Publications by authors named "Brenno Cabella"

15 Publications

  • Page 1 of 1

Relation of a Socioeconomic Index with Cognitive Function and Neuroimaging in Hypertensive Individuals.

J Alzheimers Dis 2021 ;82(2):815-826

Instituto do Coracao (InCor), Hospital das Clinicas HCFMUSP, Faculdade de Medicina, Universidade de São Paulo, São Paulo, SP, Brazil.

Background: Socioeconomic factors are important contributors to brain health. However, data from developing countries (where social inequalities are the most prominent) are still scarce, particularly about hypertensive individuals.

Objective: To evaluate the relationship between socioeconomic index, cognitive function, and cortical brain volume, as well as determine whether white matter hyperintensities are mediators of the association of the socioeconomic index with cognitive function in hypertensive individuals.

Methods: We assessed 92 hypertensive participants (mean age = 58±8.6 years, 65.2%female). Cognitive evaluation and neuroimaging were performed and clinical and sociodemographic data were collected using questionnaires. A socioeconomic index was created using education, income, occupation (manual or non-manual work), and race. The associations of the socioeconomic index with cognitive performance and brain volume were investigated using linear regression models adjusted for age, sex, time of hypertension since diagnosis, and comorbidities. A causal mediation analysis was also conducted.

Results: Better socioeconomic status was associated with better visuospatial ability, executive function, and global cognition. We found associations between a better socioeconomic index and a higher parietal lobe volume. White matter hyperintensities were also not mediators in the relationship between the socioeconomic index and cognitive performance.

Conclusion: Socioeconomic disadvantages are associated with worse cognitive performance and brain volume in individuals with hypertension.
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http://dx.doi.org/10.3233/JAD-210143DOI Listing
September 2021

Climate drivers of malaria at its southern fringe in the Americas.

PLoS One 2019 10;14(7):e0219249. Epub 2019 Jul 10.

Instituto de Física Teórica, Universidade Estadual Paulista - UNESP, São Paulo, SP, Brazil.

In this work we analyze potential environmental drivers of malaria cases in Northwestern Argentina. We inspect causal links between malaria and climatic variables by means of the convergent cross mapping technique, which provides a causality criterion from the theory of dynamic systems. Analysis is based on 12 years of weekly malaria P. vivax cases in Tartagal, Salta, Argentina-at the southern fringe of malaria incidence in the Americas-together with humidity and temperature time-series spanning the same period. Our results show that there are causal links between malaria cases and both maximum temperature, with a delay of five weeks, and minimum temperature, with delays of zero and twenty two weeks. Humidity is also a driver of malaria cases, with thirteen weeks delay between cause and effect. Furthermore we also determined the sign and strength of the effects. Temperature has always a positive non-linear effect on cases, with maximum temperature effects more pronounced above 25°C and minimum above 17°C, while effects of humidity are more intricate: maximum humidity above 85% has a negative effect, whereas minimum humidity has a positive effect on cases. These results might be signaling processes operating at short (below 5 weeks) and long (over 12 weeks) time delays, corresponding to effects related to parasite cycle and mosquito population dynamics respectively. The non-linearities found for the strength of the effect of temperature on malaria cases make warmer areas more prone to higher increases in the disease incidence. Moreover, our results indicate that an increase of extreme weather events could enhance the risks of malaria spreading and re-emergence beyond the current distribution. Both situations, warmer climate and increase of extreme events, will be remarkably increased by the end of the century in this hot spot of climate change.
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http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0219249PLOS
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6619762PMC
February 2020

Individualizing Thresholds of Cerebral Perfusion Pressure Using Estimated Limits of Autoregulation.

Crit Care Med 2017 Sep;45(9):1464-1471

1Brain Physics Laboratory, Division of Neurosurgery, Department of Clinical Neurosciences, Cambridge Biomedical Campus, University of Cambridge, Cambridge, United Kingdom. 2Institute of Electronic Systems, Warsaw University of Technology, Warsaw, Poland. 3Division of Anaesthesia, Department of Medicine, Addenbrooke's Hospital, University of Cambridge, Cambridge, United Kingdom. 4Department of Neuroscience, University of Genoa, Italy. 5Department of Anesthesia, Surgical Intensive Care, Prehospital Emergency Medicine and Pain Therapy, University Hospital Basel, University of Basel, Basel, Switzerland. 6Division of Neurosurgery, Department of Clinical Neurosciences, Addenbrooke's Hospital, University of Cambridge, Cambridge, United Kingdom. 7Department of Intensive Care, University of Maastricht, Maastricht University Medical Center, Maastricht, The Netherlands.

