Physiologic time: A hypothesis

The Relevance of Time in Biological Scaling

Various phenotypic traits relate to the size of a living system in regular but often disproportionate (allometric) ways. These "biological scaling" relationships have been studied by biologists for over a century, but their causes remain hotly debated. Here, I focus on the patterns and possible causes of the body-mass scaling of the rates/durations of various biological processes and life-history events, i.e., the "pace of life". Many biologists have regarded the rate of metabolism or energy use as the master driver of the "pace of life" and its scaling with body size. Although this "energy perspective" has provided valuable insight, here I argue that a "time perspective" may be equally or even more important. I evaluate various major ways that time may be relevant in biological scaling, including as (1) an independent "fourth dimension" in biological dimensional analyses, (2) a universal "biological clock" that synchronizes various biological rates/durations, (3) a scaling method that uses various biological time periods (allochrony) as scaling metrics, rather than various measures of physical size (allometry), as traditionally performed, (4) an ultimate body-size-related constraint on the rates/timing of biological processes/events that is set by the inevitability of death, and (5) a geological "deep time" approach for viewing the evolution of biological scaling patterns. Although previously proposed universal four-dimensional space-time and "biological clock" views of biological scaling are problematic, novel approaches using allochronic analyses and time perspectives based on size-related rates of individual mortality and species origination/extinction may provide new valuable insights.

Non-Local Kinetics: Revisiting and Updates Emphasizing Fractional Calculus Applications

Non-local kinetic problems spanning a wide area of problems where fractional calculus is applicable have been analyzed. Classical fractional kinetics based on the Continuum Time Random Walk diffusion model with the absence of stationary states, real-world problems from pharmacokinetics, and modern material processing have been reviewed. Fractional allometry has been considered a potential area of application. The main focus in the analysis has been paid to the memory functions in the convolution formulation, crossing from the classical power law to versions of the Mittag-Leffler function. The main idea is to revisit the non-local kinetic problems with an update updating on new issues relevant to new trends in fractional calculus.

Sir Isaac Newton Stranger in a Strange Land

The theme of this essay is that the time of dominance of Newton's world view in science is drawing to a close. The harbinger of its demise was the work of Poincaré on the three-body problem and its culmination into what is now called chaos theory. The signature of chaos is the sensitive dependence on initial conditions resulting in the unpredictability of single particle trajectories. Classical determinism has become increasingly rare with the advent of chaos, being replaced by erratic stochastic processes. However, even the probability calculus could not withstand the non-Newtonian assault from the social and life sciences. The ordinary partial differential equations that traditionally determined the evolution of probability density functions (PDFs) in phase space are replaced with their fractional counterparts. Allometry relation is proven to result from a system's complexity using exact solutions for the PDF of the Fractional Kinetic Theory (FKT). Complexity theory is shown to be incompatible with Newton's unquestioning reliance on an absolute space and time upon which he built his discrete calculus.

Fractal Modeling and Fractal Dimension Description of Urban Morphology

The conventional mathematical methods are based on characteristic length, while urban form has no characteristic length in many aspects. Urban area is a scale-dependence measure, which indicates the scale-free distribution of urban patterns. Thus, the urban description based on characteristic lengths should be replaced by urban characterization based on scaling. Fractal geometry is one powerful tool for the scaling analysis of cities. Fractal parameters can be defined by entropy and correlation functions. However, the question of how to understand city fractals is still pending. By means of logic deduction and ideas from fractal theory, this paper is devoted to discussing fractals and fractal dimensions of urban landscape. The main points of this work are as follows. Firstly, urban form can be treated as pre-fractals rather than real fractals, and fractal properties of cities are only valid within certain scaling ranges. Secondly, the topological dimension of city fractals based on the urban area is 0; thus, the minimum fractal dimension value of fractal cities is equal to or greater than 0. Thirdly, the fractal dimension of urban form is used to substitute the urban area, and it is better to define city fractals in a two-dimensional embedding space; thus, the maximum fractal dimension value of urban form is 2. A conclusion can be reached that urban form can be explored as fractals within certain ranges of scales and fractal geometry can be applied to the spatial analysis of the scale-free aspects of urban morphology.

