Transitioning patients from intravenous to subcutaneous infliximab and vedolizumab for inflammatory bowel disease: what is the opportunity cost of improving access to healthcare?

BACKGROUND: Biologic drugs are highly effective for inflammatory bowel disease (IBD) management but are key drivers of costs of care especially when administered intravenously (i.v.). Availability of subcutaneous (SC) formulations has increased convenience for patients and improved access to care, but at the cost of revenue to health services. AIMS: To evaluate the economic impact of transitioning a tertiary centre IBD cohort from i.v. to SC biologic administration and assess the implications for key stakeholders. METHODS: A retrospective analysis of all patients who received i.v. infliximab or vedolizumab in the outpatient infusion centre of a tertiary IBD centre between July 2019 and June 2021 was undertaken. Data were collated from electronic medical records, pharmacy dispensing systems and the hospital business intelligence unit. An economic analysis and theoretical financial/capacity impact analysis of a transition to an SC model were estimated under two scenarios using a random 10% and 30% of the patient cohort. RESULTS: Transitioning our IBD cohort from i.v. to SC administration would result in a loss to our health service of AU$2 732 123.75, composed of AU$1 463 003.75 in Weighted Inlier Equivalent Separation (WIES) and AU$1 269 120 in drug procurement revenue. However, it would ease capacity in the infusion centre by up to 5256 h. CONCLUSIONS: Transitioning patients to SC administration results in improved access to infusion centres and substantial savings to state governments; however, switching results in a loss of i.v. biologic-generated WIES to health services. Alternative funding models are required to achieve sustainability in IBD care and reduce reliance on i.v. biologic-generated income.

Comparing effects of Euclidean buffers and network buffers on associations between built environment and transport walking: the Multi-Ethnic Study of Atherosclerosis.

BACKGROUND: Transport walking has drawn growing interest due to its potential to increase levels of physical activities and reduce reliance on vehicles. While existing studies have compared built environment-health associations between Euclidean buffers and network buffers, no studies have systematically quantified the extent of bias in health effect estimates when exposures are measured in different buffers. Further, prior studies have done the comparisons focusing on only one or two geographic regions, limiting generalizability and restricting ability to test whether direction or magnitude of bias are different by context. This study aimed to quantify the degree of bias in associations between built environment exposures and transport walking when exposures were operationalized using Euclidean buffers rather than network buffers in diverse contexts. METHODS: We performed a simulations study to systematically evaluate the degree of bias in associations between built environment exposures in Euclidean buffers and network buffers and transport walking, assuming network buffers more accurately captured true exposures. Additionally, we used empirical data from a multi-ethnic, multi-site cohort to compare associations between built environment amenities and walking for transport where built environment exposures were derived using Euclidean buffers versus network buffers. RESULTS: Simulation results found that the bias induced by using Euclidean buffer models was consistently negative across the six study sites (ranging from -80% to -20%), suggesting built environment exposures measured using Euclidean buffers underestimate health effects on transport walking. Percent bias was uniformly smaller for the larger 5 km scale than the 1 km and 0.25 km spatial scales, independent of site or built environment categories. Empirical findings aligned with the simulation results: built environment-health associations were stronger for built environment exposures operationalized using network buffers than using Euclidean buffers. CONCLUSION: This study is the first to quantify the extent of bias in the magnitude of the associations between built environment exposures and transport walking when the former are measured in Euclidean buffers vs. network buffers, informing future research to carefully conceptualize appropriate distance-based buffer metrics in order to better approximate real geographic contexts. It also helps contextualize existing research in the field that used Euclidean buffers when that were the only option. Further, this study provides an example of the uncertain geographic context problem.

Phase Locking of Auditory Nerve Fibers: The Role of Lowpass Filtering by Hair Cells.

