Statistical modeling of diabetic neuropathy: Exploring the dynamics of nerve mortality.

Diabetic neuropathy is a disorder characterized by impaired nerve function and reduction of the number of epidermal nerve fibers per epidermal surface. Additionally, as neuropathy related nerve fiber loss and regrowth progresses over time, the two-dimensional spatial arrangement of the nerves becomes more clustered. These observations suggest that with development of neuropathy, the spatial pattern of diminished skin innervation is defined by a thinning process which remains incompletely characterized. We regard samples obtained from healthy controls and subjects suffering from diabetic neuropathy as realisations of planar point processes consisting of nerve entry points and nerve endings, and propose point process models based on spatial thinning to describe the change as neuropathy advances. Initially, the hypothesis that the nerve removal occurs completely at random is tested using independent random thinning of healthy patterns. Then, a dependent parametric thinning model that favors the removal of isolated nerve trees is proposed. Approximate Bayesian computation is used to infer the distribution of the model parameters, and the goodness-of-fit of the models is evaluated using both non-spatial and spatial summary statistics. Our findings suggest that the nerve mortality process changes as neuropathy advances.

Scalable and flexible inference framework for stochastic dynamic single-cell models.

Understanding the inherited nature of how biological processes dynamically change over time and exhibit intra- and inter-individual variability, due to the different responses to environmental stimuli and when interacting with other processes, has been a major focus of systems biology. The rise of single-cell fluorescent microscopy has enabled the study of those phenomena. The analysis of single-cell data with mechanistic models offers an invaluable tool to describe dynamic cellular processes and to rationalise cell-to-cell variability within the population. However, extracting mechanistic information from single-cell data has proven difficult. This requires statistical methods to infer unknown model parameters from dynamic, multi-individual data accounting for heterogeneity caused by both intrinsic (e.g. variations in chemical reactions) and extrinsic (e.g. variability in protein concentrations) noise. Although several inference methods exist, the availability of efficient, general and accessible methods that facilitate modelling of single-cell data, remains lacking. Here we present a scalable and flexible framework for Bayesian inference in state-space mixed-effects single-cell models with stochastic dynamic. Our approach infers model parameters when intrinsic noise is modelled by either exact or approximate stochastic simulators, and when extrinsic noise is modelled by either time-varying, or time-constant parameters that vary between cells. We demonstrate the relevance of our approach by studying how cell-to-cell variation in carbon source utilisation affects heterogeneity in the budding yeast Saccharomyces cerevisiae SNF1 nutrient sensing pathway. We identify hexokinase activity as a source of extrinsic noise and deduce that sugar availability dictates cell-to-cell variability.

Parameters of the diffusion leaky integrate-and-fire neuronal model for a slowly fluctuating signal.

Stochastic leaky integrate-and-fire (LIF) neuronal models are common theoretical tools for studying properties of real neuronal systems. Experimental data of frequently sampled membrane potential measurements between spikes show that the assumption of constant parameter values is not realistic and that some (random) fluctuations are occurring. In this letter, we extend the stochastic LIF model, allowing a noise source determining slow fluctuations in the signal. This is achieved by adding a random variable to one of the parameters characterizing the neuronal input, considering each interspike interval (ISI) as an independent experimental unit with a different realization of this random variable. In this way, the variation of the neuronal input is split into fast (within-interval) and slow (between-intervals) components. A parameter estimation method is proposed, allowing the parameters to be estimated simultaneously over the entire data set. This increases the statistical power, and the average estimate over all ISIs will be improved in the sense of decreased variance of the estimator compared to previous approaches, where the estimation has been conducted on each individual ISI. The results obtained on real data show good agreement with classical regression methods.

Maximum likelihood estimation of a time-inhomogeneous stochastic differential model of glucose dynamics.

Stochastic differential equations (SDEs) are assuming an important role in the definition of dynamical models allowing for explanation of internal variability (stochastic noise). SDE models are well established in many fields, such as investment finance, population dynamics, polymer dynamics, hydrology and neuronal models. The metabolism of glucose and insulin has not yet received much attention from SDE modellers, except from a few recent contributions, because of methodological and implementation difficulties in estimating SDE parameters. Here, we propose a new SDE model for the dynamics of glycemia during a euglycemic hyperinsulinemic clamp experiment, introducing system noise in tissue glucose uptake and apply for its estimation a closed-form Hermite expansion of the transition densities of the solution process. The present work estimates the new model parameters using a computationally efficient approximate maximum likelihood approach. By comparison with other currently used methods, the estimation process is very fast, obviating the need to use clusters or expensive mainframes to obtain the quick answers needed for everyday iterative modelling. Furthermore, it can introduce the demonstrably essential concept of system noise in this branch of physiological modelling.

A general approach to the apparent permeability index.

