Gas Exchange Model Research Articles

A Numerical Model of the Respiratory Modulation of Pulmonary Shunt and PaO2 Oscillations for Acute Lung Injury

It is an accepted hypothesis that the amplitude of the respiratory-related oscillations of arterial partial pressure of oxygen (DeltaPaO2) is primarily modulated by fluctuations of pulmonary shunt (Deltas), the latter generated mainly by cyclic alveolar collapse/reopening, when present. A better understanding of the relationship between DeltaPaO2, Deltas, and cyclic alveolar collapse/reopening can have clinical relevance for minimizing the severe lung damage that the latter can cause, for example during mechanical ventilation (MV) of patients with acute lung injury (ALI). To this aim, we numerically simulated the effect of such a relationship on an animal model of ALI under MV, using a combination of a model of lung gas exchange during tidal ventilation with a model of time dependence of shunt on alveolar collapse/opening. The results showed that: (a) the model could adequately replicate published experimental results regarding the complex dependence of DeltaPaO2 on respiratory frequency, driving pressure (DeltaP), and positive end-expiratory pressure (PEEP), while simpler models could not; (b) such a replication strongly depends on the value of the model parameters, especially of the speed of alveolar collapse/reopening; (c) the relationship between DeltaPaO2 and Deltas was overall markedly nonlinear, but approximately linear for PEEP>or=6 cmH2O, with very large DeltaPaO2 associated with relatively small Deltas.

A simplified method for deriving shunt and reduced VA/Q in infants

Background:Right to left shunt and regional hypoventilation (reduced ventilation/perfusion ratio (VA/Q)) have different effects on the curve relating inspired oxygen (PIO2) to oxygen saturation measured by pulse oximetry (SpO2) and...

Modelling basin-wide variations in Amazon forest productivity – Part 1: Model calibration, evaluation and upscaling functions for canopy photosynthesis

Abstract. Given the importance of Amazon rainforest in the global carbon and hydrological cycles, there is a need to parameterize and validate ecosystem gas exchange and vegetation models for this region in order to adequately simulate present and future carbon and water balances. In this study, a sun and shade canopy gas exchange model is calibrated and evaluated at five rainforest sites using eddy correlation measurements of carbon and energy fluxes. Results from the model-data evaluation suggest that with adequate parameterisation, photosynthesis models taking into account the separation of diffuse and direct irradiance and the dynamics of sunlit and shaded leaves can accurately represent photosynthesis in these forests. Also, stomatal conductance formulations that only take into account atmospheric demand fail to correctly simulate moisture and CO2 fluxes in forests with a pronounced dry season, particularly during afternoon conditions. Nevertheless, it is also the case that large uncertainties are associated not only with the eddy correlation data, but also with the estimates of ecosystem respiration required for model validation. To accurately simulate Gross Primary Productivity (GPP) and energy partitioning the most critical parameters and model processes are the quantum yield of photosynthetic uptake, the maximum carboxylation capacity of Rubisco, and simulation of stomatal conductance. Using this model-data synergy, we developed scaling functions to provide estimates of canopy photosynthetic parameters for a range of diverse forests across the Amazon region, utilising the best fitted parameter for maximum carboxylation capacity of Rubisco, and foliar nutrients (N and P) for all sites.

Electric analogue for the dynamics of decompression sickness bubbles: Numerical results

Since the development of the first decompression tables in 1908 by Boycott, Damant and Haldane, considerable research and effort have been expended in the development of safer and more rapid decompression procedures and tables. The models for gas exchange have been principally empirical and provide “safe” decompression only over a limited range of depth and bottom times. In this work a numerical method based on an electrical analogy is used to solve the system of equations simulating the growth and decay dynamics of decompression bubbles. The numerical procedure employed, which satisfies the conservation law for the flux variable and the uniqueness law for voltages, also permits the direct visualisation of the evolution of the local and/or integrated transport variables at any point or section of the medium.