Effects of Protective Mechanical Ventilation With Different PEEP Levels on Alveolar Damage and Inflammation in a Model of Open Abdominal Surgery: A Randomized Study in Obese Versus Non-obese Rats

Intraoperative positive end-expiratory pressure (PEEP) has been proposed to restore lung volumes and improve respiratory function in obesity. However, the biological impact of different PEEP levels on the lungs in obesity remains unknown. We aimed to compare the effects of PEEP = 2 cmH₂O versus PEEP = 6 cmH₂O during ventilation with low tidal volumes on lung function, histology, and biological markers in obese and non-obese rats undergoing open abdominal surgery. Forty-two Wistar rats (21 obese, 21 non-obese) were anesthetized and tracheotomized, and laparotomy was performed with standardized bowel manipulation. Rats were randomly ventilated with protective tidal volume (7 ml/kg) at PEEP = 2 cmH₂O or PEEP = 6 cmH₂O for 4 h, after which they were euthanized. Lung mechanics and histology, alveolar epithelial cell integrity, and biological markers associated with pulmonary inflammation, alveolar stretch, extracellular matrix, and epithelial and endothelial cell damage were analyzed. In obese rats, PEEP = 6 cmH₂O compared with PEEP = 2 cmH₂O was associated with less alveolar collapse (p = 0.02). E-cadherin expression was not different between the two PEEP groups. Gene expressions of interleukin (IL)-6 (p = 0.01) and type III procollagen (p = 0.004), as well as protein levels of tumor necrosis factor-alpha (p = 0.016), were lower at PEEP = 6 cmH₂O than at PEEP = 2 cmH₂O. In non-obese animals, PEEP = 6 cmH₂O compared with PEEP = 2 cmH₂O led to increased hyperinflation, reduced e-cadherin (p = 0.04), and increased gene expression of IL-6 (p = 0.004) and protein levels of tumor necrosis factor-alpha (p-0.029), but no changes in fibrogenesis. In conclusion, PEEP = 6 cmH₂O reduced lung damage and inflammation in an experimental model of mechanical ventilation for open abdominal surgery, but only in obese animals.

Practicalities of Total Intravenous Anesthesia and Target-controlled Infusion in Children

Propofol administered in conjunction with an opioid such as remifentanil is used to provide total intravenous anesthesia for children. Drugs can be given as infusion controlled manually by the physician or as automated target-controlled infusion that targets plasma or effect site. Smart pumps programmed with pharmacokinetic parameter estimates administer drugs to a preset plasma concentration. A linking rate constant parameter (keo) allows estimation of effect site concentration. There are two parameter sets, named after the first author describing them, that are commonly used in pediatric target-controlled infusion for propofol (Absalom and Kataria) and one for remifentanil (Minto). Propofol validation studies suggest that these parameter estimates are satisfactory for the majority of children. Recommended target concentrations for both propofol and remifentanil depend on the type of surgery, the degree of surgical stimulation, the use of local anesthetic blocks, and the ventilatory status of the patient. The use of processed electroencephalographic monitoring is helpful in pediatric total intravenous anesthesia and target-controlled infusion anesthesia, particularly in the presence of neuromuscular blockade.

Propofol pharmacokinetic and pharmacodynamic profile and its electroencephalographic interaction with remifentanil in children

BACKGROUND

Propofol and remifentanil are commonly combined during total intravenous anesthesia. The impact of remifentanil in this relationship is poorly quantified in children. Derivation of an integrated pharmacokinetic and pharmacodynamic propofol model, containing remifentanil pharmacodynamic interaction information, enables propofol effect-site target-controlled infusion in children with a better prediction of its hypnotic effect when both drugs are combined.