Phase locking of auditory-nerve-fiber (ANF) responses to the temporal fine structure of acoustic stimuli, a hallmark of the auditory system's temporal precision, is important for many aspects of hearing. Previous work has shown that phase-locked period histograms are often well described by exponential transfer functions relating instantaneous stimulus pressure to instantaneous spike rate, with no observed clipping of the histograms. The operating points and slopes of these functions change with stimulus level. The mechanism underlying this apparent gain control is unclear but is distinct from mechanical compression, is independent of refractoriness and spike-rate adaptation, and is apparently instantaneous. Here we show that these findings can be accounted for by a model consisting of a static Boltzmann transducer function yielding a clipped output, followed by a lowpass filter and a static exponential transfer function. Using responses to tones of ANFs from cats of both sexes, we show that, for a given ANF, the period histograms obtained at all stimulus levels for a given stimulus frequency can be described using one set of level-independent model parameters. The model also accounts for changes in the maximum and minimum instantaneous spike rates with changes in stimulus level. Notably, the estimated cutoff frequency is lower for low- than for high-spontaneous-rate ANFs, implying a synapse-specific contribution to lowpass filtering. These findings advance our understanding of ANF phase locking by highlighting the role of peripheral filtering mechanisms in shaping responses of individual ANFs.SIGNIFICANCE STATEMENT Phase locking of auditory-nerve-fiber responses to the temporal fine structure of acoustic stimuli is important for many aspects of hearing. Period histograms typically retain an approximately sinusoidal shape across stimulus levels, with the peripheral auditory system operating as though its overall transfer function is an exponential function whose slope decreases with increasing stimulus level. This apparent gain control can be accounted for by a static saturating transducer function followed by a lowpass filter. In addition to attenuating the AC component, the filter approximately recovers the sinusoidal waveform of the stimulus. The estimated cutoff frequency varies with spontaneous rate, revealing a synaptic contribution to lowpass filtering. These findings highlight the significant impact of peripheral filtering mechanisms on phase locking.

A numerical method for computing interval distributions for an inhomogeneous Poisson point process modified by random dead times.

The inhomogeneous Poisson point process is a common model for time series of discrete, stochastic events. When an event from a point process is detected, it may trigger a random dead time in the detector, during which subsequent events will fail to be detected. It can be difficult or impossible to obtain a closed-form expression for the distribution of intervals between detections, even when the rate function (often referred to as the intensity function) and the dead-time distribution are given. Here, a method is presented to numerically compute the interval distribution expected for any arbitrary inhomogeneous Poisson point process modified by dead times drawn from any arbitrary distribution. In neuroscience, such a point process is used to model trains of neuronal spikes triggered by the detection of excitatory events while the neuron is not refractory. The assumptions of the method are that the process is observed over a finite observation window and that the detector is not in a dead state at the start of the observation window. Simulations are used to verify the method for several example point processes. The method should be useful for modeling and understanding the relationships between the rate functions and interval distributions of the event and detection processes, and how these relationships depend on the dead-time distribution.

Phase Locking of Auditory-Nerve Fibers Reveals Stereotyped Distortions and an Exponential Transfer Function with a Level-Dependent Slope.

Phase locking of auditory-nerve-fiber (ANF) responses to the fine structure of acoustic stimuli is a hallmark of the auditory system's temporal precision and is important for many aspects of hearing. Period histograms from phase-locked ANF responses to low-frequency tones exhibit spike-rate and temporal asymmetries, but otherwise retain an approximately sinusoidal shape as stimulus level increases, even beyond the level at which the mean spike rate saturates. This is intriguing because apical cochlear mechanical vibrations show little compression, and mechanoelectrical transduction in the receptor cells is thought to obey a static sigmoidal nonlinearity, which might be expected to produce peak clipping at moderate and high stimulus levels. Here we analyze phase-locked responses of ANFs from cats of both sexes. We show that the lack of peak clipping is due neither to ANF refractoriness nor to spike-rate adaptation on time scales longer than the stimulus period. We demonstrate that the relationship between instantaneous pressure and instantaneous rate is well described by an exponential function whose slope decreases with increasing stimulus level. Relatively stereotyped harmonic distortions in the input to the exponential can account for the temporal asymmetry of the period histograms, including peak splitting. We show that the model accounts for published membrane-potential waveforms when assuming a power-of-three, but not a power-of-one, relationship to exocytosis. Finally, we demonstrate the relationship between the exponential transfer functions and the sigmoidal pseudotransducer functions obtained in the literature by plotting the maxima and minima of the voltage responses against the maxima and minima of the stimuli.SIGNIFICANCE STATEMENT Phase locking of auditory-nerve-fiber responses to the temporal fine structure of acoustic stimuli is important for many aspects of hearing, but the mechanisms underlying phase locking are not fully understood. Intriguingly, period histograms retain an approximately sinusoidal shape across sound levels, even when the mean rate has saturated. We find that neither refractoriness nor spike-rate adaptation is responsible for this behavior. Instead, the peripheral auditory system operates as though it contains an exponential transfer function whose slope changes with stimulus level. The underlying mechanism is distinct from the comparatively weak cochlear mechanical compression in the cochlear apex, and likely resides in the receptor cells.

