative CT scanning was not performed.

RESULTS

Three patients underwent reoperation for postoperative haematoma in the sella by three different endocrine neurosurgeons, and all three patients had progressive postoperative visual loss. All initial operations were for large macroadenomas; two had early postoperative hypertension that may have been a contributor; and one had markedly thickened bone felt to be the source of bleeding and deterioration 24 h later.

CONCLUSIONS

Reoperation for postoperative sellar haematoma is uncommon. However, postoperative progressive visual loss was clinically present in all three patients, and labile hypertension postoperatively may play a role.

Radiosurgery of growth hormone-producing pituitary adenomas: factors associated with biochemical remission

OBJECT

The authors reviewed outcomes after stereotactic radiosurgery for patients with acromegaly and analyzed factors associated with biochemical remission.

METHODS

Retrospective analysis was performed for 46 consecutive cases of growth hormone (GH)-producing pituitary adenomas treated by radiosurgery between 1991 and 2004. Biochemical remission was defined as a fasting GH less than 2 ng/ml and a normal age- and sex-adjusted insulin-like growth factor-I (IGF-I) level while patients were not receiving any pituitary suppressive medications. The median follow up after radiosurgery was 63 months (range 22-168 months). Twenty-three patients (50%) had biochemical remission documented at a median of 36 months (range 6-63 months) after one radiosurgical procedure. The actuarial rates of biochemical remission at 2 and 5 years after radiosurgery were 11 and 60%, respectively. Multivariate analysis showed that IGF-I levels less than 2.25 times the upper limit of normal (hazard ratio [HR] 2.9, 95% confidence interval [CI] 1.2-6.9, p = 0.02) and the absence of pituitary suppressive medications at the time of radiosurgery (HR 4.2, 95% CI 1.4-13.2, p = 0.01) correlated with biochemical remission. The incidence of new anterior pituitary deficits was 10% at 2 years and 33% at 5 years.

CONCLUSIONS

Discontinuation of pituitary suppressive medications at least 1 month before radiosurgery significantly improved endocrine outcomes for patients with acromegaly. Patients with GH-producing pituitary adenomas should not undergo further radiation therapy or surgery for at least 5 years after radiosurgery because GH and IGF-I levels continue to normalize over that interval.

Effect of growth hormone replacement on BMD in adult-onset growth hormone deficiency

To determine if replacement of GH improves BMD in adult-onset GHD, we administered GH in physiologic amounts to men and women with GHD. GH replacement significantly increased spine BMD in the men by 3.8%.

INTRODUCTION

Growth hormone (GH) deficiency (GHD) acquired in adulthood results in diminished BMD; the evidence that replacement of GH improves BMD is not conclusive. We therefore performed a randomized, placebo-controlled trial to determine whether GH replacement would increase lumbar spine BMD in a combined group of men and women with adult-onset GHD.

MATERIALS AND METHODS

We randomized 67 men and women to receive GH (n=33) or placebo (n=34) for 2 yr. The GH dose was initially 2 microg/kg body weight/d, increased gradually to a maximum of 12 microg/kg/d and adjusted to maintain a normal IGF-I concentration for age and sex. BMD was assessed before treatment and at 6, 12, 18, and 24 mo of treatment. Fifty-four subjects completed the protocol.

RESULTS

BMD of the lumbar spine in the entire group increased by 2.9 +/- 3.9% above baseline in the GH-treated subjects, which was significantly (p=0.037) greater than the 1.4 +/- 4.5% increase in the placebo-treated subjects. In a secondary analysis, spine BMD in GH-treated men increased 3.8 +/- 4.3% above baseline, which was significantly (p=0.001) greater than that in placebo-treated men (0.4 +/- 4.7%), but the change in GH-treated women was not significantly different from that in placebo-treated women. Treatment with GH did not increase total hip BMD more than placebo treatment after 2 yr.

CONCLUSIONS

We conclude that GH replacement in men who have adult-onset GHD improves their spine BMD, but we cannot draw any conclusions about the effect of GH replacement on spine BMD in women with adult-onset GHD.