The apparent permeability index is widely used as part of a general screening process to study drug absorption, and is routinely obtained from in vitro or ex vivo experiments. A classical example, widely used in the pharmaceutical industry, is the in vitro Caco-2 cell culture model. The index is defined as the initial flux of compound through the membrane (normalized by membrane surface area and donor concentration) and is typically computed by adapting a straight line to the initial portion of the recorded amounts in the receiver compartment, possibly disregarding the first few points when lagging of the transfer process through the membrane is evident. Modeling the transfer process via a two-compartmental system yields an immediate analogue of the common Papp as the initial slope of the receiver quantity, but the two-compartment model often does not match observations well. A three-compartment model, describing the cellular layer as well as donor and receiver compartments, typically better represents the kinetics, but has the disadvantage of always having zero initial flow rate to the receiver compartment: in these circumstances the direct analogue of the Papp index is not informative since it is always zero. In the present work an alternative definition of an apparent permeability index is proposed for three-compartment models, and is shown to reduce to the classical formulation as the cellular layer's volume tends towards zero. This new index characterizes the intrinsic permeability of the membrane to the compound under investigation, can be directly computed in a completely observer-independent fashion, and reduces to the usual Papp when the linear two-compartment representation is sufficient to accurately describe compound kinetics.

Modeling the euglycemic hyperinsulinemic clamp by stochastic differential equations.

The Euglycemic Hyperinsulinemic Clamp (EHC) is the most widely used experimental procedure for the determination of insulin sensitivity. In the present study, 16 subjects with BMI between 18.5 and 63.6 kg/m(2) have been studied with a long-duration (5 hours) EHC. In order to explain the oscillations of glycemia occurring in response to the hyperinsulinization and to the continuous glucose infusion at varying speeds, we first hypothesized a system of ordinary differential equations (ODEs), with limited success. We then extended the model and represented the experiment using a system of stochastic differential equations (SDEs). The latter allow for distinction between (i) random variation imputable to observation error and (ii) system noise (intrinsic variability of the metabolic system), due to a variety of influences which change over time. The stochastic model of the EHC was fitted to data and the system noise was estimated by means of a (simulated) maximum likelihood procedure, for a series of different hypothetical measurement error values. We showed that, for the whole range of reasonable measurement error values: (i) the system noise estimates are non-negligible; and (ii) these estimates are robust to changes in the likely value of the measurement error. Explicit expression of system noise is physiologically relevant in this case, since glucose uptake rate is known to be affected by a host of additive influences, usually neglected when modeling metabolism. While in some of the studied subjects system noise appeared to only marginally affect the dynamics, in others the system appeared to be driven more by the erratic oscillations in tissue glucose transport rather than by the overall glucose-insulin control system. It is possible that the quantitative relevance of the unexpressed effects (system noise) should be considered in other physiological situations, represented so far only with deterministic models.

Effects of levosimendan on right ventricular afterload in patients with acute respiratory distress syndrome: a pilot study.

OBJECTIVE: Acute respiratory distress syndrome (ARDS) is frequently associated with increased pulmonary vascular resistance and thus with systolic load of the right ventricle. We hypothesized that levosimendan, a new calcium sensitizer with potential pulmonary vasodilator properties, improves hemodynamics by unloading the right ventricle in patients with ARDS. DESIGN: Prospective, randomized, placebo-controlled, pilot study. SETTING: Twenty-two-bed multidisciplinary intensive care unit of a university hospital. PATIENTS: Thirty-five patients with ARDS in association with septic shock. INTERVENTIONS: Patients were randomly allocated to receive a 24-hr infusion of either levosimendan 0.2 microg/kg/min (n = 18) or placebo (n = 17). Data from right heart catheterization, cardiac magnetic resonance, arterial and mixed venous oxygen tensions and saturations, and carbon dioxide tensions were obtained before and 24 hrs after drug infusion. MEASUREMENTS AND MAIN RESULTS: At a mean arterial pressure between 70 and 80 mm Hg (sustained with norepinephrine infusion), levosimendan increased cardiac index (from 3.8 +/- 1.1 to 4.2 +/- 1.0 L/min/m) and decreased mean pulmonary artery pressure (from 29 +/- 3 to 25 +/- 3 mm Hg) and pulmonary vascular resistance index (from 290 +/- 77 to 213 +/- 50 dynes/s/cm(5)/m(2); each p < .05). Levosimendan also decreased right ventricular end-systolic volume and increased right ventricular ejection fraction (p < .05). In addition, levosimendan increased mixed venous oxygen saturation (from 63 +/- 8 to 70 +/- 8%; p < .01). CONCLUSIONS: This study provides evidence that levosimendan improves right ventricular performance through pulmonary vasodilator effects in septic patients with ARDS. A large multiple-center trial is needed to investigate whether levosimendan is able to improve the overall prognosis of patients with sepsis and ARDS.

A mathematical model of the euglycemic hyperinsulinemic clamp.

