Exploring Aeration Strategies for Enhanced Simultaneous Nitrification and Denitrification in Membrane Aerated Bioreactors: A Computational Approach.

In this study we employ computational methods to investigate the influence of aeration strategies on simultaneous nitrification-denitrification processes. Specifically, we explore the impact of periodic and intermittent aeration on denitrification rates, which typically lag behind nitrification rates under identical environmental conditions. A two-dimensional deterministic multi-scale model is employed to elucidate the fundamental processes governing the behavior of membrane aerated biofilm reactors (MABRs). We aim to identify key factors that promote denitrification under varying aeration strategies. Our findings indicate that the concentration of oxygen during the off phase and the duration of the off interval play crucial roles in controlling denitrification. Complete discontinuation of oxygen is not advisable, as it inhibits the formation of anaerobic heterotrophic bacteria, thereby impeding denitrification. Extending the length of the off interval, however, enhances denitrification. Furthermore, we demonstrate that the initial inoculation of the substratum (membrane in this study) influences substrate degradation under periodic aeration, with implications for both nitrification and denitrification. Comparison between continuous and periodic/intermittent aeration scenarios reveals that the latter can extend the operational cycle of MABRs. This extension is attributed to relatively low biofilm growth rates associated with non-continuous aeration strategies. Consequently, our study provides a comprehensive understanding of the intricate interplay between aeration strategies and simultaneous nitrification-denitrification in MABRs. The insights presented herein can contribute significantly to the optimization of MABR performance in wastewater treatment applications.

An enhanced, rational model to study acoustic vaporization dynamics of a bubble encapsulated within a nonlinearly elastic shell.

Acoustic droplet vaporization (ADV) is a new approach to generate vapor bubbles that have potentially broad medical applications. ADV-generated bubbles can be used as contrast agents in acoustic imaging, as drug carriers to deliver drugs to particular targets, and also in embolotherapy, thermal therapy, and histotripsy. However, despite much progress, ADV dynamics have still not been well understood and properly modeled. In this paper, we present a theoretical study of ultrasound-induced evaporation of a droplet encapsulated by a shell. The main emphasis of this theoretical study is on a proper description of the supercritical state occurring after bubble collapse. For this purpose, an isentropic equation of state for a van der Waals gas is used to describe the bubble behavior in the supercritical state. Sensitivity of the vaporization process is investigated for different acoustic and geometrical parameters and mechanical properties of the shell. Results show that the value of the minimum pressure required for direct vaporization (without any oscillatory behavior) depends on shell elasticity and initial size of the droplet, especially at high frequencies (greater than 2[MHz]). Moreover, it has been shown that applying an acoustic wave with proper phase such that thermal equilibrium of the bubble temperature with the surrounding liquid is attained, results in direct vaporization at lower acoustic pressure.

A mathematical study of the impact of cell plasticity on tumour control probability.

The tumour control probability (TCP) is a treatment planning tool that evaluates the probability of tumour eradication and helps in the assessment of the relative efficacy of different radiotherapy regimens. The response of tumours to radiation differs greatly even between patients with same types of cancers. Tumour heterogeneity or cellular diversity among cancer cells has a pronounced impact on the success of administered radiotherapy protocols. Tumour heterogeneity can be explained using the cancer stem cells (CSCs) hypothesis, which posits that CSCs are responsible for tumour initiation and propagation as well as therapeutic resistance. Moreover, the existence of plasticity or bidirectional transition between CSCs and non-CSCs indicates that, sometimes, non-CSCs appear to mimic CSC phenotypes, resulting in an increase in resistance. Here, we have developed a stochastic model to investigate the impact of plasticity on the efficacy of radiotherapy. The effect of plasticity on TCP is explored by applying the model to standard and hyper-fractionated schedules for a three week period of treatment as well as standard, hyper-fractionated, and accelerated hyper-fractionated schedules with an equal total dose of 30 Gy. Our results confirm that tumour control becomes increasingly difficult in the presence of plasticity as well as for the most resistant tumours. For the case with equal total dose, it is observed that increasing fractionation, at first enhances the probability of CSCs and tumour removal, but ultimately results in lower TCPS+P and TCPS. In addition, the combination of radiotherapy and targeted therapy (with increasing CSC differentiation) improves both the probability of CSC and tumour removal, in the absence of plasticity. However, in the presence of plasticity, the impact of combination therapy is not significant.