Pituitary adenoma with tumoral granulomatous reaction

Herein, we report a unique case of an adult male with a corticotrophic pituitary adenoma of silent subtype 1 exhibiting conspicuous idiopathic tumoral noncaseating granulomatous inflammation. The lesion was unassociated with clinical or laboratory evidence of either systemic sarcoidosis or infection. Histochemical and polymerase chain reaction (PCR) studies revealed neither fungi nor tubercle bacilli. We suggest that tumoral production of an as yet uncharacterized antigen may have induced the granulomatous inflammatory reaction.

Neurophysiologic studies in Morvan syndrome

This study was conducted to clarify the clinical and neurophysiologic characteristics of patients with Morvan syndrome, and to compare and contrast this syndrome with other forms of autoimmune encephalitis. A retrospective chart review of the clinical features and neurophysiologic studies of two cases of Morvan syndrome seen at the Mayo Clinic was performed. Neurophysiologic studies included polysomnography, comprehensive autonomic testing, MRI, positron emission tomography, EEG, and single-photon emission computed tomography. In two cases of Morvan syndrome, the clinical features, electrophysiologic findings, and immunologic studies (high levels of voltage-gated potassium channel antibodies) were consistent with previously reported findings. Several novel observations were made. Autonomic testing demonstrated peripheral autonomic neuropathy in addition to autonomic hyperactivity. Polysomnography showed complete absence of sleep. Neuroimaging study findings were largely normal. Morvan syndrome is an autoimmune disorder affecting both the peripheral and central nervous system. Neurophysiologic studies demonstrate hyperexcitability of peripheral nerves, autonomic dysfunction, and severe insomnia. The absence of abnormalities on imaging studies suggests that central nervous system symptoms are related to functional rather than structural disruption of neural networks.

Pituitary neurologic surgery: a unique subspecialty in evolution

OBJECTIVE

To review the evolving approaches to surgical management of pituitary tumors during the past century, which may predict future directions.

METHODS

We undertook a retrospective review of selected literature published during the past century and report the trends in the treatment of pituitary tumors.

RESULTS

Harvey Cushing's extraordinary influence on American neurosurgery and remarkably successful pituitary surgical series were the foundation for the development of a highly subspecialized neurosurgical operative field. Continued evolution in the treatment of pituitary tumors has been historically based on the following: (1) the development of exogenous cortisone and vasopressin; (2) the development of high-voltage and nuclear radiation therapy; (3) the experience gained from total hypophysectomy for "endocrine" driven malignant lesions and diabetic retinopathy; (4) the development of the image intensifier and television intraoperative fluoroscopic control; (5) the use of endoscopes in pituitary surgical procedures; (6) the application of the operating microscope to transsphenoidal approaches; (7) the development of the imaging modalities of computed tomographic scanning and subsequent magnetic resonance imaging; and (8) the concepts surrounding "minimally invasive" surgical techniques.

CONCLUSION

The pituitary surgical techniques of today have evolved primarily because of extraordinary past accomplishments. The approaches used continue to maximize tumor resection and preserve functioning pituitary tissue. New intraoperative imaging techniques will forge the future of the field of pituitary neurosurgery, and the expected outcomes will be improved surgical success and lower perioperative morbidity.)

Results of stereotactic radiosurgery in patients with hormone-producing pituitary adenomas: factors associated with endocrine normalization

OBJECT

The goal of this study was to determine factors associated with endocrine normalization after radiosurgery is performed in patients with hormone-producing pituitary adenomas.

METHODS

Between 1990 and 1999, 43 patients with hormone-producing pituitary adenomas underwent radiosurgery: 26 patients with growth hormone (GH)-producing tumors, nine with adrenocorticotrophic hormone-producing tumors, seven with tumors that produced prolactin (PRL) alone, and one with a tumor that secreted both GH and PRL. The median patient age was 42 years. Thirty-seven patients (86%) had undergone surgery earlier and in 30 (70%) there was tumor extension into the cavernous sinus. The product-limit method was used to calculate endocrine normalization while patients were not receiving any hormone-suppressive medication. The median follow-up period after radiosurgery was 36 months (range 12-108 months). In 20 patients (47%) there was normalization of hormone secretion at a median of 14 months (range 2-44 months) after radiosurgery; no correlation was found between tumor type and cure. Actuarial cure rates were 20, 32, and 61% at 1, 2, and 4 years posttreatment. Multivariate analysis demonstrated that the absence of hormone-suppressive medications at the time of radiosurgery (relative risk 8.9, 95% confidence interval [CI] 1.2-68.7, p = 0.04) and maximum radiation doses greater than 40 Gy (relative risk 3.9, 95% CI 1.3-11.7, p = 0.02) correlated with an endocrine cure. A new anterior pituitary deficiency developed in seven patients (16%), temporal lobe necrosis was identified in two patients, an asymptomatic internal carotid artery stenosis was detected in two patients, and unilateral blindness occurred in one patient.

