Rebecca A. Segal

COMPUTER SIMULATIONS OF PARTICLE DEPOSITION IN THE LUNGS OF CHRONIC OBSTRUCTIVE PULMONARY DISEASE PATIENTS

Epidemiology data show that mortality rates for chronic obstructive pulmonary disease (COPD) patients increase with an increase in concentration of ambient particulate matter (PM). This is not seen for normal subjects. Therefore, the U.S. Environmental Protection Agency (EPA) has identified COPD patients as a susceptible subpopulation to be considered in regulatory standards. In the present study, a computer model was used to calculate deposition fractions of PM within the lungs of COPD patients. The morphology of COPD lungs was characterized by two distinct components: obstruction of airways (chronic bronchitis component), and degeneration of alveolar structure (emphysema component). The chronic bronchitis component was modeled by reducing airway diameters using airway resistance measurements in vivo, and the emphysema component was modeled by increasing alveolar volumes. Calculated results were compared with experimental data obtained from COPD patients for controlled breathing trials (tidal volume of 500 ml, respiratory time of 1 s) with a particle size of 1 µm. The model successfully depicts PM deposition patterns and their dependence on the severity of disease. The findings indicate that airway obstructions are the main cause for increased deposition in the COPD lung.

Dosimetry of nasal uptake of water-soluble and reactive gases: A first study of interhuman variability

Certain inhaled chemicals, such as reactive, water-soluble gases, are readily absorbed by the nasal mucosa upon inhalation and may cause damage to the nasal epithelium. Comparisons of the spatial distribution of nasal lesions in laboratory animals exposed to formaldehyde with gas uptake rates predicted by computational models reveal that lesions usually occur in regions of the susceptible epithelium where gas absorption is highest. Since the uptake patterns are influenced by air currents in the nose, interindividual variability in nasal anatomy and ventilation rates due to age, body size, and gender will affect the patterns of gas absorption in humans, potentially putting some age groups at higher risk when exposed to toxic gases. In this study, interhuman variability in the nasal dosimetry of reactive, water-soluble gases was investigated by means of computational fluid dynamics (CFD) models in 5 adults and 2 children, aged 7 and 8 years old. Airflow patterns were investigated for allometrically scaled inhalation rates corresponding to resting breathing. The spatial distribution of uptake at the airway walls was predicted to be nonuniform, with most of the gas being absorbed in the anterior portion of the nasal passages. Under the conditions of these simulations, interhuman variability in dose to the whole nose (mass per time per nasal surface area) due to differences in anatomy and ventilation was predicted to be 1.6-fold among the 7 individuals studied. Children and adults displayed very similar patterns of nasal gas uptake; no significant differences were noted between the two age groups.

Mathematical Model of Airflow in the Lungs of Children I: Effects of Tumor Sizes and Locations

To contribute to the development of more effective aerosol therapy protocols in pediatric medicine, we examined airflow patterns in the lung of a four-year-old child. In particular, we addressed how the presence of tumors in airways affected the character of airflow patterns. To study the effects of tumors we employed a computational fluid dynamics package, FIDAP, to define flow conditions within a model lung. The results indicated that tumors have a pronounced affect on both (i) localized velocity profiles in airways and (ii) bulk flow distribution within the lung. By identifying the effects of physical factors on flow conditions the findings will lead to improved drug delivery regimens.

Mathematical model of airflow in the lungs of children ii effects of ventilatory parameters

In an effort to develop more effective aerosol therapy procedures, we examined airflow patterns in the lung of a child (age four years). In particular, we were concerned with how ventilatory parameters (i.e., breathing rate and tidal volume) affected the patterns of airflow around tumors. To conduct the study, a computational fluid dynamics package, FIDAP was used to define a model lung. The results of simulations show the extent to which changing ventilatory parameters can affect flow patterns in the neighborhood of the tumors as well as drug distribution throughout the lung.

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.

Comparison of computer simulations of total lung deposition to human subject data in healthy test subjects

ABSTRACT A mathematical model was used to predict the deposition fractions (DF) of PM within human lungs. Simulations using this computer model were previously validated with human subject data and were used as a control case. Human intersubject variation was accounted for by scaling the base lung morphology dimensions based on measured functional residual capacity (FRC) values. Simulations were performed for both controlled breathing (tidal volumes [VT] of 500 and 1000 mL, respiratory times [T] from 2 to 8 sec) and spontaneous breathing conditions. Particle sizes ranged from 1 to 5 um. The deposition predicted from the computer model compared favorably with the experimental data. For example, when VT = 1000 mL and T = 2 sec, the error was 1.5%. The errors were slightly higher for smaller tidal volumes. Because the computer model is deterministic (i.e., derived from first principles of physics), the model can be used to predict deposition fractions for a range of situations (i.e., for different ventilatory parameters and particle sizes) for which data are not available. Now that the model has been validated, it may be applied to risk assessment efforts to estimate the inhalation hazards of airborne pollutants.

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.

A mathematical system for human implantable wound model studies

In this work, we present a mathematical model, which accounts for two fundamental processes involved in the repair of an acute dermal wound. These processes include the inflammatory response and fibroplasia. Our system describes each of these events through the time evolution of four primary species or variables. These include the density of initial damage, inflammatory cells, fibroblasts and deposition of new collagen matrix. Since it is difficult to populate the equations of our model with coefficients that have been empirically derived, we fit these constants by carrying out a large number of simulations until there is reasonable agreement between the time response of the variables of our system and those reported by the literature for normal healing. Once a suitable choice of parameters has been made, we then compare simulation results with data obtained from clinical investigations. While more data is desired, we have a promising first step towards describing the primary events of wound repair within the confines of an implantable system.

Modeling Sympatric Speciation in Quasiperiodic Environments

Sympatric speciation is the emergence of new species from a single ancestral species while inhabiting the same geographic region. This process presents an interesting problem for theoretical studies of evolution. One mechanism by which sympatric speciation might occur is periodic or quasiperiodic fluctuations in the abundance of the resources. In this paper inspired by the experimental findings of (Herron and Doebeli, PLoS Biol. 11, p. e1001490, 2013), we present a number of models of asexual speciation of E. coli, which range in the level of biological detail and the degree of analytical treatment. We show that coexistence of multiple species arises as a robust phenomenon, even in the presence of spatial and temporal randomness.