Narrow Results

Diffusion is an essential component of gas exchange at the cellular and tissue level, and a mathematical analysis of diffusion is therefore important to model biological processes in many systems. When several factors affect diffusion, finding an explicit non-steady-state equation can be difficult or impossible. In an earlier work (J Biol Systems15:63–72), we described such a function for a system where oxygen diffuses from the air into a body that consumes oxygen, assuming that the exchange surface is flat. Here, an explicit solution is limited to the case where tissue oxygen consumption decreases linearly with oxygen concentration and reaches 0 only when all oxygen has been consumed. The objective of this article is the analysis of gas diffusion into a respiring tissue that is cylindrical, which applies to tree stems and is a more realistic approximation for many other organs. This approach differs from diffusion along a flat surface, resulting in formally completely different explicit solutions, and is more flexible allowing for different relationships between oxygen concentration and tissue oxygen consumption.

The respiratory system of mammalians is made of two successive branched structures with different physiological functions. The upper structure, or bronchial tree, is a fluid transportation system made of approximately 15 generations of bifurcations leading to the order of 2¹⁵ = 30,000 bronchioles with a diameter of order 0.5 mm in the human lung.¹ The branching pattern continues up to generation 23 but the structure and function of each of the subsequent structures, called the acini, is different. Each acinus is made of a branched system of ducts surrounded by alveolae and play the role of a diffusion cell where oxygen and carbon dioxide are exchanged with blood across the alveolar membrane.² We show in this paper that the bronchial tree presents simultaneously several optimal properties of totally different nature. It is first energy efficient;^3-6 second, it is space filling;⁷ and third it is "rapid" as discussed here. It is this multi-optimality that is qualified here as magic. The multi-optimality physical characteristic suggests that, in the course of evolution, an organ selected against one criterion could have been later used for a totally different reason. For example, once energetic efficiency for the transport of a viscous fluid like blood has been selected, the same genetic material could have been used for its optimized rapidity. This would have allowed the emergence of mammalian respiration made of inspiration–expiration cycles. For this phenomenon to exist, the rapid character is essential, as fresh air has to reach the gas exchange organs, the pulmonary acini, before the start of expiration.

An important challenge in respiration related studies is to investigate the influence of external stimuli on human respiration. Auditory stimulus is an important type of stimuli that influences human respiration. However, no one discovered any trend, which relates the characteristics of the auditory stimuli to the characteristics of the respiratory signal. In this paper, we investigate the correlation between auditory stimuli and respiratory signal from fractal point of view. We found out that the fractal structure of respiratory signal is correlated with the fractal structure of the applied music. Based on the obtained results, the music with greater fractal dimension will result in respiratory signal with smaller fractal dimension. In order to verify this result, we benefit from approximate entropy. The results show the respiratory signal will have smaller approximate entropy by choosing the music with smaller approximate entropy. The method of analysis could be further investigated to analyze the variations of different physiological time series due to the various types of stimuli when the complexity is the main concern.

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Flow visualization in reciprocating flow inside branching tubes was performed to investigate the mechanism of axial gas exchange in the human lung system. A bronchial tube model is employed which is geometrically similar to the average human lung system. Water is used as the working fluid. The ranges of Reynolds and Womersley numbers in the present study correspond to those of normal human respiration and HFV (high frequency ventilation), respectively. It is revealed that the axial gas exchange phenomenon occurring in the human lung system is governed by a "trap-and-release" mechanism caused by the formation-and-destruction of the separation regions, which are formed on the wall of the parent tube and or daughter tubes, depending on the direction of the reciprocating flow.

Motivation: Living systems have a complex hierarchical organization that can be viewed as a set of dynamically interacting subsystems. Thus, to simulate the internal nature and dynamics of the entire biological system, we should use the iterative way for a model reconstruction, which is a consistent composition and combination of its elementary subsystems. In accordance with this bottom-up approach, we have developed the MAthematical Models of bioMOlecular sysTems (MAMMOTh) tool that consists of the database containing manually curated MAMMOTh fitted to the experimental data and a software tool that provides their further integration.

Results: The MAMMOTh database entries are organized as building blocks in a way that the model parts can be used in different combinations to describe systems with higher organizational level (metabolic pathways and/or transcription regulatory networks). The tool supports export of a single model or their combinations in SBML or Mathematica standards. The database currently contains 110 mathematical sub-models for Escherichia coli elementary subsystems (enzymatic reactions and gene expression regulatory processes) that can be combined in at least 5100 complex/sophisticated models concerning more complex biological processes as de novo nucleotide biosynthesis, aerobic/anaerobic respiration and nitrate/nitrite utilization in E. coli. All models are functionally interconnected and sufficiently complement public model resources.

Availability: http://mammoth.biomodelsgroup.ru

To investigate whether the first intrinsic mode function, obtained from Hilbert–Huang transform (HHT), of heart rate variability is respiratory related. Electrocardiogram and chest circumference signals were recorded from 10 healthy subjects at supine rest. The HHT was applied to both R-R interval and chest circumference signals to figure out their first intrinsic mode functions (C1_RR and C1_RESP, respectively) from which the instantaneous amplitude, phase, and frequency were calculated. Although the instantaneous amplitudes and frequencies of C1_RR and C1_RESP were variable, linear regression analysis indicated a phase lock between C1_RR and C1_RESP. Intake of 500 ml water significantly elevated the amplitude ratio of C1_RR to C1_RESP; however, the phase difference of C1_RR to C1_RESP was still unchanged. The data indicate that the first intrinsic mode function of heart rate variability is respiratory related and may be equivalent to respiratory sinus arrhythmia. As compared to fast Fourier transform, HHT of respiratory sinus arrhythmia provides a comparative spatial measurement with a much higher temporal resolution.