Objectives: In severe traumatic brain injury, cerebral perfusion pressure management based on cerebrovascular pressure reactivity index has the potential to provide a personalized treatment target to improve patient outcomes. So far, the methods have focused on identifying "one" autoregulation-guided cerebral perfusion pressure target-called "cerebral perfusion pressure optimal". We investigated whether a cerebral perfusion pressure autoregulation range-which uses a continuous estimation of the "lower" and "upper" cerebral perfusion pressure limits of cerebrovascular pressure autoregulation (assessed with pressure reactivity index)-has prognostic value.

Design: Single-center retrospective analysis of prospectively collected data.

Setting: The neurocritical care unit at a tertiary academic medical center.

Patients: Data from 729 severe traumatic brain injury patients admitted between 1996 and 2016 were used. Treatment was guided by controlling intracranial pressure and cerebral perfusion pressure according to a local protocol.

Interventions: None.

Methods And Main Results: Cerebral perfusion pressure-pressure reactivity index curves were fitted automatically using a previously published curve-fitting heuristic from the relationship between pressure reactivity index and cerebral perfusion pressure. The cerebral perfusion pressure values at which this "U-shaped curve" crossed the fixed threshold from intact to impaired pressure reactivity (pressure reactivity index = 0.3) were denoted automatically the "lower" and "upper" cerebral perfusion pressure limits of reactivity, respectively. The percentage of time with cerebral perfusion pressure below (%cerebral perfusion pressure < lower limit of reactivity), above (%cerebral perfusion pressure > upper limit of reactivity), or within these reactivity limits (%cerebral perfusion pressure within limits of reactivity) was calculated for each patient and compared across dichotomized Glasgow Outcome Scores. After adjusting for age, initial Glasgow Coma Scale, and mean intracranial pressure, percentage of time with cerebral perfusion pressure less than lower limit of reactivity was associated with unfavorable outcome (odds ratio %cerebral perfusion pressure < lower limit of reactivity, 1.04; 95% CI, 1.02-1.06; p < 0.001) and mortality (odds ratio, 1.06; 95% CI, 1.04-1.08; p < 0.001).

Conclusions: Individualized autoregulation-guided cerebral perfusion pressure management may be a plausible alternative to fixed cerebral perfusion pressure threshold management in severe traumatic brain injury patients. Prospective randomized research will help define which autoregulation-guided method is beneficial, safe, and most practical.
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http://dx.doi.org/10.1097/CCM.0000000000002575DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5595234PMC
September 2017

Prediction of intracranial hypertension through noninvasive intracranial pressure waveform analysis in pediatric hydrocephalus.

Childs Nerv Syst 2017 Sep 16;33(9):1517-1524. Epub 2017 Jun 16.

Division of Pediatric Neurosurgery of the Department of Surgery and Anatomy, Ribeirão Preto Medical School, University of São Paulo, Ribeirão Preto, 14049-900, São Paulo, Brazil.

Purpose: The purpose of this study is to evaluate a noninvasive device to assess intracranial pressure wave form in children with hydrocephalus.

Methods: A prospective and non-experimental descriptive-analytic study was performed. Fifty-six patients were enrolled in this study. They were divided in four groups: group A, children with clinically compensated hydrocephalus; B, surgically treated hydrocephalus; C, patients with acute intracranial hypertension due to hydrocephalus; and D, children without neurological disease (control). Data were collected through the installation of an extracranial deformation sensor, coupled to the children's scalp, which allowed registration of noninvasive intracranial pressure curves. Parameters obtained were analyzed: P2/P1 ratio, "classification P1 and P2 and P1 slope.

Results: P2/P1 index and "classification of P1 and P2" had a sensitivity of 80% and specificity of 100% for predicting intracranial hypertension. "P1 slope" presented no statistical difference.