A computational study of combination HIFU-chemotherapy as a potential means of overcoming cancer drug resistance.

The application of local hyperthermia, particularly in conjunction with other treatment strategies (like chemotherapy and radiotherapy) has been known to be a useful means of enhancing tumor treatment outcomes. However, to our knowledge, there has been no mathematical model designed to capture the impact of the combination of hyperthermia and chemotherapies on tumor growth and control. In this study, we propose a nonlinear Partial Differential Equation (PDE) model which describes the tumor response to chemotherapy, and use the model to study the effects of hyperthermia on the response of prototypical tumor to the generic chemotherapeutic agent. Ultrasound energy is delivered to the tumor through High Intensity Focused Ultrasound (HIFU), as a noninvasive technique to elevate the tumor temperature in a controlled manner. The proposed tumor growth model is coupled with the nonlinear density dependent Westervelt and Penne's bio-heat equations, used to calculate the net delivered energy and temperature of the tumor and its surrounding normal tissue. The tumor is assumed to be composed of two species: drug-sensitive and drug-resistant. The central assumption underlying our model is that the drug-resistant species is converted to a drug-sensitive type when the tumor temperature is elevated above a certain threshold temperature. The "in silico" results obtained, confirm that hyperthermia can result in less aggressive tumor development and emphasize the importance of designing an optimized thermal dose strategy. Furthermore, our results suggest that increasing the length of the on/off cycle of the transducer is an efficient approach to treatment scheduling in the sense of optimizing tumor eradication.

A study of nitric oxide dynamics in a growing biofilm using a density dependent reaction-diffusion model.

One of a number of critical roles played by NO· as a chemical weapon (generated by the immune system) is to neutralize pathogens. However, the virulence of pathogens depends on the production activity of reductants to detoxify NO·. Broad reactivity of NO· makes it complicated to predict the fate of NO· inside bacteria and its effects on the treatment of any infection. Here, we present a mathematical model of biofilm response to NO·, as a stressor. The model is comprised of a PDE system of highly nonlinear reaction-diffusion equations that we study in computer simulations to determine the positive and negative effects of key parameters on bacterial defenses against NO·. From the reported results, we conjecture that the oscillatory behavior of NO· under a microaerobic regime is a temporal phenomenon and does not give rise to a spatial pattern. It is also shown computationally that decreasing the initial size of the biofilm colony negatively impacts the functionality of reducing agents that deactivate NO·. Whereas nutrient deprivation results in the development of biofilms with heterogeneous structure, its effect on the activity of NO· reductants depends on the oxygen availability, biofilm size, and the amount of NO·.

Tuning optimum transfection of gemini surfactant-phospholipid-DNA nanoparticles by validated theoretical modeling.

Gemini nanoparticles (NPs) are a family of non-viral gene delivery systems with potential for applications in non-invasive gene therapy. Translation of these non-viral gene delivery systems requires improvement of transfection efficiency (TE) through fine-tuning of their physicochemical properties such as electric charge and exact ratios of their components. Since high-throughput experimental screening of minute differences in NP compositions is not routinely feasible, we have developed a coarse-grained model to quantitatively study the energetics of the formation of gene delivery complexes with cationic gemini surfactants (G) (m-s-m type) and helper lipids (H) (1,2-dioleoyl-sn-glycero-3-phosphoethanolamine (DOPE) and DOPE/1,2-dipalmitoyl-sn-glycerol-3-phosphocholine (DPPC)), in order to use it as a tool to predict effective compositions. The model is based on the polymorphic structural conformational flip of NPs and incorporates the electrostatic, entropic and elastic energies, to predict the formation energy and stability of different polymorphic structures as a function of the electric charge of cationic surfactants and concentration of constituent helper lipids. Our results show that these two factors are intertwined in determining the behavior of gene delivery vectors. Specifically, we show that increasing H/G lowers free energy per DNA base pair and increases the stability of the complex. At pH 7, low H/G and charge ratio (ρ±), where the lamellar structure is favored, the formation free energy per DNA base pair is between 0 and -14kBT. At higher values of H/G (2-3) and ρ±, where HII and cubic structures are formed, the formation free energy drops down to values ≈-50kBT, indicating the stable existence of these polymorphic structures in the NPs. At pH 5, the structural transformation of NPs in the endosomes to the lamellar/HII structure with free energy values of about -40kBT is beneficial for endosomal escape, and correlates with increased transfection efficiency. The theoretical model is supported by transfection data in A7 astrocytes with a panel of 16-3-16 gemini NPs, which validates the mathematical model and supports the hypothesis that the NP polymorphic phase transition increases transfection efficiency.

