Data analysis of the unsteadily accelerating GPS and seismic records at Campi Flegrei caldera from 2000 to 2020.

Ongoing resurgence affects Campi Flegrei caldera (Italy) via bradyseism, i.e. a series of ground deformation episodes accompanied by increases in shallow seismicity. In this study, we perform a mathematical analysis of the GPS and seismic data in the instrumental catalogs from 2000 to 2020, and a comparison of them to the preceding data from 1983 to 1999. We clearly identify and characterize two overlying trends, i.e. a decennial-like acceleration and cyclic oscillations with various periods. In particular, we show that all the signals have been accelerating since 2005, and 90-97% of their increase has occurred since 2011, 40-80% since 2018. Nevertheless, the seismic and ground deformation signals evolved differently-the seismic count increased faster than the GPS data since 2011, and even more so since 2015, growing faster than an exponential function The ground deformation has a linearized rate slope, i.e. acceleration, of 0.6 cm/yr2 and 0.3 cm/yr2 from 2000 to 2020, respectively for the vertical (RITE GPS) and the horizontal (ACAE GPS) components. In addition, all annual rates show alternating speed-ups and slow-downs, consistent between the signals. We find seven major rate maxima since 2000, one every 2.8-3.5 years, with secondary maxima at fractions of the intervals. A cycle with longer period of 6.5-9 years is also identified. Finally, we apply the probabilistic failure forecast method, a nonlinear regression that calculates the theoretical time limit of the signals going to infinity (interpreted here as a critical state potentially reached by the volcano), conditional on the continuation of the observed nonlinear accelerations. Since 2000, we perform a retrospective analysis of the temporal evolution of these forecasts which highlight the periods of more intense acceleration. The failure forecast method applied on the seismic count from 2001 to 2020 produces upper time limits of [0, 3, 11] years (corresponding to the 5th, 50th and 95th percentiles, respectively), significantly shorter than those based on the GPS data, e.g. [0, 6, 21] years. Such estimates, only valid under the model assumption of continuation of the ongoing decennial-like acceleration, warn to keep the guard up on the future evolution of Campi Flegrei caldera.

Novel statistical emulator construction for volcanic ash transport model Ash3d with physically motivated measures.

Statistical emulators are a key tool for rapidly producing probabilistic hazard analysis of geophysical processes. Given output data computed for a relatively small number of parameter inputs, an emulator interpolates the data, providing the expected value of the output at untried inputs and an estimate of error at that point. In this work, we propose to fit Gaussian Process emulators to the output from a volcanic ash transport model, Ash3d. Our goal is to predict the simulated volcanic ash thickness from Ash3d at a location of interest using the emulator. Our approach is motivated by two challenges to fitting emulators-characterizing the input wind field and interactions between that wind field and variable grain sizes. We resolve these challenges by using physical knowledge on tephra dispersal. We propose new physically motivated variables as inputs and use normalized output as the response for fitting the emulator. Subsetting based on the initial conditions is also critical in our emulator construction. Simulation studies characterize the accuracy and efficiency of our emulator construction and also reveal its current limitations. Our work represents the first emulator construction for volcanic ash transport models with considerations of the simulated physical process.

A tutorial review of mathematical techniques for quantifying tumor heterogeneity.

Intra-tumor and inter-patient heterogeneity are two challenges in developing mathematical models for precision medicine diagnostics. Here we review several techniques that can be used to aid the mathematical modeller in inferring and quantifying both sources of heterogeneity from patient data. These techniques include virtual populations, nonlinear mixed effects modeling, non-parametric estimation, Bayesian techniques, and machine learning. We create simulated virtual populations in this study and then apply the four remaining methods to these datasets to highlight the strengths and weak-nesses of each technique. We provide all code used in this review at https://github.com/jtnardin/Tumor-Heterogeneity/ so that this study may serve as a tutorial for the mathematical modelling community. This review article was a product of a Tumor Heterogeneity Working Group as part of the 2018-2019 Program on Statistical, Mathematical, and Computational Methods for Precision Medicine which took place at the Statistical and Applied Mathematical Sciences Institute.

Frequency of and risk factors for medication errors by pharmacists during order verification in a tertiary care medical center.

