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Background. Postmenopausal hirsutism could be due to a myriad of causes, including ovarian and adrenal tumours, ovarian hyperthecosis, exogenous androgens, and Cushing’s syndrome. We report a patient who was found to have a rare cause of postmenopausal hirsutism. Case Presentation. A 64-year-old postmenopausal woman with a history of hypertension, thyrotoxicosis, and poorly controlled diabetes on multiple oral hypoglycaemic agents presented with gradual onset progressive excessive hair growth without any virilizing features. On examination, she did not have Cushingnoid features or clitoromegaly. Her hirsutism was quantified with Ferriman–Gallwey score which was 9. Her biochemical evaluation showed elevated testosterone levels with normal DHEAS, ODST, 17-OHP, and prolactin. Low-dose dexamethasone suppression test did not suppress testosterone more than 40%. Contrast-enhanced CT of the adrenal and pelvis did not show any adrenal or ovarian mass lesions. Transvaginal ultrasound scan showed bilateral prominent ovaries only. Combined adrenal and ovarian venous sampling was carried out to localize the source of excess androgen, but only the left adrenal vein was successfully cannulated which showed suppressed testosterone level compared to periphery. The patient underwent total abdominal hysterectomy and bilateral salphingo oophorectomy, and her testosterone level normalized postoperatively. Her glycaemic control improved. Histology showed evidence of bilateral diffuse ovarian Leydig cell hyperplasia. Conclusion. Evaluation of postmenopausal hirsutism needs careful history and examination followed by biochemical evaluation and imaging. While adrenal and ovarian venous sampling can help to arrive at a diagnosis, it is a technically demanding procedure with low success rates even at centers of excellence. Therefore, in such situations, bilateral oophorectomy may be the best course of action which will give the histological confirmation of the diagnosis. Successful treatment of hyperandrogenism can result in improvement of glycaemic control. Bilateral diffuse Leydig cell hyperplasia is a rare but important cause of postmenopausal hirsutism.

Background. Polycystic ovary syndrome (PCOS) is a common endocrine disorder with heterogeneous etiology. Typical features consist of oligo/anovulation, polycystic ovaries, and features of hyperandrogenism. Pathogenesis is multifactorial, and positive family history may have a predisposition for disease development. The syndrome is associated with multiple metabolic and nonmetabolic entities. As the disease is involved with multiple adverse outcomes, the successful treatment is pivotal. Among the more advanced options, the unilateral oophorectomy is considered as a last resort to alleviate the symptoms. Case Presentation. A 29-year-old female presented to us with oligomenorrhea, severe hirsutism, androgenic pattern hair loss, acne, increased skin pigmentation, and secondary subfertility. On examination, she was obese with a body mass index (BMI) of 29.6 kg/m2. She had evidence of acanthosis nigricans, androgenic pattern balding, acne, dorsal, supraclavicular fat deposition, and moderate-severe hirsutism. Investigations confirmed excess right ovarian testosterone secretion which led to the ultimate management with right oophorectomy with successful alleviation of clinical features. Conclusions. The multifaceted medical treatment comprises the first-line therapy in PCOS. Surgery is considered as a second-line option in resistant PCOS following failure of initial therapeutic options. We report a case of resistant polycystic ovary syndrome with secondary subfertility and moderate-to-severe hirsutism who was successfully treated with unilateral oophorectomy with favorable results.

Given a compensated Poisson process $(X_t)_{t \geq 0}$ based on $(\Omega, \mathcal{F}, \mathbb{P})$, the Wiener-Poisson isomorphism $\mathcal{W} : \mathfrak{F}_+(L^2 (\mathbb{R}_+)) \to L^2 (\Omega, \mathcal{F}, \mathbb{P})$ is constructed. We restrict the isomorphism to $\mathfrak{F}_+(L^2 [0,1])$ and prove some novel properties of the Poisson exponentials $\mathcal{E}(f) := \mathcal{W}(e(f))$. A new proof of the result $\Lambda_t + A_t + A^{\dagger}_t = \mathcal{W}^{-1}\widehat{X_t} \mathcal{W}$ is also given. The analogous results for $\mathfrak{F}_+(L^2 (\mathbb{R}_+))$ are briefly mentioned. The concept of a compensated Poisson process over $\mathbb{R}_+$ is generalised to any measure space $(M, \mathcal{M}, \mu)$ as an isometry $I : L^2(M, \mathcal{M}, \mu) \to L^2 (\Omega,\mathcal{F}, \mathbb{P})$ satisfying certain properties. For such a generalised Poisson process we recall the construction of the generalised Wiener-Poisson isomorphism, $\mathcal{W}_I : \mathfrak{F}_+(L^2(M)) \to L^2 (\Omega, \mathcal{F}, \mathbb{P})$, using Charlier polynomials. Two alternative constructions of $\mathcal{W}_I$ are also provided, the first using exponential vectors and then deducing the connection with Charlier polynomials, and the second using the theory of reproducing kernel Hilbert spaces. Given any measure space $(M, \mathcal{M}, \mu)$, we construct a canonical generalised Poisson process $I : L^2 (M, \mathcal{M}, \mu) \to L^2(\Delta, \mathcal{B}, \mathbb{P})$, where $\Delta$ is the maximal ideal space, with $\mathcal{B}$ the completion of its Borel $\sigma$-field with respect to $\mathbb{P}$, of a $C^*$-algebra $\mathcal{A} \subseteq \mathfrak{B}(\mathfrak{F}_+(L^2(M)))$. The Gelfand transform $\mathcal{A} \to \mathfrak{B}(L^2(\Delta))$ is unitarily implemented by the Wiener-Poisson isomorphism $\mathcal{W}_I: \mathfrak{F}_+(L^2(M)) \to L^2(\Delta)$. This construction only uses operator algebra theory and makes no a priori use of Poisson measures. A new Fock space proof of the quantum Ito formula for $(\Lambda_t + A_t + A^{\dagger}_t)_{0 \leq t \leq 1}$ is given. If $(F_{\ \! \! t})_{0 \leq t \leq 1}$ is a real, bounded, predictable process with respect to a compensated Poisson process $(X_t)_{0 \leq t \leq 1}$, we show that if $M_t = \int_0^t F_s dX_s$, then on $\mathsf{E}_{\mathrm{lb}} := \mathrm{linsp} \{ e(f) : f \in L^2_{\mathrm{lb}}[0,1] \}$, $\mathcal{W}^{-1} \widehat{M_t} \mathcal{W} = \int_0^t \mathcal{W}^{-1} \widehat{F_s} \mathcal{W} (d\Lambda_s + dA_s + dA^{\dagger}_s),$ and that $(\mathcal{W}^{-1} \widehat{M_t} \mathcal{W})_{0 \leq t \leq 1}$ is an essentially self-adjoint quantum semimartingale. We prove, using the classical Ito formula, that if $(J_t)_{0 \leq t \leq 1}$ is a regular self-adjoint quantum semimartingale, then $(\mathcal{W} \widehat{M_t} \mathcal{W}^{-1} + J_t)_{0 \leq t \leq 1}$ is an essentially self-adjoint quantum semimartingale satisfying the quantum Duhamel formula, and hence the quantum Ito formula. The equivalent result for the sum of a Brownian and Poisson martingale, provided that the sum is essentially self-adjoint with core $\mathsf{E}_{\mathrm{lb}}$, is also proved.