Use of Dual X-ray Absorptiometry in men with advanced cirrhosis to predict sarcopenia-associated mortality risk.

INTRODUCTION: Reduced muscle area on CT scan is an independent predictor of mortality in cirrhosis. We examine for the first time the relationship between dual energy x-ray absorptiometry (DEXA) lean mass parameters on outcomes in cirrhotic men awaiting liver transplantation. MATERIALS AND METHODS: We retrospectively reviewed DEXA scans performed during transplant assessment between 2001 and 2016. Baseline data including the presence of ascites and MELD score were recorded. DEXA lean mass measures were adjusted for height. The primary outcome was 12-month wait-list mortality. RESULTS: Four hundred twenty men with median age 55.4 years [interquartile range 49.2; 59.4] and MELD 16 [12; 20] were studied. Median follow-up was 58.5 [28.8; 109] months. 12-month wait-list mortality was 12.4%. Appendicular lean mass was inversely associated with mortality (HR 0.78 [0.62; 0.98], P = 0.03). Lean mass of arms (HR 0.37 [0.16; 0.83], P  = 0.02) rather than legs (HR 0.77 [0.58; 1.03], P  = 0.08) was responsible for this association. Upper limb lean mass showed a significant interaction with MELD score in predicting wait-list mortality, particularly within 4 months. Total lean mass was not associated with mortality but increased in conjunction with increasing ascites (OR for ascites 1.20 [1.15; 1.25], P < 0.001 for each unit increase in MELD). CONCLUSION: Upper limb lean mass by DEXA is strongly associated with mortality in men awaiting liver transplantation. The superiority of upper limb lean mass probably relates to confounding of lower limb measures by fluid retention. This DEXA parameter represents a novel and reproducible measure of sarcopenia in cirrhosis.

Spike timing in auditory-nerve fibers during spontaneous activity and phase locking.

In vertebrates, all acoustic information transmitted from the inner ear to the central auditory system is relayed by primary auditory afferents (auditory-nerve fibers; ANFs). These neurons are also the most peripheral elements to use action potentials (spikes) to encode the acoustic information. Here, we review what is known about the spiking of ANFs during spontaneous activity, when spike timing might be regarded as largely random, and during stimulation by low-frequency sounds, when spikes are phase locked to the stimulus waveform, a phenomenon generally considered a hallmark of temporal precision and speed in the auditory system. We focus on mammals, in which each ANF is driven by a single ribbon synapse in a single receptor cell, but also cover relevant research on ANFs of vertebrates from other classes. For spontaneous activity, we highlight several spike-history effects in interspike interval distributions, hazard-rate functions, serial interval correlations, and spike-count statistics. We also review models that have attempted to account for these properties. For phase locking, we focus on the responses to low-frequency tones, rather than to low-frequency components of broadband signals such as noise or clicks. We critically review the measures commonly used to quantify phase locking and urge caution when interpreting such measures with respect to spike-timing precision. We also review the dependence of phase locking on stimulus amplitude and frequency. Finally, we identify some open questions.

A model of synaptic vesicle-pool depletion and replenishment can account for the interspike interval distributions and nonrenewal properties of spontaneous spike trains of auditory-nerve fibers.

In mammalian auditory systems, the spiking characteristics of each primary afferent (type I auditory-nerve fiber; ANF) are mainly determined by a single ribbon synapse in a single receptor cell (inner hair cell; IHC). ANF spike trains therefore provide a window into the operation of these synapses and cells. It was demonstrated previously (Heil et al., 2007) that the distribution of interspike intervals (ISIs) of cat ANFs during spontaneous activity can be modeled as resulting from refractoriness operating on a non-Poisson stochastic point process of excitation (transmitter release events from the IHC). Here, we investigate nonrenewal properties of these cat-ANF spontaneous spike trains, manifest as negative serial ISI correlations and reduced spike-count variability over short timescales. A previously discussed excitatory process, the constrained failure of events from a homogeneous Poisson point process, can account for these properties, but does not offer a parsimonious explanation for certain trends in the data. We then investigate a three-parameter model of vesicle-pool depletion and replenishment and find that it accounts for all experimental observations, including the ISI distributions, with only the release probability varying between spike trains. The maximum number of units (single vesicles or groups of simultaneously released vesicles) in the readily releasable pool and their replenishment time constant can be assumed to be constant (∼4 and 13.5 ms, respectively). We suggest that the organization of the IHC ribbon synapses not only enables sustained release of neurotransmitter but also imposes temporal regularity on the release process, particularly when operating at high rates.