Conclusion: This study showed a useful and noninvasive method for monitoring intracranial pressure, which was able to indicate the intracranial hypertension in children with hydrocephalus and, thus, should be further investigated for clinical applications.
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http://dx.doi.org/10.1007/s00381-017-3475-1DOI Listing
September 2017

Associations Between Impaired Cerebral Blood Flow Autoregulation, Cerebral Oxygenation, and Biomarkers of Brain Injury and Postoperative Cognitive Dysfunction in Elderly Patients After Major Noncardiac Surgery.

Anesth Analg 2017 03;124(3):934-942

From the *Department of Anesthesia, Surgical Intensive Care, Prehospital Emergency Medicine and Pain Therapy, University Hospital Basel, University of Basel, Switzerland; †Department of Clinical Research, University Hospital Basel, University of Basel, Switzerland; ‡Department of Anesthesiology, Lausanne University Hospital, University of Lausanne, Switzerland; §Brain Physics Lab, Division of Neurosurgery, University of Cambridge, United Kingdom; ‖Department of Mathematics and Technology, Koblenz University of Applied Sciences, Koblenz, Germany; and ¶Memory Clinic, University Center for Medicine of Aging Basel, Felix Platter Hospital, Basel, Switzerland.

Background: Increasing evidence links postoperative cognitive dysfunction (POCD) to surgery and anesthesia. POCD is recognized as an important neuropsychological adverse outcome in surgical patients, particularly the elderly. This prospective cohort study aimed to investigate whether POCD is associated with impaired intraoperative cerebral autoregulation and oxygenation, and increased levels of biomarkers of brain injury.

Methods: Study subjects were patients ≥65 years of age scheduled for major noncardiac surgery. Cognitive function was assessed before and 1 week after surgery. POCD was diagnosed if a decline of >1 standard deviation of z-scores was present in ≥2 variables of the test battery. The incidence of POCD 1 week after surgery was modeled as a multivariable function of the index of autoregulation (MxA) and tissue oxygenation index (TOI), adjusting for baseline neuropsychological assessment battery (Consortium to Establish a Registry for Alzheimer's Disease-Neuropsychological Assessment Battery [CERAD-NAB]) total score and the maximum C-reactive protein (CRP) concentration. The biomarkers of brain injury neuron-specific enolase and S100β protein, age, and level of education were included in secondary multivariable logistic regression analyses.

Results: Of the 82 patients who completed the study, 38 (46%) presented with POCD 1 week after surgery. In the multivariable regression analysis, higher intraoperative MxA (odds ratio [OR; 95% confidence interval (CI)], 1.39 [1.01-1.90] for an increase of 0.1 units, P = .08 after Bonferroni adjustment), signifying less effective autoregulation, was not associated with higher odds of POCD. The univariable logistic regression model for MxA yielded an association with POCD (OR [95% CI], 1.44 [1.06-1.95], P = .020). Tissue oxygenation index (1.12 [0.41-3.01] for an increase of 10%, P = 1.0 after Bonferroni adjustment) and baseline CERAD-NAB total score (0.80 [0.45-1.42] for an increase of 10 points, P = .45) did not affect the odds of POCD. POCD was associated with elevated CRP on postoperative day 2 (median [interquartile range]; 175 [81-294] vs 112 [62-142] mg/L, P = .033); however, the maximum CRP value (OR [95% CI], 1.35 [0.97-1.87] for a 2-fold increase, P = .07) had no distinct effect on POCD.

Conclusions: Impairment of intraoperative cerebral blood flow autoregulation is not predictive of early POCD in elderly patients, although secondary analyses indicate that an association probably exists.
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http://dx.doi.org/10.1213/ANE.0000000000001803DOI Listing
March 2017

Complexity of brain signals is associated with outcome in preterm infants.

J Cereb Blood Flow Metab 2017 Oct 11;37(10):3368-3379. Epub 2017 Jan 11.