CONCLUSIONS

Radiosurgery provides an endocrine cure for many patients with persistent or recurrent hormone-producing pituitary adenomas. Further study is needed to determine whether pituitary hormone-suppressive medications have a radioprotective effect.

Cushing's disease due to plurihormonal adrenocorticotropic hormone and gonadotropin-producing pituitary adenoma

A 67-year-old woman presented with clinical features of hypercortisolism in association with an invasive pituitary macroadenoma. Adrenocorticotropic hormone (ACTH)-dependent Cushing's disease was documented, and the resected tumor was chromophobic, weakly positive with periodic-Schiff reagent, and showed immunostaining for ACTH and beta-endorphin in a minority of adenoma cells. Both luteinizing hormone and alpha-subunit staining were also observed, but no follicle-stimulating hormone reactivity was seen. Ultrastructurally, the tumor showed typical features of a gonadotroph adenoma of female type. Immunoelectron microscopy showed that ACTH was not produced in corticotrophs, but in cells with the characteristic features of gonadotrophs. This represents the second report of a plurihormonal gonadotroph adenoma producing sufficient ACTH to result in pituitary-dependent Cushing's disease.

Adrenal hemorrhage: a 25-year experience at the Mayo Clinic

OBJECTIVE

To characterize the clinical course of adrenal hemorrhage (AH) by using a systematic review of the presentation, associated conditions, and outcomes in patients with AH seen at our institution between 1972 and 1997 (a 25-year period).

PATIENTS AND METHODS

A computer search of recorded dismissal diagnoses identified 204 patients with a diagnosis of AH, but only 141 fulfilled our study criteria. Their records were analyzed systematically by presentation, bilateral or unilateral hemorrhage, corticosteroid treatment, and survival.

RESULTS

AH is a heterogeneous entity that occurs in the postoperative period, in the antiphospholipid-antibody syndrome, in heparin-associated thrombocytopenia, or in the setting of severe physical stress and multiorgan failure. Standard laboratory evaluation is not helpful in establishing the diagnosis. Of the 141 cases of AH, 78 were bilateral, and 63 were unilateral. Corticosteroid treatment in situations of severe stress or sepsis had little effect on outcome (9% vs. 6% survival with and without corticosteroid treatment, respectively). This is in sharp contrast to AH occurring postoperatively (100% vs. 17% survival with or without treatment, respectively) or in the antiphospholipid-antibody syndrome (73% vs. 0% survival, respectively).

CONCLUSIONS

A high index of suspicion is required to make a timely diagnosis of AH. Fever and hypotension in the appropriate clinical setting necessitate further investigation. Although the diagnosis of AH is infrequently made while the patient is alive, appropriate imaging techniques are useful for establishing a timely diagnosis. In severe physical stress or sepsis, AH may be a marker of severe, preterminal physiologic stress and poor outcome.

Hepatolithiasis (intrahepatic stone) during octreotide therapy for acromegaly: a case report

We report a case of hepatolithiasis (intrahepatic stone) complicated by gram-negative sepsis in a 37 year old male with acromegaly being treated with octreotide. As a child, he had suffered a traumatic injury to his liver requiring the surgical repair of a laceration. This is the first reported case of hepatolithiasis during octreotide therapy. Gallstones and bile sludge are common side effects of octreotide therapy but rarely become symptomatic or require treatment. Hepatolithiasis is uncommon in western countries but is quite prevalent in East Asia and is often associated with a predisposing condition that causes intrahepatic bile stasis (eg. bile duct stricture). In addition to its known effect on gallbladder stasis, octreotide alters bile acid composition and may thus hasten intrahepatic sludge and stone formation. Extra caution should be taken in using octreotide or its long-acting analog in patients otherwise predisposed to intrahepatic bile stasis.