Computational modeling of flow and gas exchange in models of the human maxillary sinus

The present study uses numerical modeling to increase the understanding of sinus gas exchange, which is thought to be a factor in sinus disease. Order-of-magnitude estimates and computational fluid dynamics simulations were used to investigate convective and diffusive transport between the nose and the sinus in a range of simplified geometries. The interaction between mucociliary transport and gas exchange was modeled and found to be negligible. Diffusion was the dominant transport mechanism for small ostia and large concentration differences between the sinus and the nose, whereas convection was important for larger ostia or smaller concentration differences. The presence of one or more accessory ostia can increase the sinus ventilation rate by several orders of magnitude, because it allows a net flow through the sinus. Estimates of nitric oxide (NO) transport through the ostium based on measured sinus and nasal NO concentrations suggest that the sinuses cannot supply all the NO in nasally exhaled air.

Gross primary production simulation in a coniferous forest using a daily gas exchange model with seasonal change of leaf physiological parameters derived from remote sensing data

The importance of including the seasonal changes of canopy physiology in carbon balance simulation models was emphasized in earlier research. This paper proposes a new approach to combine the commonly available Normalized Difference Vegetation Index (NDVI) to derive the seasonal changes of canopy physiology with a modified daily step gas exchange model to simulate the gross primary production (GPP) in a coniferous forest stand. For validation, four years (1997–2000) of continuous time‐series data for GPP were derived using the observations of net ecosystem carbon dioxide exchange obtained with eddy covariance techniques. A variety of scenarios were designed to simulate the GPP with the daily model and the results (1) reaffirm the importance of including seasonal changes of canopy physiology in the carbon balance model; (2) demonstrate the feasibility of deriving the seasonal change information of canopy physiology from NDVI time‐series; (3) show the importance of the quality of NDVI time‐series. The results suggest that the daily model can be linked with remote sensing data, which provides information on the seasonal changes of canopy physiology, and can be an efficient tool for regional carbon balance simulation.

Multiscale modelling of gas exchange in fruit tissues

Multiscale modelling of gas exchange in fruit tissues

A quantitative approach to developing more mechanistic gas exchange models for field grown potato: A new insight into chemical and hydraulic signalling

In this study we introduce new gas exchange models that are developed under natural conditions of field grown potato. The new models could explain about 85% of the stomatal conductance variations, which was much higher than the well-known gas exchange models such as the Ball-Berry model [Ball, Woodrow, Berry, 1987. In: Nijhoff, M. (Eds.), Progress in Photosynthesis Research, vol. 4. Dordrecht, The Netherlands, pp. 5.221–5.224]. To overcome the limitations of previous models in simulating stomatal conductance when plants are exposed to drought stress, we proposed a down-regulating factor of chemical and hydraulic signalling on stomatal conductance as exp(− β[ABA])exp(− δ| ψ|) in which [ABA] and | ψ| are xylem ABA concentration and absolute value of leaf or stem water potential. In this study we found that stem water potential could be a very reliable indicator of how plant water status affects the stomatal conductance regulation. While previous models considered the same weighting for relative humidity and photosynthesis rate, we found that relative humidity has a more pronounced regulating effect on stomatal conductance than photosynthesis rate and the weightings for relative humidity and photosynthesis rate, respectively, were significantly higher and lower than unity.

Modelling the level of the major glucosinolates in broccoli as affected by controlled atmosphere and temperature