3 Department of Clinical Neurosciences, University of Cambridge, Cambridge, UK.

A characteristic feature of complex healthy biological systems is the ability to react and adapt to minute changes in the environment. This 'complexity' manifests itself in highly irregular patterns of various physiological measurements. Here, we apply Multiscale Entropy (MSE) analysis to assess the complexity of systemic and cerebral near-infrared spectroscopy (NIRS) signals in a cohort of 61 critically ill preterm infants born at median (range) gestational age of 26 (23-31) weeks, before 24 h of life. We further correlate the complexity of these parameters with brain injury and mortality. Lower complexity index (CoI) of oxygenated haemoglobin (HbO), deoxygenated haemoglobin (Hb) and tissue oxygenation index (TOI) were observed in those infants who developed intraventricular haemorrhage (IVH) compared to those who did not (P = 0.002, P = 0.010 and P = 0.038, respectively). Mean CoI of HbO, Hb and total haemoglobin index (THI) were lower in those infants who died compared to those who survived (P = 0.012, P = 0.004 and P = 0.003, respectively). CoI-HbO was an independent predictor of IVH (P = 0.010). Decreased complexity of brain signals was associated with mortality and brain injury. Measurement of brain signal complexity in preterm infants is feasible and could represent a significant advance in the brain-oriented care.
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http://dx.doi.org/10.1177/0271678X16687314DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5624386PMC
October 2017

An Association Between ICP-Derived Data and Outcome in TBI Patients: The Role of Sample Size.

Neurocrit Care 2017 Aug;27(1):103-107

Division of Neurosurgery, Department of Clinical Neurosciences, University of Cambridge, Cambridge, UK.

Background: Many demographic and physiological variables have been associated with TBI outcomes. However, with small sample sizes, making spurious inferences is possible. This paper explores the effect of sample sizes on statistical relationships between patient variables (both physiological and demographic) and outcome.

Methods: Data from head-injured patients with monitored arterial blood pressure, intracranial pressure (ICP) and outcome assessed at 6 months were included in this retrospective analysis. A univariate logistic regression analysis was performed to obtain the odds ratio for unfavorable outcome. Three different dichotomizations between favorable and unfavorable outcomes were considered. A bootstrap method was implemented to estimate the minimum sample sizes needed to obtain reliable association between physiological and demographic variables with outcome.

Results: In a univariate analysis with dichotomized outcome, samples sizes should be generally larger than 100 for reproducible results. Pressure reactivity index, ICP, and ICP slow waves offered the strongest relationship with outcome. Relatively small sample sizes may overestimate effect sizes or even produce conflicting results.

Conclusion: Low power tests, generally achieved with small sample sizes, may produce misleading conclusions, especially when they are based only on p values and the dichotomized criteria of rejecting/not-rejecting the null hypothesis. We recommend reporting confidence intervals and effect sizes in a more complete and contextualized data analysis.
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http://dx.doi.org/10.1007/s12028-016-0319-xDOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5524874PMC
August 2017

Characterization of Intracranial Pressure Behavior in Chronic Epileptic Animals: A Preliminary Study.

Acta Neurochir Suppl 2016 ;122:329-33

Physics Institute of Sao Carlos, University of Sao Paulo, Sao Carlos, Brazil.

Intracranial pressure (ICP) is a major neurological parameter in animals and humans. ICP is a function of the relationship between the contents of the cranium (brain parenchyma, cerebrospinal fluid, and blood) and the volume of the skull. Increased ICP can cause serious physiological effects or even death in patients who do not quickly receive proper care, which includes ICP monitoring. Epilepsies are a set of central nervous system disorders resulting from abnormal and excessive neuronal discharges, usually associated with hypersynchronism and/or hyperexcitability. Temporal lobe epilepsy (TLE) is one of the most common forms of epilepsy and is also refractory to medication. ICP characteristics of subjects with epilepsy have not been elucidated because there are few studies associating these two important neurological factors. In this work, an invasive (ICPi) and the new minimally invasive (ICPmi) methods were used to evaluate ICP features in rats with chronic epilepsy, induced by the experimental model of pilocarpine, capable of generating the main features of human TLE in these animals.
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http://dx.doi.org/10.1007/978-3-319-22533-3_65DOI Listing
July 2017

Characterization of ICP Behavior in an Experimental Model of Hemorrhagic Stroke in Rats.

Acta Neurochir Suppl 2016 ;122:121-4

Physics Institute of Sao Carlos, University of Sao Paulo, Sao Carlos, Brazil.