Basic response properties of auditory nerve fibers: a review.

All acoustic information from the periphery is encoded in the timing and rates of spikes in the population of spiral ganglion neurons projecting to the central auditory system. Considerable progress has been made in characterizing the physiological properties of type-I and type-II primary auditory afferents and understanding the basic properties of type-I afferents in response to sounds. Here, we review some of these properties, with emphasis placed on issues such as the stochastic nature of spike timing during spontaneous and driven activity, frequency tuning curves, spike-rate-versus-level functions, dynamic-range and spike-rate adaptation, and phase locking to stimulus fine structure and temporal envelope. We also review effects of acoustic trauma on some of these response properties.

The prevalence of phenotypic silver resistance in clinical isolates.

UNLABELLED: Research has shown silver to be an effective antimicrobial agent against bacteria, virus, yeast, and fungi. Due to the increased use of silver-based wound products during the past decade, concerns of widespread silver resistance have been raised.1 The purpose of this study was to assess the prevalence of phenotypic silver resistance in clinical isolates. METHODS: A total of 130 different microorganism strains were collected from patients admitted to a tertiary care hospital. To determine phenotypic silver resistance, a corrected zone of inhibition (CZOI) test was used. The isolate (0.1 mL) was streaked on nutrient agar in 3 directions to form a confluent lawn. A silver dressing and a control gauze dressing were placed on the lawn and incubated for 24 hours. The CZOI was determined by averaging the zone of clearance in both directions across the dressing and then subtracting the dressing size. Corrected zone of inhibition tests were conducted in duplicate. To confirm the silver dressing killed the microorganism and did not simply hinder bacterial growth, a culture was taken from underneath each silver dressing and plated separately. RESULTS: All of the isolates showed no growth when tested against the silver-based dressing. The CZOI values ranged between 0.0 mm and 7.25 mm. No growth was observed in the secondary culture from underneath the dressing, indicating the silver dressing was bactericidal for all 130 isolates tested and not simply bacteriostatic. The control gauze dressing did not show any antimicrobial properties. CONCLUSION: The threat of widespread silver resistance in clinical isolates remains low. However, continued monitoring for silver resistance should be maintained.

Exploring the spatial scale effects of built environments on transport walking: Multi-Ethnic Study of Atherosclerosis.

We employed a longitudinal distributed lag modeling approach to systematically estimate how associations between built environment features and transport walking decayed with the increase of distance from home to built environment destinations. Data came from a cohort recruited from six U.S. cities (follow-up 2000-2010, N = 3913, baseline mean age 60). Built environment features included all walkable destinations, consisting of common and popular destinations for daily life. We also included two subsets frequent social destinations and food stores to examine if the spatial scale effects differed by varying density for different types of built environment destinations. Adjusted results found that increases in transport walking diminished when built environment destinations were farther, although distance thresholds varied across different types of built environment destinations. Higher availability of walking destinations within 2-km and frequent social destinations within 1.6-km were associated with transport walking. Food stores were not associated with transport walking. This new information will help policymakers and urban designers understand at what distances each type of built environment destinations influences transport walking, in turn informing the development of interventions and/or the placement of amenities within neighborhoods to promote transport walking. The findings that spatial scales depend on specific built environment features also highlight the need for methods that can more flexibly estimate associations between outcomes and different built environment features across varying contexts, in order to improve our understanding of the spatial mechanisms involved in said associations.

Dark matter from axion strings with adaptive mesh refinement.

Axions are hypothetical particles that may explain the observed dark matter density and the non-observation of a neutron electric dipole moment. An increasing number of axion laboratory searches are underway worldwide, but these efforts are made difficult by the fact that the axion mass is largely unconstrained. If the axion is generated after inflation there is a unique mass that gives rise to the observed dark matter abundance; due to nonlinearities and topological defects known as strings, computing this mass accurately has been a challenge for four decades. Recent works, making use of large static lattice simulations, have led to largely disparate predictions for the axion mass, spanning the range from 25 microelectronvolts to over 500 microelectronvolts. In this work we show that adaptive mesh refinement simulations are better suited for axion cosmology than the previously-used static lattice simulations because only the string cores require high spatial resolution. Using dedicated adaptive mesh refinement simulations we obtain an over three order of magnitude leap in dynamic range and provide evidence that axion strings radiate their energy with a scale-invariant spectrum, to within ~5% precision, leading to a mass prediction in the range (40,180) microelectronvolts.