Phenotypic heterogeneity in modeling cancer evolution.

The unwelcome evolution of malignancy during cancer progression emerges through a selection process in a complex heterogeneous population structure. In the present work, we investigate evolutionary dynamics in a phenotypically heterogeneous population of stem cells (SCs) and their associated progenitors. The fate of a malignant mutation is determined not only by overall stem cell and non-stem cell growth rates but also differentiation and dedifferentiation rates. We investigate the effect of such a complex population structure on the evolution of malignant mutations. We derive exactly calculated results for the fixation probability of a mutant arising in each of the subpopulations. The exactly calculated results are in almost perfect agreement with the numerical simulations. Moreover, a condition for evolutionary advantage of a mutant cell versus the wild type population is given in the present study. We also show that microenvironment-induced plasticity in invading mutants leads to more aggressive mutants with higher fixation probability. Our model predicts that decreasing polarity between stem and non-stem cells' turnover would raise the survivability of non-plastic mutants; while it would suppress the development of malignancy for plastic mutants. The derived results are novel and general with potential applications in nature; we discuss our model in the context of colorectal/intestinal cancer (at the epithelium). However, the model clearly needs to be validated through appropriate experimental data. This novel mathematical framework can be applied more generally to a variety of problems concerning selection in heterogeneous populations, in other contexts such as population genetics, and ecology.

High Concentrations of H2O2 Make Aerobic Glycolysis Energetically More Favorable for Cellular Respiration.

Since the original observation of the Warburg Effect in cancer cells, over 8 decades ago, the major question of why aerobic glycolysis is favored over oxidative phosphorylation has remained unresolved. An understanding of this phenomenon may well be the key to the development of more effective cancer therapies. In this paper, we use a semi-empirical method to throw light on this puzzle. We show that aerobic glycolysis is in fact energetically more favorable than oxidative phosphorylation for concentrations of peroxide (H2O2) above some critical threshold value. The fundamental reason for this is the activation and high engagement of the pentose phosphate pathway (PPP) in response to the production of reactive oxygen species (ROS) H2O2 by mitochondria and the high concentration of H2O2 (produced by mitochondria and other sources). This makes oxidative phosphorylation an inefficient source of energy since it leads (despite high levels of ATP production) to a concomitant high energy consumption in order to respond to the hazardous waste products resulting from cellular processes associated with this metabolic pathway. We also demonstrate that the high concentration of H2O2 results in an increased glucose consumption, and also increases the lactate production in the case of glycolysis.

Drug-induced reactive oxygen species (ROS) rely on cell membrane properties to exert anticancer effects.

Pharmacological concentrations of small molecule natural products, such as ascorbic acid, have exhibited distinct cell killing outcomes between cancer and normal cells whereby cancer cells undergo apoptosis or necrosis while normal cells are not adversely affected. Here, we develop a mathematical model for ascorbic acid that can be utilized as a tool to understand the dynamics of reactive oxygen species (ROS) induced cell death. We determine that not only do endogenous antioxidants such as catalase contribute to ROS-induced cell death, but also cell membrane properties play a critical role in the efficacy of ROS as a cytotoxic mechanism against cancer cells vs. normal cells. Using in vitro assays with breast cancer cells, we have confirmed that cell membrane properties are essential for ROS, in the form of hydrogen peroxide (H2O2), to induce cell death. Interestingly, we did not observe any correlation between intracellular H2O2 and cell survival, suggesting that cell death by H2O2 is triggered by interaction with the cell membrane and not necessarily due to intracellular levels of H2O2. These findings provide a putative mechanistic explanation for the efficacy and selectivity of therapies such as ascorbic acid that rely on ROS-induced cell death for their anti-tumor properties.