AIMS

We designed this study to derive an integrated propofol pharmacokinetic-pharmacodynamic model in children and to describe the pharmacodynamic interaction between propofol and remifentanil on the electroencephalographic bispectral index effect.

METHODS

Thirty children (mean age: 5.45 years, range 1.3-11.9; mean weight: 23.5 kg, range 8.5-61) scheduled for elective surgery with general anesthesia were studied. After sevoflurane induction, maintenance of anesthesia was based on propofol and remifentanil. Blood samples to measure propofol concentration were collected during anesthesia maintenance and up to 6 hours in the postoperative period. Bispectral index data were continuously recorded throughout the study. A pharmacokinetic-pharmacodynamic model was developed using population modeling. The Greco model was used to examine the pharmacokinetic-pharmacodynamic interaction between propofol and remifentanil for BIS response RESULTS: Propofol pharmacokinetic data from a previous study in 53 children were pooled with current data and simultaneously analyzed. Propofol pharmacokinetics were adequately described by a three-compartment distribution model with first-order elimination. Theory-based allometric relationships based on TBW improved the model fit. The Greco model supported an additive interaction between propofol and remifentanil. Remifentanil showed only a minor effect in BIS response.

CONCLUSION

We have developed an integrated propofol pharmacokinetic-pharmacodynamic model that can describe the pharmacodynamic interaction between propofol and remifentanil for BIS response. An additive interaction was supported by our modeling analysis.

Modeling the pharmacokinetics and pharmacodynamics of sevoflurane using compartment models in children and adults

BACKGROUND

Sevoflurane pharmacokinetics have been traditionally described using physiological models, while pharmacodynamics employed the use of minimal alveolar concentration.

AIMS

The integrated pharmacokinetic-pharmacodynamic relationship of sevoflurane in both adults and children was reviewed using compartment models. We wished to delineate age-related changes in both pharmacokinetics and pharmacodynamics.

METHODS

The bispectral index and sevoflurane endtidal concentration were continuously measured in 50 patients, aged 3-71 years, scheduled for minor surgery. During maintenance of anesthesia and after stable bispectral index values of 60-65 were obtained, the inspired concentration of sevoflurane was increased to 5 vol % for 5 minutes or until BIS 40 and then decreased. Data were analyzed using mammillary compartments with nonlinear mixed effects population modeling. The covariate effects of age and size were investigated.

RESULTS

A three-compartment PK model adequately described sevoflurane pharmacokinetics. Size standardization using allometry explained clearance and volume changes with age. The equilibration half-time (1.48 minutes) increased with age, but could be predicted using allometry in those under 40 years. The effect site concentration eliciting half the maximum response at age 40 years was 1.3% (95%CI 1.22, 1.42) decreased with age from 1.6% at 3 years to 1.1% at 70 years.

CONCLUSION

Pharmacokinetic compartment models offer an alternative method to describe inhalation anesthetic drug disposition and effects.

Misconceptions and issues regarding allometric scaling during the drug development process

INTRODUCTION

Allometry is the study of size and its consequences. The simple hypothesis of allometric scaling is that all physiological parameters are proportional to body size or body mass. This review examines the development of theory-based allometry or fixed exponents (0.75 and 1.0 for basal metabolic rate and volume, respectively) and the evidence for or against the theory. The main focus of this report is to show the readers that there is enough evidence from experimental data that negate the concept of theory-based allometry in biology, physiology, and pharmacokinetics. Areas covered: In this review, the history of the development of theoretical allometry and the strong evidence against theory-based allometry demonstrated by experimental data is provided. During drug development, allometry is applied to both inter-species (from animals to humans) and intra-species (adults to children) scaling. These two forms of allometric scaling in the context of theory-based allometry are discussed and provide insight on scientific progress that refute theory-based allometry. Expert opinion: Theory-based allometry is a mere theory and experimental data and real-life observations strongly negate the existence of such a theory. Pharmacostatistical and physiological models based on theory-based allometry can be misleading and incorrect because the theory-based allometric exponent 0.75 is not universal. The exponents of allometry are data dependent and are not fixed in the universe.