This study describes the effects of controlled atmosphere (CA) and temperature on glucosinolate (GLS) levels in broccoli. Gas exchange rates were measured in three climate rooms with twelve containers each holding 20 randomly selected broccoli (cv ‘1997’) taken from one large batch of broccoli during a three-week period. Broccoli heads were stored at three temperatures and subjected to four levels of O 2 and three levels of CO 2. GLS were measured on individual broccoli heads using a HPLC-based protocol. Information about the GLS development over time was extracted by analysing ‘replicate’ broccoli containers (containers stored at the same temperature and gas conditions) that were removed periodically during the storage period. The most striking feature was the large variation in GLS concentrations at harvest with the propagation of variation over time clearly affected by CA and temperature. Decay of the four most important GLS over time was described by a sigmoid model based on the decompartmentalisation of the enzyme myrosinase that hydrolyses GLS. Gas exchange parameters were estimated using the standard gas exchange model; the parameters of the GLS decay were estimated using a batch model that describes the propagation of the GLS variation as function of O 2, CO 2, time, temperature, the average biological age and biological variation ( R adj 2 88%). This approach was used to study the effect of regular and modified atmosphere conditions on GLS keeping quality. Storage under regular atmosphere during chain simulation showed that the keeping quality for all four GLS is between four and seven days, while storage under 1.5 kPa O 2 and 15 kPa CO 2 showed a keeping quality of at least 14 d, indicating that to preserve the nutritional quality of broccoli, MA packaging is a viable option.

Integrating effects of leaf nitrogen, age, rank, and growth temperature into the photosynthesis-stomatal conductance model LEAFC3-N parameterised for barley ( Hordeum vulgare L.)

A crucial challenge for including biophysical photosynthesis–transpiration models into complex crop growth models is to integrate the plasticity of photosynthetic processes that is related to factors like nitrogen (N) content, age, and rank of leaves, or to the adaptation of plants to growth temperature ( T g). Here we present a new version of the combined photosynthesis-stomatal conductance model LEAFC3-N [Müller, J., Wernecke, P., Diepenbrock, W., 2005. LEAFC3-N: a nitrogen sensitive extension of the CO 2 and H 2O gas exchange model LEAFC3 parameterised and tested for winter wheat ( Triticum aestivum L.). Ecological Modelling 183, 183–210.] that was revised, extended and completely re-parameterised for barley ( Hordeum vulgare L.) with special regard for these factors to facilitate the use of the model in ecophysiological studies and in crop modelling. The analysis is based on novel comprehensive data on photosynthetic CO 2 and light response curves measured at two oxygen concentrations and different temperatures on leaves of barley ( H. vulgare L.) differing in leaf N and chlorophyll content. Plants were grown in climatic chambers or in the field at different N and T g. We thoroughly revised the existing and introduced new nitrogen relations for key model parameters that account for a linear increase with leaf N of V max, J max, T p, and R dmax (maximum rates of carboxylation, electron transport, triose phosphate export, and mitochondrial respiration), a saturation-type increase of φ (quantum yield of electron transport), and a non-linear decrease of θ and m (curvature of the light dependence of electron transport rate, scaling factor of the stomata model). The adaptation of photosynthetic characteristics to T g was included into the model by linear relations that were observed between T g and the activation energy Δ H a of the temperature response characteristics of V max, J max, and T p as well as of the nitrogen dependency of these characteristics. Based on an analysis of diurnal time courses of gas exchange rates it was found necessary including not only the relation between leaf water potential ( Ψ) and stomatal conductance as used originally in LEAFC3, but additional effects on V max and J max. With the above-listed extensions, the model was capable to reproduce the observed plasticity and the recorded diurnal time courses of gas exchange rates fairly well. Thus, we conclude that the new model version can be used under a broad range of conditions, both for ecophysiological studies and as a submodel of crop growth models. The results presented here for barley will facilitate adapting photosynthesis models like LEAFC3-N to other C 3-species as well. The modelling of the effects of drought stress should be further elaborated in future based on more specific experiments.

Functional–structural plant modelling in crop production. Wageningen UR Frontis Series, vol. 22

Functional–structural plant modelling in crop production. Wageningen UR Frontis Series, vol. 22

An optimality‐based model of the dynamic feedbacks between natural vegetation and the water balance

The hypothesis that vegetation adapts optimally to its environment gives rise to a novel framework for modeling the interactions between vegetation dynamics and the catchment water balance that does not rely on prior knowledge about the vegetation at a particular site. We present a new model based on this framework that includes a multilayered physically based catchment water balance model and an ecophysiological gas exchange and photosynthesis model. The model uses optimization algorithms to find those static and dynamic vegetation properties that would maximize the net carbon profit under given environmental conditions. The model was tested at a savanna site near Howard Springs (Northern Territory, Australia) by comparing the modeled fluxes and vegetation properties with long‐term observations at the site. The results suggest that optimality may be a useful way of approaching the prediction and estimation of vegetation cover, rooting depth, and fluxes such as transpiration and CO2 assimilation in ungauged basins without model calibration.