Mechanics of the brain: perspectives, challenges, and opportunities.

The human brain is the continuous subject of extensive investigation aimed at understanding its behavior and function. Despite a clear evidence that mechanical factors play an important role in regulating brain activity, current research efforts focus mainly on the biochemical or electrophysiological activity of the brain. Here, we show that classical mechanical concepts including deformations, stretch, strain, strain rate, pressure, and stress play a crucial role in modulating both brain form and brain function. This opinion piece synthesizes expertise in applied mathematics, solid and fluid mechanics, biomechanics, experimentation, material sciences, neuropathology, and neurosurgery to address today's open questions at the forefront of neuromechanics. We critically review the current literature and discuss challenges related to neurodevelopment, cerebral edema, lissencephaly, polymicrogyria, hydrocephaly, craniectomy, spinal cord injury, tumor growth, traumatic brain injury, and shaken baby syndrome. The multi-disciplinary analysis of these various phenomena and pathologies presents new opportunities and suggests that mechanical modeling is a central tool to bridge the scales by synthesizing information from the molecular via the cellular and tissue all the way to the organ level.

Stochastic model for tumor control probability: effects of cell cycle and (a)symmetric proliferation.

BACKGROUND: Estimating the required dose in radiotherapy is of crucial importance since the administrated dose should be sufficient to eradicate the tumor and at the same time should inflict minimal damage on normal cells. The probability that a given dose and schedule of ionizing radiation eradicates all the tumor cells in a given tissue is called the tumor control probability (TCP), and is often used to compare various treatment strategies used in radiation therapy. METHOD: In this paper, we aim to investigate the effects of including cell-cycle phase on the TCP by analyzing a stochastic model of a tumor comprised of actively dividing cells and quiescent cells with different radiation sensitivities. Moreover, we use a novel numerical approach based on the method of characteristics for partial differential equations, validated by the Gillespie algorithm, to compute the TCP as a function of time. RESULTS: We derive an exact phase-diagram for the steady-state TCP of the model and show that at high, clinically-relevant doses of radiation, the distinction between active and quiescent tumor cells (i.e. accounting for cell-cycle effects) becomes of negligible importance in terms of its effect on the TCP curve. However, for very low doses of radiation, these proportions become significant determinants of the TCP. We also present the results of TCP as a function of time for different values of asymmetric division factor. CONCLUSION: We observe that our results differ from the results in the literature using similar existing models, even though similar parameters values are used, and the reasons for this are discussed.

Tumour control probability in cancer stem cells hypothesis.

The tumour control probability (TCP) is a formalism derived to compare various treatment regimens of radiation therapy, defined as the probability that given a prescribed dose of radiation, a tumour has been eradicated or controlled. In the traditional view of cancer, all cells share the ability to divide without limit and thus have the potential to generate a malignant tumour. However, an emerging notion is that only a sub-population of cells, the so-called cancer stem cells (CSCs), are responsible for the initiation and maintenance of the tumour. A key implication of the CSC hypothesis is that these cells must be eradicated to achieve cures, thus we define TCPS as the probability of eradicating CSCs for a given dose of radiation. A cell surface protein expression profile, such as CD44high/CD24low for breast cancer or CD133 for glioma, is often used as a biomarker to monitor CSCs enrichment. However, it is increasingly recognized that not all cells bearing this expression profile are necessarily CSCs, and in particular early generations of progenitor cells may share the same phenotype. Thus, due to the lack of a perfect biomarker for CSCs, we also define a novel measurable TCPCD+, that is the probability of eliminating or controlling biomarker positive cells. Based on these definitions, we use stochastic methods and numerical simulations parameterized for the case of gliomas, to compare the theoretical TCPS and the measurable TCPCD+. We also use the measurable TCP to compare the effect of various radiation protocols.