Measuring impact of storyline engagement on health knowledge, attitudes, and norms: A digital evaluation of an online health-focused serial drama in West Africa.

Background: "Cest la Vie!" (CLV) is a serial drama that entertains, educates, and promotes positive health behaviors and social change for West African audiences. The purpose of this study was to evaluate if watching the CLV Season 2 series online had an impact on people's health knowledge, attitudes, and norms, focusing on populations in francophone West Africa. Methods: Between July 2019 and October 2019, viewers of CLV and non-viewers were recruited from Facebook and YouTube. We conducted an online longitudinal cohort study that assessed changes in health knowledge, attitudes, and norms (KAN) between these groups. Participants completed a baseline survey prior to the online airing and up to three follow-up surveys corresponding to specific health stories in the series, including sexual violence, emergency contraception, and female circumcision. We used descriptive statistics to describe viewers and non-viewers, and an item response theory (IRT) analysis to identify the effect of viewing CLV on overall KAN. Results: A total of 1674 respondents participated in the study. One in four participants (23%, n = 388) had seen one of the three storylines from CLV Season 2 (ie, CLV viewers). At follow-up, viewers were more likely than non-viewers to know when to correctly use emergency contraception (P < 0.001) and to believe that the practice of female circumcision should end (P = 0.001). Compared to people who did not see CLV, viewers of the series had 26% greater odds of answering pro-health responses at follow-up about sexual assault, emergency contraception, and female circumcision. Further, the level of engagement with specific storylines was associated with a differential impact on overall outcome questions. Conclusions: As internet access continues to grow across the globe and health education materials are created and adapted for new media environments, our study provides a novel approach to examining the impact of online entertainment-education content on health knowledge, attitudes, and norms.

A simplified physiological model of rate-level functions of auditory-nerve fibers.

Several approaches have been used to describe the rate-level functions of auditory-nerve fibers (ANFs). One approach uses descriptive models that can be fitted easily to data. Another derives rate-level functions from comprehensive physiological models of auditory peripheral processing. Here, we seek to identify the minimal set of components needed to provide a physiologically plausible account of rate-level functions. Our model consists of a first-order Boltzmann mechanoelectrical transducer function relating the instantaneous stimulus pressure to an instantaneous output, followed by a lowpass filter that eliminates the AC component, followed by an exponential synaptic transfer function relating the DC component to the mean spike rate. This is perhaps the simplest physiologically plausible model capable of accounting for rate-level functions under the assumption that the model parameters for a given ANF and stimulus frequency are level-independent. We find that the model typically accounts well for rate-level functions from cat ANFs for all stimulus frequencies. More complicated model variants having saturating synaptic transfer functions do not perform significantly better, implying the system operates far away from synaptic saturation. Rate saturation in the model is caused by saturation of the DC component of the filter output (e.g., the receptor potential), which in turn is due to the saturation of the transducer function. The maximum mean spike rate is approximately constant across ANFs, such that the slope parameter of the exponential synaptic transfer function decreases with increasing spontaneous rate. If the synaptic parameters for a given ANF are assumed to be constant across stimulus frequencies, then frequency- and level-dependent input nonlinearities are derived that are qualitatively similar to those reported in the literature. Contrary to assumptions in the literature, such nonlinearities are obtained even for ANFs having high spontaneous rates. Finally, spike-rate adaptation is examined and found to be accounted for by a decrease in the slope parameter of the synaptic transfer function over time following stimulus onset.

Nelson's notch in the rate-level functions of auditory-nerve fibers might be caused by PIEZO2-mediated reverse-polarity currents in hair cells.