PURPOSE: The frequency of and risk factors for medication errors by pharmacists during order verification in a tertiary care medical center were reviewed. METHODS: This retrospective, secondary database study was conducted at a large tertiary care medical center in Houston, Texas. Inpatient and outpatient medication orders and medication errors recorded between July 1, 2011, and June 30, 2012, were reviewed. Independent variables assessed as risk factors for medication errors included workload (mean number of orders verified per pharmacist per shift), work environment (type of day, type of shift, and mean number of pharmacists per shift), and nonmodifiable characteristics of the pharmacist (type of pharmacy degree obtained, age, number of years practicing, and number of years at the institution). RESULTS: A total of 1,887,751 medication orders, 92 medication error events, and 50 pharmacists were included in the study. The overall error rate was 4.87 errors per 100,000 verified orders. An increasing medication error rate was associated with an increased number of orders verified per pharmacist (p = 0.007), the type of shift (p = 0.021), the type of day (p = 0.002), and the mean number of pharmacists per shift (p = 0.001). Pharmacist demographic variables were not associated with risk of error. The number of orders per shift was identified as a significant independent risk factor for medication errors (p = 0.019). CONCLUSION: An increase in the number of orders verified per shift was associated with an increased rate of pharmacist errors during order verification in a tertiary care medical center.

TGF-mediated dynamics in a system of many coupled nephrons.

This paper presents a mathematical model of a system of many coupled nephrons branching from a common cortical radial artery, and accompanying analysis of that system. This modeling effort is a first step in understanding how coupling magnifies the tendency of nephrons to oscillate owing to tubuloglomerular feedback. Central to the present work is the single nephron integral model (as in Pitman et al., The IMA Volumes in Mathematics and Its Applications, vol. 129, pp. 345-364, 2002 and in Zaritski, Ph.D. Dissertation, 1999) which is a simplification of the single nephron PDE model of Layton et al. (Am. J. Physiol. 261, F904-F919, 1991). A second principal idea used in the present model is a coupling of model nephrons, generalizing the work of Pitman et al. (Bull. Math. Biol. 66, 1463-1492, 2004) who proposed a model of two coupled nephrons. In this study, we couple nephrons through a nearest neighbor interaction.Speaking generally, our results suggest that a series of similar nephrons coupled to their nearest neighbors are more prone to be found in an oscillatory mode, relative to a single nephron with the same properties. More specifically, we show analytically that, for N coupled identical nephrons, the region supporting oscillatory solutions in the time delay-gain parameter plane increases with N. Numerical simulations suggest that, if N nephrons have gains and time delays that do not differ by much, the system is, again, more prone to oscillate, relative to a single nephron, and the oscillations tend to be approximately synchronous and in-phase. We examine the effect of parameters on bifurcation. We also examine alternative models of coupling; this analysis allows us to conclude that the increased propensity of coupled nephrons to oscillate is a robust finding, true for several models of nephron interaction.

A two-fluid model for avalanche and debris flows.

Geophysical mass flows--debris flows, avalanches, landslides--can contain O(10(6)-10(10)) m(3) or more of material, often a mixture of soil and rocks with a significant quantity of interstitial fluid. These flows can be tens of meters in depth and hundreds of meters in length. The range of scales and the rheology of this mixture presents significant modelling and computational challenges. This paper describes a depth-averaged 'thin layer' model of geophysical mass flows containing a mixture of solid material and fluid. The model is derived from a 'two-phase' or 'two-fluid' system of equations commonly used in engineering research. Phenomenological modelling and depth averaging combine to yield a tractable set of equations, a hyperbolic system that describes the motion of the two constituent phases. If the fluid inertia is small, a reduced model system that is easier to solve may be derived.

Feedback-mediated dynamics in two coupled nephrons.

Previously, we developed a dynamic model for the tubuloglomerular feedback (TGF) system in a single, short-looped nephron of the mammalian kidney. In that model, a semi-linear hyperbolic partial differential equation was used to represent two fundamental processes of solute transport in the nephron's thick ascending limb (TAL): chloride advection by fluid flow along the TAL lumen and transepithelial chloride transport from the lumen to the interstitium. An empirical function and a time delay were used to relate glomerular filtration rate to the chloride concentration at the macula densa of the TAL. Analysis of the model equations indicated that stable limit-cycle oscillations (LCO) in nephron fluid flow and chloride concentration can emerge for sufficiently large feedback gain magnitude and time delay. In this study, the single-nephron model was extended to two nephrons, which were coupled through their filtration rates. Explicit analytical conditions were obtained for bifurcation loci corresponding to two special cases: (1) identical time delays but differing feedback gains, and (2) identical gains but differing delays. Similar to the case of a single nephron, our analysis indicates that stable LCO can emerge in coupled nephrons for sufficiently large gains and delays. However, these LCO may emerge at lower values of the feedback gain, relative to a single (i.e., uncoupled) nephron, or at shorter delays, provided the delays are sufficiently close. These results suggest that, in vivo, if two nephrons are sufficiently similar, then coupling will tend to increase the likelihood of LCO.