Methane in the Changjiang (Yangtze River) Estuary and its adjacent marine area: riverine input, sediment release and atmospheric fluxes

Dissolved methane (CH4) was measured in the waters of the Changjiang (Yangtze River) Estuary and its adjacent marine area during five surveys from 2002 to 2006. Dissolved CH4 concentrations ranged from 2.71 to 89.2 nM and had seasonal variation with the highest values occurring in summer and lowest in autumn. The horizontal distribution of dissolved CH4 decreased along the freshwater plume from the river mouth to the open sea. Dissolved CH4 in surface waters of the Changjiang was observed monthly at the most downstream main channel station Xuliujing (121o2′E, 31o46′N), which ranged from 16.2 to 126.2 nM with an average of 71.6 ± 36.3 nM. The average annual input of CH4 from the Changjiang to the Estuary and its adjacent area was estimated to be 2.24 mol s−1 equal to 70.6 × 106 mol year−1. Mean CH4 emission rate from the sediments of the Changjiang Estuary in spring was 1.97 μmol m−2 day−1, but it may be higher in summer due to hypoxia in the bottom waters and higher temperatures. The annual sea to air CH4 fluxes from the Changjiang Estuary and its adjacent marine area were estimated to be 61.4 ± 22.6 and 16.0 ± 6.1 μmol m−2 day−1, respectively, using three different gas exchange models. Hence the Changjiang Estuary and its adjacent marine area are net sources of atmospheric CH4.

Development of colour of broccoli heads as affected by controlled atmosphere storage and temperature

Colour is one of the most important quality attributes of broccoli. Yellowing due to senescence of broccoli florets is the main external quality problem. Controlled atmosphere (CA) storage is a very effective method to maintain broccoli quality. The aim of this paper is to characterise the colour behaviour (measured by RGB colour image analysis) of broccoli as affected by CA and temperature. Data on colour behaviour and gas exchange were gathered for broccoli heads stored in containers at three temperatures and subjected to four levels of O 2 and three levels of CO 2 concentrations. An integrated colour model is proposed that combines a colour model with a standard gas exchange model. The colour model is based on an existing colour model that describes the formation of (blue/green) chlorophyllide from the colourless precursor, the bidirectional conversion of chlorophyllide into (blue/green) chlorophyll and the decay of chlorophyllide. A multi-response approach was applied, accounting for 92% of the variance. Gas exchange parameters were estimated using the gas exchange model, the colour parameters were estimated using the colour model. Both models are linked via the reaction rate constant that describes the decay of chlorophyllide, as this reaction rate constant was found to be affected by the gas conditions. The integrated model might be applied to predict colour changes of MAP packaged broccoli as a low level of O 2 and a high level of CO 2 will only affect colour retention at higher temperatures.

Validation and application of a high-fidelity, computational model of acute respiratory distress syndrome to the examination of the indices of oxygenation at constant lung-state