To estimate the respiration-induced dosimetric change at beam edge during a beam-on interval of radiotherapy, by the integration of a mathematical model for organ motion and a modeled beam profile. A method is proposed which incorporated the effects of intra-treatment organ motion due to breathing on the dosimetric change for the treatment of liver cancer. The basic algorithm was to assume the motion of infra-abdominal organs was predominantly in the superior-inferior (S-I) direction. The starting phase was defined as the mid-phase at exhale, to reproduce the same situation of computed tomography simulation for liver cancer. The S-I extent of motion was defined as 1.5cm. The period of a breathing cycle was defined as 4.2 seconds. The shape parameter of the respiratory model was defined as 3. The radiation dose of 100 cGy given with the rate of 300 MU/minute was designed for the model analysis. The position at the beam edge as a function of time could be parameterized for a 10cm x 10cm field with a setup of SAD 100cm. The dose profiles of both 6MV and 18MV photons were applied for the dosimetric calculation of the beam-edge point during the dynamic movement in a beam-on time interval of radiotherapy. The point doses at the superior beam edge for 6MV photons and18MV photons during a beam-one interval of 22.8 seconds were 73.5% and 77.2% of the isocenter dose, respectively. The point doses at the inferior beam edge for the two energies were 31.2% and 32.4%, respectively. There were 147-154% dose increase for superior beam edge and 62.4-64.8% dose decrease for inferior beam edge, as compared to the 50% isocenter dose with the static dose distribution. It is simple and feasible to use the mathematical model to estimate the dosimetric change of the intra-abdominal organ motion from respiration. The impact of respiration on the dosimetric difference deserves more attention in the prescription of radiation treatment. Further measurement of the exact organ motion during the real treatment is warranted to optimize the model.

Purpose: This paper presented a new approach to noninvasively evaluate the upper airway stenosis for obstructive sleep apnea syndrome (OSAS) patients. Methods: In the proposed method, thoracic and abdominal movements were selected to calculate the respiratory movement (RM) and to indicate the change of lung volume. Due to the cumulative effect of thermal sensor, the oronasal-thermistor signal (T_flow) is applied to estimate the air mass change in lung. Based on the mathematical relationship, the “RM–T_flow curves”, drawn by RM and T_flow, together with the correlation coefficients ($r_{\mathrm{\text{RM}}\text{-}\mathrm{\text{TF}}})$ were used to analyze the upper airway stenosis. Results: This method was verified through portable monitoring (PM) based experiments, and numerical analysis of the polysomnography (PSG) data from 20 OSAS patients and 15 non-OSAS controls. Our results indicate the $r_{\mathrm{\text{RM}}\text{-}\mathrm{\text{TF}}}$ values decrease with the narrowing of the upper airway. At each sleep stage, the $r_{\mathrm{\text{RM}}\text{-}\mathrm{\text{TF}}}$ mean values of OSAS subjects are significantly ($p<0.01$) smaller than those of the controls. These facts demonstrate that the $r_{\mathrm{\text{RM}}\text{-}\mathrm{\text{TF}}}$ value can be used to quantify the upper airway stenosis and the analysis of “RM–T_flow curves” is an efficient way to assess upper airway condition associated with the breathing phase. Conclusions: As this method can be used in spontaneous sleep and home sleep testing, we believe it will benefit the popularity of the diagnosis and evaluation of OSAS.

Metabolism is one of the best studied fields of biochemistry, but its regulation involves processes on many different levels, some of which are still not understood well enough to allow for quantitative modeling and prediction. Glycolysis in yeast is a good example: although high-quality quantitative data are available, well-established mathematical models typically only cover direct regulation of the involved enzymes by metabolite binding. The effect of various metabolites on the enzyme kinetics is summarized in carefully developed mathematical formulae. However, this approach implicitly assumes that the enzyme concentrations themselves are constant, thus neglecting other regulatory levels – e.g. transcriptional and translational regulation – involved in the regulation of enzyme activities. It is believed, however, that different experimental conditions result in different enzyme activities regulated by the above mechanisms. Detailed modeling of all regulatory levels is still out of reach since some of the necessary data – e.g. quantitative large scale enzyme concentration data sets – are lacking or rare. Nevertheless, a viable approach is to include the regulation of enzyme concentrations into an established model and to investigate whether this improves the predictive capabilities. Proteome data are usually hard to obtain, but levels of mRNA transcripts may be used instead as clues for changes in enzyme concentrations. Here we investigate whether including mRNA data into an established model of yeast glycolysis allows to predict the steady state metabolic concentrations for different experimental conditions. To this end, we modified an established ODE model for the glycolytic pathway of yeast to include changes of enzyme concentrations. Presumable changes were inferred from mRNA transcript level measurement data. We investigate how this approach can be used to predict metabolite concentrations for steady-state yeast cultures at five different oxygen levels ranging from anaerobic to fully aerobic conditions. We were partly able to reproduce the experimental data and present a number of changes that were necessary to improve the modeling result.

The following sections are included:

• Summary

• Introduction

• Opportunities for Mitochondrial Therapeutics

• Acknowledgments

• References