Angela Reynolds

A mathematical model of pulmonary gas exchange under inflammatory stress

During a severe local or systemic inflammatory response, immune mediators target lung tissue. This process may lead to acute lung injury and impaired diffusion of gas molecules. Although several mathematical models of gas exchange have been described, none simulate acute lung injury following inflammatory stress. In view of recent laboratory and clinical progress in the understanding of the pathophysiology of acute lung injury, such a mathematical model would be useful. We first derived a partial differential equations model of gas exchange on a small physiological unit of the lung ( approximately 25 alveoli), which we refer to as a respiratory unit (RU). We next developed a simple model of the acute inflammatory response and implemented its effects within a RU, creating a single RU model. Linking multiple RUs with various ventilation/perfusion ratios and taking into account pulmonary venous blood remixing yielded our lung-scale model. Using the lung-scale model, we explored the predicted effects of inflammation on ventilation/perfusion distribution and the resulting pulmonary venous partial pressure oxygen level during systemic inflammatory stresses. This model represents a first step towards the development of anatomically faithful models of gas exchange and ventilation under a broad range of local and systemic inflammatory stimuli resulting in acute lung injury, such as infection and mechanical strain of lung tissue.

An in silico approach to the analysis of acute wound healing

The complex interactions that characterize acute wound healing have stymied the development of effective therapeutic modalities. The use of computational models holds the promise to improve our basic approach to understanding the process. By modifying an existing ordinary differential equation model of systemic inflammation to simulate local wound healing, we expect to improve the understanding of the underlying complexities of wound healing and thus allow for the development of novel, targeted therapeutic strategies. The modifications in this local acute wound healing model include: evolution from a systemic model to a local model, the incorporation of fibroblast activity, and the effects of tissue oxygenation. Using these modifications we are able to simulate impaired wound healing in hypoxic wounds with varying levels of contamination. Possible therapeutic targets, such as fibroblast death rate and rate of fibroblast recruitment, have been identified by computational analysis. This model is a step toward constructing an integrative systems biology model of human wound healing.

Modeling the effects of systemic mediators on the inflammatory phase of wound healing

The normal wound healing response is characterized by a progression from clot formation, to an inflammatory phase, to a repair phase, and finally, to remodeling. In many chronic wounds there is an extended inflammatory phase that stops this progression. In order to understand the inflammatory phase in more detail, we developed an ordinary differential equation model that accounts for two systemic mediators that are known to modulate this phase, estrogen (a protective hormone during wound healing) and cortisol (a hormone elevated after trauma that slows healing). This model describes the interactions in the wound between wound debris, pathogens, neutrophils and macrophages and the modulation of these interactions by estrogen and cortisol. A collection of parameter sets, which qualitatively match published data on the dynamics of wound healing, was chosen using Latin Hypercube Sampling. This collection of parameter sets represents normal healing in the population as a whole better than one single parameter set. Including the effects of estrogen and cortisol is a necessary step to creating a patient specific model that accounts for gender and trauma. Utilization of math modeling techniques to better understand the wound healing inflammatory phase could lead to new therapeutic strategies for the treatment of chronic wounds. This inflammatory phase model will later become the inflammatory subsystem of our full wound healing model, which includes fibroblast activity, collagen accumulation and remodeling.

A Differential Equation Model of Collagen Accumulation in a Healing Wound

Wound healing is a complex biological process which involves many cell types and biochemical signals and which progresses through multiple, overlapping phases. In this manuscript, we develop a model of collagen accumulation as a marker of wound healing. The mathematical model is a system of ordinary differential equations which tracks fibroblasts, collagen, inflammation and pathogens. The model was validated by comparison to the normal time course of wound healing where appropriate activity for the inflammatory, proliferative and remodeling phases was recorded. Further validation was made by comparison to collagen accumulation experiments by Madden and Peacock (Ann. Surg. 174(3):511–520, 1971). The model was then used to investigate the impact of local oxygen levels on wound healing. Finally, we present a comparison of two wound healing therapies, antibiotics and increased fibroblast proliferation. This model is a step in developing a comprehensive model of wound healing which can be used to develop and test new therapeutic treatments.

Aging effects on airflow dynamics and lung function in human bronchioles

Background and objective The mortality rate for patients requiring mechanical ventilation is about 35% and this rate increases to about 53% for the elderly. In general, with increasing age, the dynamic lung function and respiratory mechanics are compromised, and several experiments are being conducted to estimate these changes and understand the underlying mechanisms to better treat elderly patients. Materials and methods Human tracheobronchial (G1 ~ G9), bronchioles (G10 ~ G22) and alveolar sacs (G23) geometric models were developed based on reported anatomical dimensions for a 50 and an 80-year-old subject. The aged model was developed by altering the geometry and material properties of the model developed for the 50-year-old. Computational simulations using coupled fluid-solid analysis were performed for geometric models of bronchioles and alveolar sacs under mechanical ventilation to estimate the airflow and lung function characteristics. Findings The airway mechanical characteristics decreased with aging, specifically a 38% pressure drop was observed for the 80-year-old as compared to the 50-year-old. The shear stress on airway walls increased with aging and the highest shear stress was observed in the 80-year-old during inhalation. A 50% increase in peak strain was observed for the 80-year-old as compared to the 50-year-old during exhalation. The simulation results indicate that there is a 41% increase in lung compliance and a 35%-50% change in airway mechanical characteristics for the 80-year-old in comparison to the 50-year-old. Overall, the airway mechanical characteristics as well as lung function are compromised due to aging. Conclusion Our study demonstrates and quantifies the effects of aging on the airflow dynamics and lung capacity. These changes in the aging lung are important considerations for mechanical ventilation parameters in elderly patients. Realistic geometry and material properties need to be included in the computational models in future studies.

