Intensive care management of coronavirus disease 2019 (COVID-19): challenges and recommendations.

The molecular basis of retinal ganglion cell death in glaucoma.

In this research, we aim to propose a new fractional model for human liver involving Caputo–Fabrizio derivative with the exponential kernel. Concerning the new model, the existence of a unique solution is explored by using the Picard–Lindelof approach and the fixed-point theory. In addition, the mathematical model is implemented by the homotopy analysis transform method whose convergence is also investigated. Eventually, numerical experiments are carried out to better illustrate the results. Comparative results with the real clinical data indicate the superiority of the new fractional model over the pre-existent integer-order model with ordinary time-derivatives.

A new study on the mathematical modelling of human liver with Caputo–Fabrizio fractional derivative

Respiratory Physiology—the essentials

A biomechanical paradigm for axonal insult within the optic nerve head in aging and glaucoma.

Background Influenza viruses are thought to be spread by droplets, but the role of aerosol dissemination is unclear and has not been assessed by previous studies. Oxygen therapy, nebulised medication and ventilatory support are treatments used in clinical practice to treat influenzal infection are thought to generate droplets or aerosols. Objectives Evaluation of the characteristics of droplet/aerosol dispersion around delivery systems during non-invasive ventilation (NIV), oxygen therapy, nebuliser treatment and chest physiotherapy by measuring droplet size, geographical distribution of droplets, decay in droplets over time after the interventions were discontinued. Methods Three groups were studied: (1) normal controls, (2) subjects with coryzal symptoms and (3) adult patients with chronic lung disease who were admitted to hospital with an infective exacerbation. Each group received oxygen therapy, NIV using a vented mask system and a modified circuit with non-vented mask and exhalation filter, and nebulised saline. The patient group had a period of standardised chest physiotherapy treatment. Droplet counts in mean diameter size ranges from 0.3 to > 10 µm were measured with an counter placed adjacent to the face and at a 1-m distance from the subject/patient, at the height of the nose/mouth of an average health-care worker. Results NIV using a vented mask produced droplets in the large size range (> 10 µm) in patients (p = 0.042) and coryzal subjects (p = 0.044) compared with baseline values, but not in normal controls (p = 0.379), but this increase in large droplets was not seen using the NIV circuit modification. Chest physiotherapy produced droplets predominantly of > 10 µm (p = 0.003), which, as with NIV droplet count in the patients, had fallen significantly by 1 m. Oxygen therapy did not increase droplet count in any size range. Nebulised saline delivered droplets in the small- and medium-size aerosol/droplet range, but did not increase large-size droplet count. Conclusions NIV and chest physiotherapy are droplet (not aerosol)-generating procedures, producing droplets of > 10 µm in size. Due to their large mass, most fall out on to local surfaces within 1 m. The only device producing an aerosol was the nebuliser and the output profile is consistent with nebuliser characteristics rather than dissemination of large droplets from patients. These findings suggest that health-care workers providing NIV and chest physiotherapy, working within 1 m of an infected patient should have a higher level of respiratory protection, but that infection control measures designed to limit aerosol spread may have less relevance for these procedures. These results may have infection control implications for other airborne infections, such as severe acute respiratory syndrome and tuberculosis, as well as for pandemic influenza infection.

https://njl-admin.nihr.ac.uk/document/download/2001958

Evaluation of droplet dispersion during non-invasive ventilation, oxygen therapy, nebuliser treatment and chest physiotherapy in clinical practice: implications for management of pandemic influenza and other airborne infections

Techniques for automated local activation time annotation and conduction velocity estimation in cardiac mapping