Intracranial pressure (ICP) monitoring is sometimes required in clinical pictures of stroke, as extensive intraparenchymal hematomas and intracranial bleeding may severely increase ICP, which can lead to irreversible conditions, such as dementia and cognitive derangement. ICP monitoring has been accepted as a procedure for the safe diagnosis of increased ICP, and for the treatment of intracranial hypertension in some diseases. In this work, we evaluated ICP behavior during the induction of an experimental model of autologous blood injection in rats, simulating a hemorrhagic stroke. Rats were subjected to stereotactic surgery for the implantation of a unilateral cannula into the left striatal region of the brain. Autologous blood was infused into the left striatal region with an automatic microinfusion pump. ICP monitoring was performed throughout the procedure of hemorrhagic stroke induction. Analyses consisted of short-time Fourier transform for ICP before and after stroke induction and the histological processing of the animals' brains. Short-time Fourier transform analysis demonstrated oscillations in the ICP frequency components throughout time after the microinjections compared with data before them. Histological analysis revealed neuropathological changes in the striatum in all microinjected animals.
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http://dx.doi.org/10.1007/978-3-319-22533-3_24DOI Listing
July 2017

Validation of a New Minimally Invasive Intracranial Pressure Monitoring Method by Direct Comparison with an Invasive Technique.

Acta Neurochir Suppl 2016 ;122:97-100

University of São Paulo, Sao Paulo, Brazil.

In this chapter we present in vivo experiments with a new minimally invasive method of monitoring intracranial pressure (ICP). Strain gauge deformation sensors are externally glued onto the exposed skull. The signal from these sensors is amplified, filtered, and sent to a computer with appropriate software for analysis and data storage. Saline infusions into the spinal channel of rats were performed to produce ICP changes, and minimally invasive ICP and direct Codman intraparenchymal ICP were simultaneously acquired in six animals. The similarity between the invasive and minimally invasive methods in response to ICP increase was assessed using Pearson's correlation coefficient. It demonstrated good agreement between the two measures < r > = 0.8 ± 0.2, with a range of 0.31-0.99.
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http://dx.doi.org/10.1007/978-3-319-22533-3_19DOI Listing
July 2017

Validation of a New Noninvasive Intracranial Pressure Monitoring Method by Direct Comparison with an Invasive Technique.

Acta Neurochir Suppl 2016 ;122:93-6

University of São Paulo, São Paulo, Brazil.

The search for a completely noninvasive intracranial pressure (ICPni) monitoring technique capable of real-time digitalized monitoring is the Holy Grail of brain research. If available, it may facilitate many fundamental questions within the range of ample applications in neurosurgery, neurosciences and translational medicine, from pharmaceutical clinical trials, exercise physiology, and space applications. In this work we compare invasive measurements with noninvasive measurements obtained using the proposed new noninvasive method. Saline was infused into the spinal channel of seven rats to produce ICP changes and the simultaneous acquisition of both methods was performed. The similarity in the invasive and noninvasive methods of ICP monitoring was calculated using Pearson's correlation coefficients (r). Good agreement between measures < r > = 0.8 ± 0.2 with a range 0.28-0.96 was shown.
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http://dx.doi.org/10.1007/978-3-319-22533-3_18DOI Listing
July 2017

Prospective Study on Noninvasive Assessment of Intracranial Pressure in Traumatic Brain-Injured Patients: Comparison of Four Methods.

J Neurotrauma 2016 Apr 17;33(8):792-802. Epub 2015 Dec 17.

1 Brain Physics Laboratory, Division of Neurosurgery, Department of Clinical Neurosciences, University of Cambridge , Cambridge, United Kingdom .