Limit-cycle oscillations and tubuloglomerular feedback regulation of distal sodium delivery.

A mathematical model was used to evaluate the potential effects of limit-cycle oscillations (LCO) on tubuloglomerular feedback (TGF) regulation of fluid and sodium delivery to the distal tubule. In accordance with linear systems theory, simulations of steady-state responses to infinitesimal perturbations in single-nephron glomerular filtration rate (SNGFR) show that TGF regulatory ability (assessed as TGF compensation) increases with TGF gain magnitude gamma when gamma is less than the critical value gamma(c), the value at which LCO emerge in tubular fluid flow and NaCl concentration at the macula densa. When gamma > gamma(c) and LCO are present, TGF compensation is reduced for both infinitesimal and finite perturbations in SNGFR, relative to the compensation that could be achieved in the absence of LCO. Maximal TGF compensation occurs when gamma approximately gamma(c). Even in the absence of perturbations, LCO increase time-averaged sodium delivery to the distal tubule, while fluid delivery is little changed. These effects of LCO are consequences of nonlinear elements in the TGF system. Because increased distal sodium delivery may increase the rate of sodium excretion, these simulations suggest that LCO enhance sodium excretion.

Mechanisms by which thrombolytic therapy results in nonuniform lysis and residual thrombus after reperfusion.

A transport-reaction model describing penetration of plasmin by diffusion and permeation into a dissolving fibrin gel was solved numerically to explore mechanisms that lead to the formation and growth of dissolution fingers through blood clots during thrombolytic therapy. Under conditions of fluid permeation driven by arterial pressures, small random spatial variations in the initial fibrin density within clots (+/-4 to 25% peak variations) were predicted by the simulation to result in dramatic dissolution fingers that grew in time. With in vitro experiments, video microscopy revealed that the shape of the proximal face of a fibrin gel, when deformed by pressure-driven permeation, led to lytic breakthrough in the center of the clot, consistent with model predictions of increased velocities in this region leading to cannulation. Computer simulation of lysis of fibrin retracted by platelets (where more permeable regions are expected in the middle of the clot due to retraction) predicted cannulation of the clot during thrombolysis. This residual, annular thrombus was predicted to lyse more slowly, because radial pressure gradients to drive inner clot permeation were quite small. In conjunction with kinetic models of systemic pharmacodynamics and plasminogen activation biochemistry, a two-dimensional transport-reaction model can facilitate the prediction of the time and causes of clot cannulation, poor reperfusion, and embolism during thrombolysis.

Nonlinear filter properties of the thick ascending limb.

A mathematical model was used to investigate the filter properties of the thick ascending limb (TAL), that is, the response of TAL luminal NaCl concentration to oscillations in tubular fluid flow. For the special case of no transtubular NaCl backleak and for spatially homogeneous transport parameters, the model predicts that NaCl concentration in intratubular fluid at each location along the TAL depends only on the fluid transit time up the TAL to that location. This exact mathematical result has four important consequences: 1) when a sinusoidal component is added to steady-state TAL flow, the NaCl concentration at the macula densa (MD) undergoes oscillations that are bounded by a range interval envelope with magnitude that decreases as a function of oscillatory frequency; 2) the frequency response within the range envelope exhibits nodes at those frequencies where the oscillatory flow has a transit time to the MD that equals the steady-state fluid transit time (this nodal structure arises from the establishment of standing waves in luminal concentration, relative to the steady-state concentration profile, along the length of the TAL); 3) for any dynamically changing but positive TAL flow rate, the luminal TAL NaCl concentration profile along the TAL decreases monotonically as a function of TAL length; and 4) sinusoidal oscillations in TAL flow, except at nodal frequencies, result in nonsinusoidal oscillations in NaCl concentration at the MD. Numerical calculations that include NaCl backleak exhibit solutions with these same four properties. For parameters in the physiological range, the first few nodes in the frequency response curve are separated by antinodes of significant amplitude, and the nodes arise at frequencies well below the frequency of respiration in rat. Therefore, the nodal structure and nonsinusoidal oscillations should be detectable in experiments, and they may influence the dynamic behavior of the tubuloglomerular feedback system.