Transcranial-transdural real-time ultrasonography during transsphenoidal resection of a large pituitary tumor. Case report

Ultrasonography has been used in neurosurgical operative procedures for several decades. The authors report the case of a large pituitary tumor that was subtotally resected using endoscopy via the transnasal-transsphenoidal approach, with the aid of transcranial real-time ultrasound. To our knowledge, this is the first reported case in which intraoperative transcranial-transdural real-time ultrasound was used to facilitate the resection of a skull base tumor.

Tension pneumocranium, a rare complication of transsphenoidal pituitary surgery: Mayo Clinic experience 1976-1998

We describe four cases of symptomatic pneumocranium, a rare, potentially life-threatening complication of transsphenoidal pituitary surgery. Symptomatic pneumocranium manifested as impaired mental status, headaches, and grand mal seizures, early in the postoperative course after transsphenoidal pituitary surgery. Furthermore, a Cushing response, including systemic hypertension and bradycardia (secondary to intracranial hypertension) was seen, which has not been previously described in association with symptomatic pneumocranium. We describe a previously unreported risk factor for tension pneumocranium, untreated obstructive sleep apnea. Other factors predisposing to tension pneumocranium in our patients included: cerebrospinal fluid leaks, postoperative positive-pressure mask ventilation, large pituitary tumors, and intraoperative lumbar drainage catheters. Surgical drainage of the pneumocranium and repair of any coexistent cerebrospinal fluid leak markedly improved neurologic status. Symptomatic pneumocranium occurring early in the postoperative course after transsphenoidal pituitary surgery is rare, but prompt recognition and treatment of this condition can be life-saving.

Preliminary comparison of the endoscopic transnasal vs the sublabial transseptal approach for clinically nonfunctioning pituitary macroadenomas

OBJECTIVE

To assess the advantages and disadvantages of an endoscopic transnasal approach to pituitary surgery for a select group of clinically nonfunctioning macroadenomas and to compare results of this approach with the sublabial transseptal approach at a single institution.

PATIENTS AND METHODS

We retrospectively reviewed the records of 26 patients with clinically nonfunctioning pituitary macroadenomas approached endoscopically and 44 matched control patients with the same tumors approached sublabially between January 1, 1995, and October 31, 1997.

RESULTS

At baseline, the groups were not significantly different for age, sex distribution, number of comorbid conditions, visual field defects, degree of anterior pituitary insufficiency, or preoperative assessment of tumor volume or invasiveness. Mean (SD) operative times were significantly reduced in the endoscopic group vs the sublabial group: 2.7 (0.7) hours vs 3.4 (0.9) hours (P < .001). Postoperative assessment of surgical resection and postoperative alterations of anterior pituitary function or visual fields were not significantly different between groups, and complication rates were similar in both groups.

CONCLUSION

This endoscopic transnasal approach to pituitary resection results in significantly shorter operative time without compromising the extent of tumor resection. The distinct disadvantage of this approach is an off-center view of the sella and a diminished working channel to the sella turcica. For these reasons, the endoscopic approach or its variation is an alternative to the sublabial approach but should be considered only by experienced pituitary neurosurgeons.

Is there a case for DHEA replacement?

There are many hormonal changes that occur with ageing in humans, of which the most dramatic and intriguing change occurs for the adrenal androgenic steroid dehydroepiandosterone (DHEA). There are tantalizing epidemiological data demonstrating a significant association between the changes in circulating DHEA level and changes in the incidence of malignancy, atherosclerosis, Alzheimer's disease and other age-related changes. The pharmacological effects in animals such as rodents and rabbits have demonstrated many beneficial effects, for example increased immune function, the prevention of atherosclerosis, cancer, diabetes and obesity, and the improvement of memory. Clinical studies carried out in small groups of subjects have clearly demonstrated that the administration of DHEA to the elderly increases many hormone levels, including that of insulin-like growth factor-1, (free and total) testosterone, dihydrotestosterone, oestrone and oestradiol. It remains to be clearly defined whether these changes are clinically beneficial, and there is only insufficient information on the side-effects on long-term use. Results from short-term intervention studies in small groups of subjects have not demonstrated any convincing beneficial effects so far. A judgement on whether DHEA replacement has a place in preventing age-related disabilities could be determined only on the basis of results from studies of long-term DHEA replacement in elderly people.