Elderly Mobility and the Occupancy Status of Single-Family Homes

This research explores the occupancy status and tenure transitions of single-family homes from which elderly homeowners recently moved. First, we compare the housing and neighborhood characteristics of homes vacated by nonelderly and elderly homeowners. Then, we use a multinomial logit model to test the extent to which these characteristics are associated with the homes subsequent vacancy and tenure status. The results indicate that a lack of recent updates and modern amenities may hinder subsequent owner occupancy of homes vacated by the oldest homeowners.

Conservative fluid management prevents age-associated ventilator induced mortality

BACKGROUND Approximately 800 thousand patients require mechanical ventilation in the United States annually with an in-hospital mortality rate of over 30%. The majority of patients requiring mechanical ventilation are over the age of 65 and advanced age is known to increase the severity of ventilator-induced lung injury (VILI) and in-hospital mortality rates. However, the mechanisms which predispose aging ventilator patients to increased mortality rates are not fully understood. Ventilation with conservative fluid management decreases mortality rates in acute respiratory distress patients, but to date there has been no investigation of the effect of conservative fluid management on VILI and ventilator associated mortality rates. We hypothesized that age-associated increases in susceptibility and incidence of pulmonary edema strongly promote age-related increases in ventilator associated mortality. METHODS 2month old and 20month old male C57BL6 mice were mechanically ventilated with either high tidal volume (HVT) or low tidal volume (LVT) for up to 4h with either liberal or conservative fluid support. During ventilation, lung compliance, total lung capacity, and hysteresis curves were quantified. Following ventilation, bronchoalveolar lavage fluid was analyzed for total protein content and inflammatory cell infiltration. Wet to dry ratios were used to directly measure edema in excised lungs. Lung histology was performed to quantify alveolar barrier damage/destruction. Age matched non-ventilated mice were used as controls. RESULTS At 4h, both advanced age and HVT ventilation significantly increased markers of inflammation and injury, degraded pulmonary mechanics, and decreased survival rates. Conservative fluid support significantly diminished pulmonary edema and improved pulmonary mechanics by 1h in advanced age HVT subjects. In 4h ventilations, conservative fluid support significantly diminished pulmonary edema, improved lung mechanics, and resulted in significantly lower mortality rates in older subjects. CONCLUSION Our study demonstrates that conservative fluid alone can attenuate the age associated increase in ventilator associated mortality.

Quantification of Age‐Related Lung Tissue Mechanics under Mechanical Ventilation

Elderly patients with obstructive lung diseases often receive mechanical ventilation to support their breathing and restore respiratory function. However, mechanical ventilation is known to increase the severity of ventilator-induced lung injury (VILI) in the elderly. Therefore, it is important to investigate the effects of aging to better understand the lung tissue mechanics to estimate the severity of ventilator-induced lung injuries. Two age-related geometric models involving human bronchioles from generation G10 to G23 and alveolar sacs were developed. The first is for a 50-year-old (normal) and second is for an 80-year old (aged) model. Lung tissue mechanics of normal and aged models were investigated under mechanical ventilation through computational simulations. Results obtained indicated that lung tissue strains during inhalation (t = 0.2 s) decreased by about 40% in the alveolar sac (G23) and 27% in the bronchiole (G20), respectively, for the 80-year-old as compared to the 50-year-old. The respiratory mechanics parameters (work of breathing per unit volume and maximum tissue strain) over G20 and G23 for the 80-year-old decreased by about 64% (three-fold) and 80% (four-fold), respectively, during the mechanical ventilation breathing cycle. However, there was a significant increase (by about threefold) in lung compliance for the 80-year-old in comparison to the 50-year-old. These findings from the computational simulations demonstrated that lung mechanical characteristics are significantly compromised in aging tissues, and these effects were quantified in this study.

Aging Effects on Alveolar Sacs Under Mechanical Ventilation

Alveolar sacs are primarily responsible for gas exchange in the human respiratory system and lose their functionality with aging. Three-dimensional (3D) models of young and old human alveolar sacs were constructed and fluid-solid interaction was employed to investigate the contribution of age-related changes to decline in alveolar sacs function under mechanical ventilation (MV). Simulation results illustrated that compliance and pressure reduced in the alveolar sacs of the elderly adults, and they have to work harder to breathe. Morphological changes were found to be mainly responsible for the decline in alveolar sacs function. Influence of individual differences on the alveolar sacs function was negligible and 95% confidence intervals for compliance and work of breathing (WOB) using measures from different individuals also support this finding. Moreover, higher mortality risk was recorded for elderly adults who undergo MV. Specifically, ventilator devices setting has been identified as a potential parameter for compromising respiratory function in the elderly adults. Volume-controlled ventilation applied less pressure, whereas, pressure-controlled ventilation resulted in higher compliance in the alveolar sacs and decreased WOB. Sensitivity of alveolar sacs to ventilator setting under the volume-controlled mode illustrated that increasing breathing frequency and decreasing the ratio of inhalation to exhalation times and TV caused an increase in alveolar sacs expansion and compliance in older patients. Results from this study can help clinicians to develop individualized and effective ventilator protocols and to improve respiratory function in the elderly adults.

Correction to: A mathematical model of the effects of resistance exercise-induced muscle hypertrophy on body composition

There is a typo in the original equation describing lean mass, and it has also been pointed out to the authors that the model is not strictly energy balanced.