New insights into the comorbid conditions of Turner syndrome: results from a long-term monocentric cohort study.

PURPOSE: Many questions concerning Turner syndrome (TS) remain unresolved, such as the long-term complications and, therefore, the optimal care setting for adults. The primary aim of this long-term cohort study was to estimate the incidence of comorbid conditions along the life course. METHODS: A total of 160 Italian patients with TS diagnosed from 1967 to 2010 were regularly and structurally monitored from the diagnosis to December 2019 at the University Hospital of Bologna using a structured multidisciplinary monitoring protocol. RESULTS: The study cohort was followed up for a median of 27 years (IQR 12-42). Autoimmune diseases were the comorbid condition with the highest incidence (61.2%), followed by osteoporosis and hypertension (23.8%), type 2 diabetes (16.2%) and tumours (15.1%). Median age of onset ranged from 22 years for autoimmune diseases to 39 years for type 2 diabetes. Malignant tumours were the most prominent type of neoplasm, with a cumulative incidence of 11.9%. Papillary thyroid carcinoma was the most common form of cancer, followed by skin cancer and cancer of the central nervous system. Only one major cardiovascular event (acute aortic dissection) was observed during follow-up. No cases of ischaemic heart disease, heart failure, stroke or death were recorded. CONCLUSIONS: This cohort study confirms the need for continuous, structured and multidisciplinary lifelong monitoring of TS, thus ensuring the early diagnosis of important comorbid conditions, including cancer, and their appropriate and timely treatment. In addition, these data highlight the need for the increased surveillance of specific types of cancer in TS, including thyroid carcinoma.

Modeling of cardiovascular variability using a differential delay equation.

The influence of time delay in the baroreflex control of the heart activity is analyzed by using a simple mathematical model of the short-term pressure regulation. The mean arterial pressure in a Windkessel model is controlled by a nonlinear feedback driving a nonpulsatile model of the cardiac pump in accordance with the steady-state characteristics of the arterial baroreceptor reflex. A pure time delay is placed in the feedback branch to simulate the latent period of the baroreceptor regulation. Because of system nonlinearity model dynamics is found to be highly sensitive to time delay and changes of this parameter within a physiological range cause the model to exhibit different patterns of behavior. For low values of time delay (shorter than 0.5 s) the model remains in a steady state. When time delay is longer than 0.5 s, a Hopf bifurcation is crossed and spontaneous oscillations occur with frequencies in the high-frequency (HF) band. Further increases of time delay above 1.2s cause the oscillations to become more complex, and following the typical Feigenbaum cascade, the system becomes chaotic. In this condition heart rate, and flow show evident variability. The heart rate power spectrum exhibits a peak whose frequency moves from the HF to LF band depending on whether simulated time delay is as short as the vagal-mediated control or long as the sympathetic one.

The role of pressure pulsatility in the carotid baroreflex control: a computer simulation study.

The role of pressure pulsatility in the arterial pressure control by the carotid baroreflex was investigated by means of a mathematical model. The model describes the main hemodynamic properties of the cardiovascular system in pulsating conditions, the static and dynamic components of the carotid baroreflex, and their effect on systemic arterial resistance, heart frequency and systemic venous capacity. Experimental findings on the role of pressure pulsatility in the carotid baroreflex were reproduced in terms of a non-linear interaction between the static and dynamic components. Simulations of physiological experiments (mild haemorrhage, carotid occlusion manoeuvres, genesis of self-sustained arterial pressure waves) reveal that the role of pressure pulsatility is meaningful in response to those perturbations (such as carotid occlusion manoeuvres) characterized by different alterations in the mean and pulsating components.

Role of active changes in venous capacity by the carotid baroreflex: analysis with a mathematical model.

To elucidate the role of venous capacity active changes in short-term cardiovascular homeostasis, a mathematical model of the carotid-sinus baroreflex system has been developed. In the model the cardiovascular system is represented as the series arrangement of six lumped compartments, which synthesize the fundamental hemodynamic properties of the systemic arterial, systemic venous, pulmonary arterial, and pulmonary venous circulations as well as of the left and right cardiac volumes. Cardiac outputs from the left and right ventricles are computed as a function of both downstream arterial pressure (afterload) and upstream atrial pressure (preload). Four distinct feedback regulatory mechanisms, working on systemic arterial resistance, heart rate, systemic venous unstressed volume, and systemic venous compliance, are assumed to operate on the cardiovascular system in response to carotid sinus pressure changes. All model parameters, both in the cardiovascular system and in feedback regulatory mechanisms, have been assigned on the basis of physiological data now available. The model is used here to simulate the pattern of the main hemodynamic quantities in the short time period (1-2 min) after acute carotid sinus activation in vagotomized subjects. Simulation results indicate that the model can reproduce experimental data quite well, with reference both to open-loop experiments and to an acute blood hemorrhage performed in closed-loop conditions. Moreover, computer simulations indicate that active changes in venous unstressed volume are of primary importance in regulating cardiac output and systemic arterial pressure during activation of the carotid sinus baroreflex.