Insulin-like growth factor system abnormalities in hepatitis C-associated osteosclerosis. Potential insights into increasing bone mass in adults

Hepatitis C-associated osteosclerosis (HCAO) is a rare disorder characterized by a marked increase in bone mass during adult life. Despite the rarity of HCAO, understanding the mediator(s) of the skeletal disease is of great interest. The IGFs-I and -II have potent anabolic effects on bone, and alterations in the IGFs and/or IGF-binding proteins (IGFBPs) could be responsible for the increase in bone formation in this disorder. Thus, we assayed sera from seven cases of HCAO for IGF-I, IGF-II, IGF-IIE (an IGF-II precursor), and IGFBPs. The distribution of the serum IGFs and IGFBPs between their ternary ( approximately 150 kD) and binary (approximately 50 kD) complexes was also determined to assess IGF bioavailability. HCAO patients had normal serum levels of IGF-I and -II, but had markedly elevated levels of IGF-IIE. Of the IGFBPs, an increase in IGFBP-2 was unique to these patients and was not found in control hepatitis C or hepatitis B patients. IGF-I and -II in sera from patients with HCAO were carried, as in the case of sera from control subjects, bound to IGFBP-3 in the approximately 150-kD complex, which is retained in the circulation. However, IGF-IIE was predominantly in the approximately 50-kD complex in association with IGFBP-2; this complex can cross the capillary barrier and access target tissues. In vitro, we found that IGF-II enhanced by over threefold IGFBP-2 binding to extracellular matrix produced by human osteoblasts and that in an extracellular matrix-rich environment, the IGF-II/IGFBP-2 complex was as effective as IGF-II alone in stimulating human osteoblast proliferation. Thus, IGFBP-2 may facilitate the targeting of IGFs, and in particular IGF-IIE, to skeletal tissue in HCAO patients, with a subsequent stimulation by IGFs of osteoblast function. Our findings in HCAO suggest a possible means to increase bone mass in patients with osteoporosis.

Dehydroepiandrosterone Supplements: Bringing Sense to Sensational Claims

OBJECTIVE

To summarize the current information about dehydroepiandrosterone (DHEA), a steroid hormone produced in the adrenal cortex.

METHODS

The biochemical and physiologic features of DHEA and its purported effects on overall age-related decline and on various disorders are reviewed. In addition, the potential side effects from administration of DHEA are discussed.

RESULTS

During the normal life cycle, levels of DHEA fluctuate, beginning with production of large quantities in the fetus, stopping at birth, resuming during ages 5 to 7 years, and increasing throughout puberty to maximal production in the 20s. Thereafter, DHEA levels progressively decline. This age-related decline in physiologic levels of DHEA has prompted speculation about a relationship between relative "DHEA deficiency" in older age and diseases of aging as well as the possibility of deriving benefits from administration of DHEA. Certain studies in animals (primarily rodents) have suggested anticancer effects of DHEA in pharmacologic doses and improvement in metabolism. In various studies in animals and humans, discrepant results have been found in the assessment of the association between DHEA levels and coronary artery disease. Likewise, the clinical significance of changes in immune function with DHEA treatment is unknown. Because DHEA is classified as a "nutritional supplement," it is not subjected to government regulation, and a potential exists for inaccurate dosage and impurities.

CONCLUSION

Studies have shown that DHEA influences multiple systems and disease processes in animals and humans; some of these effects could be considered beneficial and others detrimental. To date, no long-term health benefits from DHEA in "replacement" doses have been demonstrated.

Evaluation and management of amenorrhea

All women who enter menopause experience amenorrhea unless they receive hormone replacement therapy. In younger women, amenorrhea unrelated to pregnancy and lactation can be a distressing symptom. In addition to its psychologic morbidity, amenorrhea may be the manifesting feature of a wide array of anatomic and endocrine abnormalities. Amenorrhea results in impaired fertility. When estrogen levels are low, changes in mineral, glucose, and fat metabolism accompany amenorrhea. These metabolic changes affect bone and cardiovascular health, increasing the risk of osteoporosis and coronary heart disease in later life. Amenorrhea with hyperandrogenism, most commonly caused by the polycystic ovarian syndrome, may cause endometrial hyperplasia and increases the risk of endometrial adenocarcinoma. Because of the broad differential diagnosis of amenorrhea, establishing an accurate diagnosis can prove challenging. In this article, we outline one approach to the assessment of patients with amenorrhea and to the management of its common causes and consequences.