Spectral properties of the tubuloglomerular feedback system.

A simple mathematical model was used to investigate the spectral properties of the tubuloglomerular feedback (TGF) system. A perturbation, consisting of small-amplitude broad-band forcing, was applied to simulated thick ascending limb (TAL) flow, and the resulting spectral response of the TGF pathway was assessed by computing a power spectrum from resulting TGF-regulated TAL flow. Power spectra were computed for both open- and closed-feedback-loop cases. Open-feedback-loop power spectra are consistent with a mathematical analysis that predicts a nodal pattern in TAL frequency response, with nodes corresponding to frequencies where oscillatory flow has a TAL transit time that equals the steady-state fluid transit time. Closed-feedback-loop spectra are dominated by the open-loop spectral response, provided that gamma, the magnitude of feedback gain, is less than the critical value gamma c required for emergence of a sustained TGF-mediated oscillation. For gamma exceeding gamma c, closed-loop spectra have peaks corresponding to the fundamental frequency of the TGF-mediated oscillation and its harmonics. The harmonics, expressed in a nonsinusoidal waveform for tubular flow, are introduced by nonlinear elements of the TGF pathway, notably TAL transit time and the TGF response curve. The effect of transit time on the flow waveform leads to crests that are broader than troughs and to an asymmetry in the magnitudes of increasing and decreasing slopes. For feedback gain magnitude that is sufficiently large, the TGF response curve tends to give a square waveshape to the waveform. Published waveforms and power spectra of in vivo TGF oscillations have features consistent with the predictions of this analysis.

Granulomatous hepatitis associated with glyburide.

A wide variety of diseases and injuries can cause granulomatous hepatitis, and drug-induced granulomatous hepatitis is a well-described entity. Sulfonylurea derivatives, which are commonly used oral hypoglycemic agents in the treatment of non-insulin-dependent diabetes mellitus, have been implicated in liver disease. However, glyburide, a second-generation sulfonylurea and a potent hypoglycemic drug, is considered to have less hepatic side effects than chlorpropamide. It has been reportedly associated with cholestatic jaundice and hepatitis and with hypersensitivity angitis. A case of necrotizing granuloma has been reported. We present a second case of granulomatous hepatitis occurring in a patient who had been taking glyburide for approximately three years, and we review the literature for glyburide-associated hepatitis.

Instantaneous and steady-state gains in the tubuloglomerular feedback system.

The load of water and solute entering each nephron of the mammalian kidney is regulated by the tubuloglomerular feedback (TGF) mechanism, a negative feedback loop. Experiments in rats have shown that key variables of this feedback system may exhibit TGF-mediated oscillations. Mathematical modeling studies have shown that the open-feedback-loop gain is a crucial parameter for determining whether oscillations will emerge. However, two different formulations of this gain have been used. The first is the steady-state gain, a readily measurable quantity corresponding to the steady-state reduction in single-nephron glomerular filtration rate (SNGFR) subsequent to a sustained increased in ascending limb flow rate. The second is an instantaneous gain, a variable arising from theoretical considerations corresponding to the maximum reduction in SNGFR resulting from an instantaneous shift of the ascending limb flow column, with the assumption that the SNGFR response is also instantaneous. Here we show by an analytic argument how the steady-state and instantaneous open-feedback-loop gains for the ascending limb are related. In the case of no solute backleak into the ascending limb, the two formulations of gain are equivalent; however, in the presence of solute backleak, the instantaneous gain is larger in magnitude than the steady-state gain. With typical physiological parameters for the rat, calculations with a model previously devised by us show that the gains differ by 5-10%. Hence, experimental measurements of the steady-state gain may provide useful lower-bound estimates of the instantaneous gain of the feedback system in the normal rat. However, the gains may diverge significantly in pathophysiological states where ascending limb transport is compromised by abnormally high NaCl permeability.