Elevation of intracranial pressure (ICP) may occur in many diseases, and therefore the ability to measure it noninvasively would be useful. Flow velocity signals from transcranial Doppler (TCD) have been used to estimate ICP; however, the relative accuracy of these methods is unclear. This study aimed to compare four previously described TCD-based methods with directly measured ICP in a prospective cohort of traumatic brain-injured patients. Noninvasive ICP (nICP) was obtained using the following methods: 1) a mathematical "black-box" model based on interaction between TCD and arterial blood pressure (nICP_BB); 2) based on diastolic flow velocity (nICP_FVd); 3) based on critical closing pressure (nICP_CrCP); and 4) based on TCD-derived pulsatility index (nICP_PI). In time domain, for recordings including spontaneous changes in ICP greater than 7 mm Hg, nICP_PI showed the best correlation with measured ICP (R = 0.61). Considering every TCD recording as an independent event, nICP_BB generally showed to be the best estimator of measured ICP (R = 0.39; p < 0.05; 95% confidence interval [CI] = 9.94 mm Hg; area under the curve [AUC] = 0.66; p < 0.05). For nICP_FVd, although it presented similar correlation coefficient to nICP_BB and marginally better AUC (0.70; p < 0.05), it demonstrated a greater 95% CI for prediction of ICP (14.62 mm Hg). nICP_CrCP presented a moderate correlation coefficient (R = 0.35; p < 0.05) and similar 95% CI to nICP_BB (9.19 mm Hg), but failed to distinguish between normal and raised ICP (AUC = 0.64; p > 0.05). nICP_PI was not related to measured ICP using any of the above statistical indicators. We also introduced a new estimator (nICP_Av) based on the average of three methods (nICP_BB, nICP_FVd, and nICP_CrCP), which overall presented improved statistical indicators (R = 0.47; p < 0.05; 95% CI = 9.17 mm Hg; AUC = 0.73; p < 0.05). nICP_PI appeared to reflect changes in ICP in time most accurately. nICP_BB was the best estimator for ICP "as a number." nICP_Av demonstrated to improve the accuracy of measured ICP estimation.
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http://dx.doi.org/10.1089/neu.2015.4134DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4841086PMC
April 2016

Richards-like two species population dynamics model.

Theory Biosci 2014 Dec 13;133(3-4):135-43. Epub 2014 Aug 13.

Departamento de Ciências Exatas (DEX), Universidade Federal de Lavras (UFLA), Caixa Postal 3037, Lavras, Minas Gerais, Brazil,

The two-species population dynamics model is the simplest paradigm of inter- and intra-species interaction. Here, we present a generalized Lotka-Volterra model with intraspecific competition, which retrieves as particular cases, some well-known models. The generalization parameter is related to the species habitat dimensionality and their interaction range. Contrary to standard models, the species coupling parameters are general, not restricted to non-negative values. Therefore, they may represent different ecological regimes, which are derived from the asymptotic solution stability analysis and are represented in a phase diagram. In this diagram, we have identified a forbidden region in the mutualism regime, and a survival/extinction transition with dependence on initial conditions for the competition regime. Also, we shed light on two types of predation and competition: weak, if there are species coexistence, or strong, if at least one species is extinguished.
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http://dx.doi.org/10.1007/s12064-014-0205-zDOI Listing
December 2014

Generalized Allee effect model.

Theory Biosci 2014 Jun 17;133(2):117-24. Epub 2014 Mar 17.

Faculdade de Filosofia, Ciências e Letras de Ribeirão Preto (FFCLRP), Universidade de São Paulo (USP), Avenida dos Bandeirantes, 3900, 14.040-901, Ribeirão Preto, SP, Brazil,

The Allee effect consists of a positive correlation between very small population size and fitness. Offering a new view point on the weak and strong demographic Allee effect, we propose to combine them with the Richards growth model. In particular, a peculiar manifestation of the Allee effect is analytically predicted and still not validated by experiments. Model validation with ecological data is presented for some special situations.
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http://dx.doi.org/10.1007/s12064-014-0199-6DOI Listing
June 2014

Data collapse, scaling functions, and analytical solutions of generalized growth models.

Phys Rev E Stat Nonlin Soft Matter Phys 2011 Jun 2;83(6 Pt 1):061902. Epub 2011 Jun 2.

Departamento de Física, Faculdade de Filosofia, Ciências e Letras de Ribeirão Preto, Universidade de São Paulo, Ribeirão Preto, São Paulo, Brazil.

We consider a nontrivial one-species population dynamics model with finite and infinite carrying capacities. Time-dependent intrinsic and extrinsic growth rates are considered in these models. Through the model per capita growth rate we obtain a heuristic general procedure to generate scaling functions to collapse data into a simple linear behavior even if an extrinsic growth rate is included. With this data collapse, all the models studied become independent from the parameters and initial condition. Analytical solutions are found when time-dependent coefficients are considered. These solutions allow us to perceive nontrivial transitions between species extinction and survival and to calculate the transition's critical exponents. Considering an extrinsic growth rate as a cancer treatment, we show that the relevant quantity depends not only on the intensity of the treatment, but also on when the cancerous cell growth is maximum.
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http://dx.doi.org/10.1103/PhysRevE.83.061902DOI Listing
June 2011
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