Prediction of Clearance, Volume of distribution, and Half-life of Drugs in Extremely Low to Low Birth Weight Neonates: An Allometric Approach

BACKGROUND AND OBJECTIVES

More than 20 million infants worldwide (15.5 % of all births) are born with low birth weight. Low birth weight is associated with poor growth in childhood and a higher incidence of adult diseases, such as type 2 diabetes, hypertension and cardiovascular disease. The objective of this study was to evaluate the predictive performance of allometric models to predict clearance, volume of distribution, and half-life in extremely low to low birth weight neonates (<1 to 2.5 kg body weight).

METHODS

Several allometric models were used to predict clearance (4 models), volume of distribution (2 models), and half-life (2 models) in extremely low to low birth weight neonates. From the literature, clearance, volume of distribution, and half-life values for 16 drugs for these neonates were obtained. The predictive performance of these allometric models was evaluated by comparing the predicted values of the aforementioned pharmacokinetic parameters with the observed pharmacokinetic parameters in an individual neonate. For the evaluation of the predictive performance of these allometric models, there were 16 drugs with 36 (n = 279), 34 (n = 261), and 31 (n = 197) weight groups for clearance, volume of distribution, and half-life, respectively.

RESULTS

The prediction error of ≤50 % for mean clearance, volume of distribution, and half-life values were 69, 79, and 58 %, respectively, by proposed allometric models. The prediction error of ≤50 % for mean clearance, volume of distribution, and half-life values by theoretical allometric exponents were 0 % (exponent = 0.75), 71 % (exponent = 1.0), and 0 % (exponent = 0.25), respectively. In this analysis, out of 16 drugs, there were three drugs (ibuprofen, zidovudine, and buprenorphine) which are metabolized by glucuronidation and one drug (furosemide) is renally secreted. The predicted clearances of these four drugs were substantially higher by the proposed allometric methods. It seems that drugs of these physiological characteristics may require different method(s) to improve the prediction of clearance in the neonates.

CONCLUSIONS

Overall, the proposed allometric methods can predict mean pharmacokinetic parameters of drugs in extremely low to low birth weight neonates with reasonable accuracy and are of practical value during neonatal drug development.

Postoperative Delirium, Learning, and Anesthetic Neurotoxicity: Some Perspectives and Directions

Evidence of anesthetic neurotoxicity is unequivocal when studied in animal models. These findings have translated poorly to the clinical domain when equated to postoperative delirium (POD) in adults and postoperative cognitive dysfunction (POCD) in either children or the elderly. In this perspective, we examine various reasons for the differences between animal modeling of neurotoxicity and the clinical situation of POD and POCD and make suggestions as to potential directions for ongoing research. We hypothesize that the animal anesthetic neurotoxicity models are limited, in part, due to failed scaling correction of physiological time. We posit that important insights into POCD in children and adults may be gleaned from studies in adults examining alterations in perioperative management designed to limit POD. In this way, POD may be more useful as the proxy for POCD rather than neuronal dropout or behavioral abnormalities that have been used in animal models but which may not be proxies for the human condition. We argue that it is time to move beyond animal models of neurotoxicity to directly examine these problems in well-conducted clinical trials with comprehensive preoperative neuropsychometric and psychiatric testing, high fidelity intraoperative monitoring of physiological parameters during the anesthetic course and postoperative assessment of subthreshold and full classification of POD. In this manner, we can “model ourselves” to better understand these important and poorly understood conditions.