Theoretical analysis of pressure pulse propagation in arterial vessels.

An original mathematical model of viscous fluid motion in a tapered and distensible tube is presented. The model equations are deduced by assuming a two-dimensional flow and taking into account the nonlinear terms in the fluid motion equations, as well as the nonlinear deformation of the tube wall. One distinctive feature of the model is the formal integration with respect to the radial coordinate of the Navier-Stokes equations by power series expansion. The consequent computational frame allows an easy, accurate evaluation of the effects produced by changing the values of all physical and geometrical tube parameters. The model is employed to study the propagation along an arterial vessel of a pressure pulse produced by a single flow pulse applied at the proximal vessel extremity. In particular, the effects of the natural taper angle of the arterial wall on pulse propagation are investigated. The simulation results show that tapering considerably influences wave attenuation but not wave velocity. The substantially different behavior of pulse propagation, depending upon whether it travels towards the distal extremity or in the opposite direction, is observed: natural tapering causes a continuous increase in the pulse amplitude as it moves towards the distal extremity; on the contrary, the reflected pulse, running in the opposite direction, is greatly damped. For a vessel with physical and geometrical properties similar to those of a canine femoral artery and 0.1 degree taper angle, the forward amplification is about 0.9 m-1 and the backward attenuation is 1.4 m-1, so that the overall tapering effect gives a remarkably damped pressure response. For a natural taper angle of 0.14 degrees the perturbation is almost extinct when the pulse wave returns to the proximal extremity.

Pressure drops through arterial stenosis models in steady flow condition.

Measures of pressure drops were made in two different plexiglass models of axial-symmetric arterial stenoses. The stenosis models had the same area reduction (86 percent) but were of different length so as to have a different tapering degree. Pressures were measured in steady flow condition at three equidistant points of the stenosis: upstream, in the middle, and downstream. Results indicate that: the upstream-middle pressure drop is independent of tapering degree but is highly influenced by area reduction; moreover it is much greater than the middle-downstream drop. The upstream-middle pressure drop can be accurately predicted by means of a relationship deduced by the momentum equation.

A mathematical analysis of vasomotion in the peripheral vascular bed.

Arterioles and microvascular venules often show rhythmic spontaneous changes in diameter, called vasomotion. In this study, we analyze the possibility that vasomotion originates from the activity of the local myogenic mechanism. This analysis uses an original mathematical model of the peripheral circulation. The peripheral vascular bed has been represented as a series of three consecutive segments, each characterized by its value of vascular resistance per unit weight of tissue. The internal radius of the vessels in the last two segments, and hence their hydraulic resistance, has been assumed to be affected by the local myogenic response of the vascular smooth muscle. This dependence has been reproduced using the Laplace law. Both the static and dynamic (i.e. rate-dependent) components of the myogenic response have been included in the model, in accordance with recent experimental results. Simulations demonstrate that rhythmic, self-sustained oscillations can develop when the dynamic component of the myogenic response of terminal arterioles is much greater than that of more proximal microvessels. A moderate increase in arterial pressure favors the occurrence of oscillations, whereas vasodilatory stimuli tend to suppress vasomotion and contribute to the stabilization of vascular diameters.

Pressure changes induced by whole body acceleration shocks.

In the present paper pressure changes induced by sudden body acceleration are studied "in vivo" on the dog and compared to the results obtainable with a recently developed mathematical model. A dog was fixed to a movable table, which was accelerated by a compressed air piston for less than 1 s. Acceleration was varied by changing the air pressure in the piston. Pressure was measured during the experiment at different points along the vascular bed. However, only data obtained in the carotid artery and abdominal aorta are presented here. The results demonstrated that impulse body accelerations cause significant pressure peaks in the vessel examined (about + 25 mmHg in the carotid artery with body acceleration of g/2). Moreover, pressure changes are rapidly damped, with a time constant of about 0.1s. From the present results it may be concluded that, according to the prediction of the mathematical model, body accelerations such as those occurring in normal life can induce pressure changes well beyond the normal pressure value.

A linear propagation model adapted to the study of fast perturbations in arterial hemodynamics.