Half a century ago, Nelson Kiang and colleagues observed that some spike rate versus stimulus level functions of auditory-nerve-fiber responses to tones are nonmonotonic, exhibiting a sharp notch ("Nelson's notch") at high stimulus levels. The notch is associated with an abrupt change in the phase of the response by ∼180°. To account for these findings, Kiang proposed a "two-factor cancellation hypothesis" according to which excitation of an auditory-nerve fiber is produced by the sum of two phase-locked factors with opposite phase and with different dependencies on stimulus level, cancelling each other at stimulus levels within the notch. The first factor, which dominates at lower stimulus levels, is likely based on the mechanoelectrical transducer current through mechanoelectrical transducer channels in the tips of the inner-hair-cell stereocilia. The identity of the second factor, which dominates at high stimulus levels, has remained elusive. Here, we hypothesize that the second factor is based on the "anomalous" or "reverse-polarity" currents entering inner hair cells via a second type of mechanosensitive channel, PIEZO2, recently identified in the apical surface of hair cells rather than the tips of their stereocilia.

Epidemiology and outcomes of acute liver failure in Australia.

BACKGROUND: Acute liver failure (ALF) is a life-threatening syndrome with varying aetiologies requiring complex care and multidisciplinary management. Its changing incidence, aetiology and outcomes over the last 16 years in the Australian context remain uncertain. AIM: To describe the changing incidence, aetiology and outcomes of ALF in South Eastern Australia. METHODS: The database of the Victorian Liver Transplant Unit was interrogated to identify all cases of ALF in adults (> 16 years) in adults hospitalised between January 2002 and December 2017. Overall, 169 patients meeting criteria for ALF were identified. Demographics, aetiology of ALF, rates of transplantation and outcomes were collected for all patients. Transplant free survival and overall survival (OS) were assessed based on survival to discharge from hospital. Results were compared to data from a historical cohort from the same unit from 1988-2001. RESULTS: Paracetamol was the most common aetiology of acute liver failure, accounting for 50% of cases, with an increased incidence compared with the historical cohort (P = 0.046). Viral hepatitis and non-paracetamol drug or toxin induced liver injury accounted for 15% and 10% of cases respectively. Transplant free survival (TFS) improved significantly compared to the historical cohort (52% vs 38%, P = 0.032). TFS was highest in paracetamol toxicity with spontaneous recovery in 72% of cases compared to 31% of non-paracetamol ALF (P < 0.001). Fifty-nine patients were waitlisted for emergency liver transplantation. Nine of these died while waiting for an organ to become available. Forty-two patients (25%) underwent emergency liver transplantation with a 1, 3 and 5 year survival of 81%, 78% and 72% respectively. CONCLUSION: Paracetamol toxicity is the most common aetiology of ALF in South-Eastern Australia with a rising incidence over 30 years. TFS has improved, however it remains low in non-paracetamol ALF.

A simple model of the inner-hair-cell ribbon synapse accounts for mammalian auditory-nerve-fiber spontaneous spike times.

The initial neural encoding of acoustic information occurs by means of spikes in primary auditory afferents. Each mammalian primary auditory afferent (type-I auditory-nerve fiber; ANF) is associated with only one ribbon synapse in one receptor cell (inner hair cell; IHC). The properties of ANF spike trains therefore provide an indirect view of the operation of individual IHC synapses. We showed previously that a point process model of presynaptic vesicle pool depletion and deterministic exponential replenishment, combined with short postsynaptic neural refractoriness, accounts for the interspike interval (ISI) distributions, serial ISI correlations, and spike-count statistics of a population of cat-ANF spontaneous spike trains. Here, we demonstrate that this previous synapse model produces unrealistic properties when spike rates are high and show that this problem can be resolved if the replenishment of each release site is stochastic and independent. We assume that the depletion probability varies between synapses to produce differences in spontaneous rate and that the other model parameters are constant across synapses. We find that this model fits best with only four release sites per IHC synapse, a mean replenishment time of 17 ms, and absolute and mean relative refractory periods of 0.6 ms each. This model accounts for ANF spontaneous spike timing better than two influential, comprehensive models of the auditory periphery. It also reproduces ISI distributions from spontaneous and steady-state driven activity from other studies and other mammalian species. Adding fractal noise to the rate of depletion of each release site can yield long-range correlations as typically observed in long spike trains. We also examine two model variants having more complex vesicle cycles, but neither variant yields a markedly improved fit or a different estimate of the number of release sites. In addition, we examine a model variant having both short and long relative refractory components and find that it cannot account for all aspects of the data. These model results will be beneficial for understanding ribbon synapses and ANF responses to acoustic stimulation.