In this paper, we develop a mathematical model of blood circulation in the liver lobule. We aim to find the pressure and flux distributions within a liver lobule. We also investigate the effects of changes in pressure that occur following a resection of part of the liver, which often leads to high pressure in the portal vein. The liver can be divided into functional units called lobules. Each lobule has a hexagonal cross-section, and we assume that its longitudinal extent is large compared with its width. We consider an infinite lattice of identical lobules and study the two-dimensional flow in the hexagonal cross-sections. We model the sinusoidal space as a porous medium, with blood entering from the portal tracts (located at each of the vertices of the cross-section of the lobule) and exiting via the centrilobular vein (located in the center of the cross-section). We first develop and solve an idealized mathematical model, treating the porous medium as rigid and isotropic and blood as a Newtonian fluid. The pressure drop across the lobule and the flux of blood through the lobule are proportional to one another. In spite of its simplicity, the model gives insight into the real pressure and velocity distribution in the lobule. We then consider three modifications of the model that are designed to make it more realistic. In the first modification, we account for the fact that the sinusoids tend to be preferentially aligned in the direction of the centrilobular vein by considering an anisotropic porous medium. In the second, we account more accurately for the true behavior of the blood by using a shear-thinning model. We show that both these modifications have a small quantitative effect on the behavior but no qualitative effect. The motivation for the final modification is to understand what happens either after a partial resection of the liver or after an implantation of a liver of small size. In these cases, the pressure is observed to rise significantly, which could cause deformation of the tissue. We show that including the effects of tissue compliance in the model means that the total blood flow increases more than linearly as the pressure rises.

Mathematical Modeling of the Circulation in the Liver Lobule

Fluid mechanical processes are an intrinsic part of several aspects of the physiology and pathology of the human eye. In this article we describe selected phenomena that are amenable to particularly interesting mathematical, experimental, or numerical analyses. We initially focus on glaucoma, a condition often associated with raised intraocular pressure. The mechanics in this disease is by no means fully understood, but we present some of the modeling work that provides a partial explanation. We next focus on other features of the dynamics of the two specialized ocular fluids: the aqueous and vitreous humors. With regard to the aqueous humor, we discuss problems concerning the transport of heat and proteins and the hydration of the cornea. With regard to the vitreous humor, we discuss the possibility of flow, which occurs primarily as a result of saccades or motions of the eyeball. Finally, we describe a model of the degradation of Bruch's membrane in the retina.

Fluid Mechanics of the Eye

We present a mathematical model of blood and interstitial flow in the liver. The liver is treated as a lattice of hexagonal ‘classic’ lobules, which are assumed to be long enough that end effects may be neglected and a two-dimensional problem considered. Since sinusoids and lymphatic vessels are numerous and small compared to the lobule, we use a homogenized approach, describing the sinusoidal and interstitial spaces as porous media. We model plasma filtration from sinusoids to the interstitium, lymph uptake by lymphatic ducts, and lymph outflow from the liver surface. Our results show that the effect of the liver surface only penetrates a depth of a few lobules’ thickness into the tissue. Thus, we separately consider a single lobule lying sufficiently far from all external boundaries that we may regard it as being in an infinite lattice, and also a model of the region near the liver surface. The model predicts that slightly more lymph is produced by interstitial fluid flowing through the liver surface than that taken up by the lymphatic vessels in the liver and that the non-peritonealized region of the surface of the liver results in the total lymph production (uptake by lymphatics plus fluid crossing surface) being about 5 % more than if the entire surface were covered by the Glisson–peritoneal membrane. Estimates of lymph outflow through the surface of the liver are in good agreement with experimental data. We also study the effect of non-physiological values of the controlling parameters, particularly focusing on the conditions of portal hypertension and ascites. To our knowledge, this is the first attempt to model lymph production in the liver. The model provides clinically relevant information about lymph outflow pathways and predicts the systemic response to pathological variations.

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Jennifer H. Siggers

Papers

Evaluation of droplet dispersion during non-invasive ventilation, oxygen therapy, nebuliser treatment and chest physiotherapy in clinical practice: implications for management of pandemic influenza and other airborne infections

Techniques for automated local activation time annotation and conduction velocity estimation in cardiac mapping

Mathematical Modeling of the Circulation in the Liver Lobule

Fluid Mechanics of the Eye

Mathematical model of blood and interstitial flow and lymph production in the liver