Prediction of Human Glomerular Filtration Rate from Preterm Neonates to Adults: Evaluation of Predictive Performance of Several Empirical Models

The objective of this study was to evaluate the predictive performance of several allometric empirical models (body weight dependent, age dependent, fixed exponent 0.75, a data-dependent single exponent, and maturation models) to predict glomerular filtration rate (GFR) in preterm and term neonates, infants, children, and adults without any renal disease. In this analysis, the models were developed from GFR data obtained from inulin clearance (preterm neonates to adults; n = 93) and the predictive performance of these models were evaluated in 335 subjects (preterm neonates to adults). The primary end point was the prediction of GFR from the empirical allometric models and the comparison of the predicted GFR with measured GFR. A prediction error within ±30% was considered acceptable. Overall, the predictive performance of the four models (BDE, ADE, and two maturation models) for the prediction of mean GFR was good across all age groups but the prediction of GFR in individual healthy subjects especially in neonates and infants was erratic and may be clinically unacceptable.

Considerations when using pharmacokinetic/pharmacodynamic modeling to determine the effectiveness of simple analgesics in children

INTRODUCTION

Assessment of analgesic drugs includes comparative studies to other analgesics and local anesthesia blockade, number needed to treat estimates and opioid sparing descriptions. An additional methodology is to define the concentration-response relationship using pharmacokinetic/pharmacodynamic (PK/PD) modeling.

AREAS COVERED

A concentration-response relationship allows analgesic effect comparison between drugs for different acute pain types. Covariates such as size, age and organ function impact greatly on PK in children. The cumulative effect of confounding factors (e.g., pharmacogenetics, placebo and changes in baseline pain over time) complicates PD. Other factors (outcome measures, method of measurement, failure to account for study attrition) impact on outcome. Population PK/PD modeling approaches allow us to account for these various factors to some extent.

EXPERT OPINION

Nonlinear mixed effects models help interpret analgesic data and their use is increasing. The PK is relatively well understood. The next investigative step will involve investigation into covariate effects for PD. Mathematical functions for both placebo models and dropout models are well described and should be incorporated into analgesic effectiveness studies that investigate a range of doses. Improvements in pain assessment tools and a greater understanding of pharmacogenomics factors will help individualize analgesic therapy.

Indexing cardiovascular and respiratory variables: allometric scaling principles

OBJECTIVES

To describe the allometric scaling principles underlying appropriate indexing of cardiovascular and respiratory measurements obtained in adult mammals, and to propose guidelines for indexing experimental cardiovascular and respiratory data.

DATABASE USED

PubMed, using the terms 'allometry', 'allometric', 'indexing', 'cardiovascular' and 'respiratory'.

CONCLUSIONS

Indexing of cardiopulmonary variables is commonly used in attempts to account for the effects of body size on measurements and to standardize them. Some cardiopulmonary variables have been indexed using various functions of body mass in a process that often ignores the underlying relationship between the variable of interest and body size, as described in the allometry literature. This can result in a failure to ideally reduce the effect of body size on measurements in a manner that highlights differences. We review how commonly measured cardiopulmonary variables are related to body mass in mammalian species according to the allometry literature, and offer suggestions on how this information can be used to appropriately index cardiopulmonary variables in a simple and informative manner.

Prediction of drug clearance in children: an evaluation of the predictive performance of several models

The objective of this study is to evaluate the predictive performance of several models to predict drug clearance in children ≤5 years of age. Six models (allometric model (data-dependent exponent), fixed exponent of 0.75 model, maturation model, body weight-dependent model, segmented allometric model, and age-dependent exponent model) were evaluated in this study. From the literature, the clearance values for six drugs from neonates to adults were obtained. External data were used to evaluate the predictive performance of these models in children ≤5 years of age. With the exception of a fixed exponent of 0.75, the mean predicted clearance in most of the age groups was within ≤50% prediction error. Individual clearance prediction was erratic by all models and cannot be used reliably to predict individual clearance. Maturation, body weight-dependent, and segmented allometric models to predict clearances of drugs in children ≤5 years of age are of limited practical value during drug development due to the lack of availability of data. Age-dependent exponent model can be used for the selection of first-in-children dose during drug development.