A dynamic numerical method for models of renal tubules.

We show that an explicit method for solving hyperbolic partial differential equations can be applied to a model of a renal tubule to obtain both dynamic and steady-state solutions. Appropriate implementation of this method eliminates numerical instability arising from reversal of intratubular flow direction. To obtain second-order convergence in space and time, we employ the recently developed ENO (Essentially Non-Oscillatory) methodology. We present examples of computed flows and concentration profiles in representative model contexts. Finally, we indicate briefly how model tubules may be coupled to construct large-scale simulations of the renal counterflow system.

Numerical simulation of propagating concentration profiles in renal tubules.

Method-dependent mechanisms that may affect dynamic numerical solutions of a hyperbolic partial differential equation that models concentration profiles in renal tubules are described. Some numerical methods that have been applied to the equation are summarized, and ways by which the methods may misrepresent true solutions are analysed. Comparison of these methods demonstrates the need for thoughtful application of computational mathematics when simulating complicated time-dependent phenomena.

An international perspective of active euthanasia: attitudes of nurses in seven countries.

This exploratory study examines the ethical justification that cancer care and dementia care nurses gave for active voluntary euthanasia. A convenient sample of 319 nurses working in seven countries was interviewed using a structured interview guide. The great majority of the nurses could not ethically justify active voluntary euthanasia. Even if the law changed, only 96 of the total sample viewed active voluntary euthanasia as ethical. For those nurses who could ethically justify active voluntary euthanasia, the majority did so because of the patients' suffering.

Bifurcation analysis of TGF-mediated oscillations in SNGFR.

Recent micropuncture studies in rats have demonstrated the existence of oscillatory states in nephron filtration mediated by tubuloglomerular feedback (TGF). We develop a minimal mathematical model of the TGF system, consisting of a first-order hyperbolic partial differential equation describing thick ascending limb (TAL) NaCl reabsorption and an empirical feedback relation. An analytic bifurcation analysis of this model provides fundamental insight into how oscillatory states depend on the physiological parameters of the model. In the special case of no solute backleak in the TAL, the emergence of oscillations explicitly depends on two nondimensional parameters. The first corresponds to the delay time of the TGF response across the juxtaglomerular apparatus, and the second corresponds to the product of the slope of the TGF response curve at the steady-state operating point and the space derivative of the steady-state NaCl concentration profile in the TAL at the macula densa. Numerical calculations for the case without TAL backleak are consistent with this result. Numerical simulation of the more general case with TAL backleak shows that the bifurcation analysis still provides useful predictions concerning nephron dynamics. With typical parameter values, the analysis predicts that the TGF system will be in oscillatory state. However, the system is near enough to the boundary of the nonoscillatory region so that small changes in parameter values could result in nonoscillatory behavior.

Ethical reasoning associated with the feeding of terminally ill elderly cancer patients. An international perspective.

An international nursing research study examined the ethical decision-making of "good and experienced" registered nurses in eight countries. The subjects were asked about their decision to feed or not to feed a hypothetical terminally ill, mentally alert, elderly cancer patient who refuses to eat. Cultural variations were demonstrated in the decisions as well as differences in ethical justification. The majority of nurses who would not feed appeared to use the principle of autonomy, whereas nurses who would feed the patient used beneficence as justification. Conditions under which nurses would change their decision to either feed or not feed the patient against her will included doctor's orders and lack of peer support for the decision. The majority of nurses clearly experienced a dilemma.

Squamous papilloma of esophagus.

Four additional cases of squamous papilloma of the esophagus are reported. They were diagnosed and resected endoscopically by the excisional biopsy technique and confirmed histologically. A brief survey of the literature is included. This report is presented to stress the recognition and clinical implications of this entity.

Computed tomography: regression of periventricular enhancing lesions in multiple sclerosis.

A patient with two periventricular enhancing lesions on computed tomography subsequently demonstrated clearing of these abnormalities without treatment and a clinical course compatible with multiple sclerosis. CT scans obtained in disease processes associated with acute demyelination and alteration of the blood-brain barrier can show enhancing lesions. These lesions can initially be confused with primary or secondary neoplasms, enhancing infarcts or arteriovenous malformation. The differential diagnosis of enhancing lesions without significant mass effect should initially include the acute phase of multiple sclerosis and other demyelinating processes.