A MATHEMATICAL INVESTIGATION OF THE ROLE OF INTRACRANIAL PRESSURE PULSATIONS AND SMALL GRADIENTS IN THE PATHOGENESIS OF HYDROCEPHALUS.

Cerebrospinal fluid (CSF) pulsations have been proposed as a possible causative mechanism for the ventricular enlargement that characterizes the neurological condition known as hydrocephalus. This paper summarizes recent work by the authors to anaylze the effect of CSF pulsations on brain tissue to determine if they are mechanically capable of enlarging the cerebral ventricles. First a poroelastic model is presented to analyze the interactions that occur between the fluid and porous solid constituents of brain tissue due to CSF pulsations. A viscoelastic model is then presented to analyze the effects of the fluid pulsations on the solid brain tissue. The combined results indicate that CSF pulsations in a healthy brain are incapable of causing tissue damage and thus the ventricular enlargement observed in hydrocephalus. Therefore they cannot be the primary cause of this condition. Finally, a hyper-viscoelastic model is presented and used to demonstrate that small long-term transmantle pressure gradients may be a possible cause of communicating hydrocephalus in infants.

Deriving mechanisms responsible for the lack of correlation between hypoxia and acidity in solid tumors.

Hypoxia and acidity are two main microenvironmental factors intimately associated with solid tumors and play critical roles in tumor growth and metastasis. The experimental results of Helmlinger and colleagues (Nature Medicine 3, 177, 1997) provide evidence of a lack of correlation between these factors on the micrometer scale in vivo and further show that the distribution of pH and pO(2) are heterogeneous. Here, using computational simulations, grounded in these experimental results, we show that the lack of correlation between pH and pO(2) and the heterogeneity in their shapes are related to the heterogeneous concentration of buffers and oxygen in the blood vessels, further amplified by the network of blood vessels and the cell metabolism. We also demonstrate that, although the judicious administration of anti-angiogenesis agents (normalization process) in tumors may lead to recovery of the correlation between hypoxia and acidity, it may not normalize the pH throughout the whole tumor. However, an increase in the buffering capacity inside the blood vessels does appear to increase the extracellular pH throughout the whole tumor. Based on these results, we propose that the application of anti-angiogenic agents and at the same time increasing the buffering capacity of the tumor extracellular environment may be the most efficient way of normalizing the tumor microenvironment. As a by-product of our simulation we show that the recently observed lack of correlation between glucose consumption and hypoxia in cells which rely on respiration is related to the inhomogeneous consumption of glucose to oxygen concentration. We also demonstrate that this lack of correlation in cells which rely on glycolysis could be related to the heterogeneous concentration of oxygen inside the blood vessels.

Fingerprint of cell metabolism in the experimentally observed interstitial pH and pO2 in solid tumors.

Understanding cancer cell metabolism and targeting associated pathways is a field of increasing interest. Helmlinger and colleagues measured average pH and pO(2) as functions of distance from a single blood vessel on the micrometer scale. We show that these results provide unique insight into cancer cell metabolism in vivo when combined with an appropriate mathematical model. We calculate pH as a function of distance from a single blood vessel and for a given metabolism while incorporating a single CO(2) buffer with effective diffusion constants. By assuming that cancer cell metabolism is dominated by respiration with a smaller component of glycolysis in the normoxic state, by more balanced respiration and glycolysis in the hypoxic state, and by glycolysis alone in the anoxic state, we are able to semiquantitatively derive the experimental results of Helmlinger and colleagues. We also apply our model to glycolysis-impaired metabolism and show that the low pH and high pO(2) observed in these tumors may be related to the substantial shift from a respiration-dominated metabolism to one in which glutaminolysis dominates. Based on this, we propose an in vivo experimental measurement of pH in a glycolysis-impaired tumor to validate the modeling results.