BACKGROUND: The Euglycemic Hyperinsulinemic Clamp (EHC) is the most widely used experimental procedure for the determination of insulin sensitivity, and in its usual form the patient is followed under insulinization for two hours. In the present study, sixteen subjects with BMI between 18.5 and 63.6 kg/m(2) were studied by long-duration (five hours) EHC. RESULTS: From the results of this series and from similar reports in the literature it is clear that, in obese subjects, glucose uptake rates continue to increase if the clamp procedure is prolonged beyond the customary 2 hours. A mathematical model of the EHC, incorporating delays, was fitted to the recorded data, and the insulin resistance behaviour of obese subjects was assessed analytically. Obese subjects had significantly less effective suppression of hepatic glucose output and higher pancreatic insulin secretion than lean subjects. Tissue insulin resistance appeared to be higher in the obese group, but this difference did not reach statistical significance. CONCLUSION: The use of a mathematical model allows a greater amount of information to be recovered from clamp data, making it easier to understand the components of insulin resistance in obese vs. normal subjects.

Prophylactic fenoldopam for renal protection in sepsis: a randomized, double-blind, placebo-controlled pilot trial.

OBJECTIVE: Acute renal failure is common in septic patients. Fenoldopam, a dopamine-1 receptor agonist, increases renal blood flow and may, therefore, reduce the risk of acute renal failure in such patients. Accordingly, we sought to determine the safety and efficacy of fenoldopam for the prevention of acute renal failure in septic patients. DESIGN: Prospective, double-blind, placebo-controlled trial. SETTING: Three multidisciplinary intensive care units at a university hospital. PATIENTS: Three hundred septic patients with baseline serum creatinine concentrations <150 micromol/L. INTERVENTIONS: We randomized patients to a continuous infusion of either fenoldopam (n = 150) at 0.09 microg x kg x min or placebo (n = 150) while in the intensive care unit. The primary outcome measure was the incidence of acute renal failure, defined as a serum creatinine concentration increase to >150 micromol/L, during study drug infusion. MEASUREMENTS AND MAIN RESULTS: The incidence of acute renal failure was significantly lower in the fenoldopam group compared with the control group (29 vs. 51 patients; p = .006). The odds ratio of developing acute renal failure for patients treated with fenoldopam was estimated to be 0.47 (p = .005). The difference in the incidence of severe acute renal failure (creatinine >300 mumol/L), however, failed to achieve statistical significance (10 vs. 21; p = .056). The length of intensive care unit stay in surviving patients was significantly lower in the fenoldopam group compared with the control group (10.64 +/- 9.3 vs. 13.4 +/- 14.0; p < .001). There were no complications of fenoldopam infusion. A direct effect of treatment on the probability of death, beyond its effect on acute renal failure, was not significant (odds ratio = 0.68, p = .1). CONCLUSIONS: Compared with placebo, low-dose fenoldopam resulted in a smaller increase in serum creatinine in septic patients. The clinical significance of this finding is uncertain. A large multiple-center trial is now needed to confirm these findings.

Terlipressin versus norepinephrine to counteract anesthesia-induced hypotension in patients treated with renin-angiotensin system inhibitors: effects on systemic and regional hemodynamics.

BACKGROUND: Terlipressin has been suggested as the ideal drug to treat anesthesia-induced hypotension in patients under long-term renin-angiotensin system inhibitor treatment for arterial hypertension. The authors compared the effects of terlipressin and norepinephrine on systemic hemodynamic parameters and gastric mucosal perfusion using a laser Doppler flowmetry technique in patients treated with renin-angiotensin system inhibitors who experienced hypotension at induction of anesthesia. METHODS: Thirty-two patients scheduled for carotid endarterectomy under general anesthesia and treated with renin-angiotensin system inhibitors had hypotension after induction of general anesthesia. They were randomized to receive 1 mg of terlipressin (n = 16) or norepinephrine infusion (n = 16) to counteract anesthesia-induced hypotension. A laser Doppler probe was introduced into the gastric lumen. All measurements were performed just before surgery, during hypotension, at 30 min, and at 4 h. RESULTS: Terlipressin produced an increase in mean arterial pressure and a decrease in gastric mucosal perfusion detected by laser Doppler flowmetry (P < 0.05) over 30 min that were sustained for 4 h. During the infusion, norepinephrine produced an increase in mean arterial pressure and in gastric mucosal perfusion detected by laser Doppler flowmetry (P < 0.05). If compared to norepinephrine, terlipressin reduced oxygen delivery and oxygen consumption (P < 0.05) and increased arterial lactate concentrations (P < 0.05). CONCLUSION: This study showed the efficacy of terlipressin in the treatment of hypotension episodes in anesthetized patients chronically treated with renin-angiotensin system inhibitors, angiotensin converting-enzyme inhibitors, and angiotensin II receptor antagonists. However, the negative effects on gastric mucosal perfusion and the risk of iatrogenic oxygen supply dependency of terlipressin need to be taken into account.