The hemodynamic effect of rapid body accelerations is studied in this work using two different models of wave propagation in blood vessels. Simulation curves have been obtained with both models and compared with those measured in vivo on a dog's carotid artery. Results of the first model demonstrate that classic linear theories, based on linearization of the Navier-Stokes and continuity equations, provide a good explanation of the initial effect of body acceleration on pressure. However, the same models significantly underestimate the subsequent pressure perturbation damping. Modified empirical expressions for wave propagation, able to furnish a more accurate description of pressure energy losses occurring during fast hemodynamic phenomena, are thus utilized in the second model and their biophysical significance discussed.

A new nonlinear two-dimensional model of blood motion in tapered and elastic vessels.

An original mathematical model for the local study of blood motion in tapered and distensible arteries was developed. The theory takes into account the nonlinear terms of the Navier-Stokes equations, as well as wall motion and instantaneous taper angle, and allows the calculation of axial and radial velocity profiles with low computational complexity. The relationship between instantaneous flow and the pressure gradient in steady and dynamic conditions is evaluated by means of the mathematical model. The results obtained by simulation agree with experimental evidence and also indicate that the anatomic tapering of arteries and pulsatile changes in diameter highly influence blood motion.

A preliminary theoretical study of arterial pressure perturbations under shock acceleration.

The artero-venous system is often stressed by accelerative perturbation, not only during exceptional performances, but also in normal life. For example, when the body is subject to fast pressure changes, accelerative perturbations combined with a change in hydrostatic pressure could have severe effects on the circulation. In such cases a preliminary mathematical inquiry, whose results allow qualitative evaluation of the perturbation produced is useful. Pressure variations are studied in this work when the body is subjected both to rectilinear and rotational movements as well as posture change. The dominant modes of the hemodynamic oscillations are emphasized and the numerical simulation results presented. The artery model used for simulation is obviously simplified with respect to the anatomical structure of an artery. Nevertheless, behavior of the main arteries (like the common carotid and aorta) can be approximately described, choosing suitable model parameters. The frequency of blood oscillations strictly depends on the Young modulus of the arterial wall. This connection could be employed for new clinical tests on the state of the arteries.

A mathematical model of cerebral blood flow chemical regulation--Part I: Diffusion processes.

This paper proposes a mathematical model which describes the production and diffusion of vasoactive chemical factors involved in oxygen-dependent cerebral blood flow (CBF) regulation in the rat. Partial differential equations describing the relations between input and output variables have been replaced with simpler ordinary differential equations by using mathematical approximations of the hyperbolic functions in the Laplace transform domain. This model is composed of two submodels. In the first, oxygen transport from capillary blood to cerebral tissue is analyzed to link changes in mean tissue oxygen pressure with CBF and arterial oxygen concentration changes. The second submodel presents equations describing the production of vasoactive metabolites by cerebral parenchyma, due to a lack of oxygen, and their diffusion towards pial perivascular space. These equations have been used to simulate the time dynamics of mean tissue PO2, perivascular adenosine concentration, and perivascular pH to changes in CBF. The present simulation points out that the time delay introduced by diffusion processes is negligible if compared with the other time constants of the system under study. In a subsequent work the same equations will be included in a model of the cerebral vascular bed to clarify the metabolite role in CBF regulation.

A mathematical model of cerebral blood flow chemical regulation--Part II: Reactivity of cerebral vascular bed.

In the present paper an original mathematical model of the chemical oxygen-dependent cerebral blood flow (CBF) regulation in the rat is proposed. Taking into account recent experimental works, the model assumes that oxygen acts on cerebral vessels through an indirect mechanism, mediated by the release of two metabolic substances (adenosine and H+) from tissue, and that any change in perivascular concentration of these substances affects the diameter of both the medium and small pial arteries as well as of intracerebral arterioles. The model is composed of several submodels, each closely related to a different physiological event. mathematical equations, which describe the reaction of the vasoactive portion of the cerebral vascular bed, are reported in detail and justified. The model permits the simulation of the role played by chemical factors in the control of CBF under many different physiological and pathological conditions in an attempt to clarify their relevance. Several events associated with an alteration in oxygen supply to tissue (auto-regulation to changes in arterial and venous pressure, reactive hyperemia following on cerebral ischemia, arterial hypoxia) have been simulated with the model. The results suggest that chemical factors, adenosine and H+, play a significant but not exclusive role in the regulation of the cerebral vascular bed. The action of other mechanisms (which are probably neurogenic) must be hypothesized to explain completely the CBF changes occurring in vivo.