BackgroundCalculated venous admixture (Qs/Qt) is considered the best index of oxygenation; surrogates have been developed (Pao2/Fio2, respiratory index, and arterioalveolar Po2 difference), but these vary with Fio2, falsely indicating a change in lung-state. Using a novel model, we aimed to quantify the behaviour of the indices of oxygenation listed above during physiological and treatment factor variation. The study is the first step in developing an accurate and non-invasive tool to quantify oxygenation defects. MethodsWe present the static and dynamic validation of a novel computational model of gas exchange in acute respiratory distress syndrome (ARDS) based upon the Nottingham Physiology Simulator. Arterial gas tension predictions were compared with data derived from ARDS patients. The subsequent study examined the indices’ susceptibility to variation induced by independent changes in Fio2 (0.3–1.0), haemoglobin concentration (Hb: 6–14 g dl−1), oxygen consumption (Vo2: 250–350 ml min−1), and Paco2 (4–8 kPa). ResultsStatic validation produced a mean error of −0.3%, a 10-fold improvement over previous models. Dynamic validation produced a mean prediction error of −0.05 kPa for Pao2 and 0.09 kPa for Paco2. Every parameter, especially Fio2, induced variation in all indices. The least Fio2-dependent index was Qs/Qt (variation: 5.1%). In contrast, Pao2/Fio2 varied by 77% through the range of Fio2. ConclusionsWe have improved simulation of gas exchange in ARDS by using a sophisticated respiratory model. Using the validated model, we have demonstrated that the current indices of oxygenation vary with alteration in Hb, Paco2, and Vo2 in addition to their previously well-documented dependence on Fio2.

Testing different decoupling coefficients with measurements and models of contrasting canopies and soil water conditions

Abstract. Four different approaches for the calculation of the well established decoupling coefficient Ω are compared using measurements at three experimental sites (Tharandt – spruce forest, Grillenburg and Melpitz – grass) and simulations from the soil-vegetation boundary layer model HIRVAC. These investigations aimed to quantify differences between the calculation routines regarding their ability to describe the vegetation-atmosphere coupling of grass and forest with and without water stress. The model HIRVAC used is a vertically highly resolved atmospheric boundary layer model, which includes vegetation. It is coupled with a single-leaf gas exchange model to simulate physiologically based reactions of different vegetation types to changing atmospheric conditions. A multilayer soil water module and a functional parameterisation are the base in order to link the stomata reaction of the gas exchange model to the change of soil water. The omega factor was calculated for the basic formulation according to McNaughton and Jarvis (1983) and three modifications. To compare measurements and simulations for the above mentioned spruce and grass sites, the summer period 2007 as well as a dry period in June 2000 were used. Additionally a developing water stress situation for three forest canopies (spruce, pine and beech) and for a grass site was simulated. The results showed large differences between the different omega approaches which depend on the vegetation type and the soil moisture. Between the omega values, which were calculated by the used approach, the ranking was always the same not only for the measurements but also for the adapted simulations. The lowest values came from the first modification including doubling factors and summands in all parts of omega equation in relation to the original approach. And the highest values were calculated with the second modification missing one doubling factor in the denominator of the omega equation. For example, the averages of omega ranged in the summer period 2007 from 0.11 to 0.19 for the spruce site and moderate soil wetness and from 0.42 to 0.58 for the grass site and higher soil wetness. In the case of the simulated drying out of four different canopies the forest stands showed a similar change of omega from about 0.65 (moderate soil wetness) to 0.1 (low soil wetness). The absolute change of omega for the grass canopy was smaller than for the forest canopies (on average from 0.95 to 0.7). But the differences between the used omega approaches increased. Especially the results from the longer period in summer 2007 demonstrate that the various modifications of the decoupling coefficient lead to a change in the long-term quantity of omega. This has, for example, consequences for the description of the coupling of heterogeneous landscapes.

Towards a virtual lung: multi-scale, multi-physics modelling of the pulmonary system

The essential function of the lung, gas exchange, is dependent on adequate matching of ventilation and perfusion, where air and blood are delivered through complex branching systems exposed to regionally varying transpulmonary and transmural pressures. Structure and function in the lung are intimately related, yet computational models in pulmonary physiology usually simplify or neglect structure. The geometries of the airway and vascular systems and their interaction with parenchymal tissue have an important bearing on regional distributions of air and blood, and therefore on whole lung gas exchange, but this has not yet been addressed by modelling studies. Models for gas exchange have typically incorporated considerable detail at the level of chemical reactions, with little thought for the influence of structure. To date, relatively little attention has been paid to modelling at the cellular or subcellular level in the lung, or to linking information from the protein structure/interaction and cellular levels to the operation of the whole lung. We review previous work in developing anatomically based models of the lung, airways, parenchyma and pulmonary vasculature, and some functional studies in which these models have been used. Models for gas exchange at several spatial scales are briefly reviewed, and the challenges and benefits from modelling cellular function in the lung are discussed.

A closed loop model of pulmonary gas exchange

Objectives: To model acute lung injury (ACI), we previously developed a partial differential equation (PDE) model of gas exchange and inflammation on a respiratory unit (RU). We increase biological fidelity by incorporating metabolism. We explored the computational and theoretical challenges of this more realistic closed loop system of gas exchange under inflammatory stress. Method: First, we added the loss of O2 and gain of CO2 during metabolism to the PDE model creating time-dependent boundary conditions on pulmonary arterial PO2 and PCO2. Then, the PDE model for gas exchange and inflammation on a single RU was simplified mathematically to a system of ordinary differential equations. The model was reduced such that arterial PO2 and PCO2 reflect the combined effects of metabolism and inflammation. Computational gains allow themodel to operate in a closed loop, and with more biological fidelity. Results: The output of the ordinary differential equation full lung model (multiple linked RUs) matches those seen in the PDE full model when heterogeneity of the lung is introduced via a normal distribution of tidal volumes over the total number of RUs. The reduced form of the RU allows heterogeneity in the full lung by changing both alveolar ventilation and perfusion. As with the previous model, we see the shunting is a major contributor to the reduction of PO2 during inflammation. Conclusions: The reduction of our previous model is the final step in developing a useable multiscale model of the lung. The results of this reduced multi-RU model are comparable to time courses of ACI. This model will be linked with an organ model to explore the spread of inflammation.

Broadband simple ratio closely traced seasonal trajectory of canopy photosynthetic capacity

In this study, we investigated the relationship between meteorological‐based broadband simple ratio (SR) and canopy photosynthetic capacity (maximum carboxylation rate normalized to 25°C, Vc,25) in three Fagus crenata stands in the cold‐temperate zone of Japan. Broadband SR was calculated from recorded up‐ and down‐looking photosynthetically active radiation (PAR) and global radiation (GR) data. The study reveals that broadband SR seasonal courses closely follow Vc,25 seasonal trajectories, with a statistically significant linear regression relationship between the two. Linear regression models show that R2 ranges from 0.59 (for 550 m site) to 0.91 (for 1500 m site), but eventually drops to 0.37 when all data pool together. Despite variations in R2 for the different sites, the relationship remains statistically significant (P < 0.000). Though spatially limited, broadband SR can serve as an easy but robust indicator of seasonal variations in Vc,25 required for accurate carbon fixation simulations in gas exchange models.

A Continuum Model for Metabolic Gas Exchange in Pear Fruit

Exchange of O2 and CO2 of plants with their environment is essential for metabolic processes such as photosynthesis and respiration. In some fruits such as pears, which are typically stored under a controlled atmosphere with reduced O2 and increased CO2 levels to extend their commercial storage life, anoxia may occur, eventually leading to physiological disorders. In this manuscript we have developed a mathematical model to predict the internal gas concentrations, including permeation, diffusion, and respiration and fermentation kinetics. Pear fruit has been selected as a case study. The model has been used to perform in silico experiments to evaluate the effect of, for example, fruit size or ambient gas concentration on internal O2 and CO2 levels. The model incorporates the actual shape of the fruit and was solved using fluid dynamics software. Environmental conditions such as temperature and gas composition have a large effect on the internal distribution of oxygen and carbon dioxide in fruit. Also, the fruit size has a considerable effect on local metabolic gas concentrations; hence, depending on the size, local anaerobic conditions may result, which eventually may lead to physiological disorders. The model developed in this manuscript is to our knowledge the most comprehensive model to date to simulate gas exchange in plant tissue. It can be used to evaluate the effect of environmental stresses on fruit via in silico experiments and may lead to commercial applications involving long-term storage of fruit under controlled atmospheres.