The Fractal Viewpoint of Tumors and Nanoparticles.

Even though the promising therapies against cancer are rapidly improved, the oncology patients population has seen exponential growth, placing cancer in 5th place among the ten deadliest diseases. Efficient drug delivery systems must overcome multiple barriers and maximize drug delivery to the target tumors, simultaneously limiting side effects. Since the first observation of the quantum tunneling phenomenon, many multidisciplinary studies have offered quantum-inspired solutions to optimized tumor mapping and efficient nanodrug design. The property of a wave function to propagate through a potential barrier offer the capability of obtaining 3D surface profiles using imaging of individual atoms on the surface of a material. The application of quantum tunneling on a scanning tunneling microscope offers an exact surface roughness mapping of tumors and pharmaceutical particles. Critical elements to cancer nanotherapeutics apply the fractal theory and calculate the fractal dimension for efficient tumor surface imaging at the atomic level. This review study presents the latest biological approaches to cancer management based on fractal geometry.

Current Trends of Computational Tools in Geriatric Medicine and Frailty Management.

While frailty corresponds to a multisystem failure, geriatric assessment can recognize multiple pathophysiological lesions and age changes. Up to now, a few frailty indexes have been introduced, presenting definitions of psychological problems, dysregulations in nutritional intake, behavioral abnormalities, and daily functions, genetic, environmental, and cardiovascular comorbidities. The geriatric evaluation includes a vast range of health professionals; therefore, we describe a broad range of applications and frailty scales-biomarkers to investigate and formulate the relationship between frailty lesions, diagnosis, monitoring, and treatment. Additionally, artificial intelligence applications and computational tools are presented, targeting a more efficacy individualized geriatric management of healthy aging.

Number of Brain States in an N-Body Dynamical Scenario According to the Universal Bekenstein Entropy Bound.

There is an intense interest in the modulation of brain neural circuits and its correlations with different behavioral states, memory, learning, as well as neuropsychological disorders. It is believed that brain cells form functional circuits, process information and mediate behavior. Therefore, the brain system may be thought of as a super-computing machine that turns information into thoughts, memories, and cognitions. Moreover, according to the quantum brain dynamics and quantum conscience hypotheses, quantum theory, the most fundamental theory of matter, may help explain the function of the brain. In the intersection of the architecture of the brain's biological substrate, the processing of information and entropy (as a measure of information processing capacity), and the generation of input to this system (either externally or internally), one may expect to find the foundations of cognition and behavior as an emergent phenomenon. In this chapter, we calculate the entropy Bekenstein bound of the brain, and from that the number of information N in bits that is required to describe the brain down to its tiniest detail. Furthermore, we define the quantity cmbRb as brain quantum of action b. Next, we estimate the possible number of states b in the human brain as related to the number of information bits N. Furthermore, we derive an expression for the kinetic energy of a pair of neurons as a function of brain temperature T, the number of information N in bits, and the neuron mass mn as well as the number density of neurons n. We introduce the conjecture that the time rate of r(t) might represent the velocity at which a pair of neurons can approach or recede from each other upon experiencing a transfer of N number of information bits.

Biological Relevance of Network Architecture.

Mathematical representations of brain networks in neuroscience through the use of graph theory may be very useful for the understanding of neurological diseases and disorders and such an explanatory power is currently under intense investigation. Graph metrics are expected to vary across subjects and are likely to reflect behavioural and cognitive performances. The challenge is to set up a framework that can explain how behaviour, cognition, memory, and other brain properties can emerge through the combined interactions of neurons, ensembles of neurons, and larger-scale brain regions that make information transfer possible. "Hidden" graph theoretic properties in the construction of brain networks may limit or enhance brain functionality and may be representative of aspects of human psychology. As theorems emerge from simple mathematical properties of graphs, similarly, cognition and behaviour may emerge from the molecular, cellular and brain region substrate interactions. In this review report, we identify some studies in the current literature that have used graph theoretical metrics to extract neurobiological conclusions, we briefly discuss the link with the human connectome project as an effort to integrate human data that may aid the study of emergent patterns and we suggest a way to start categorizing diseases according to their brain network pathologies as these are measured by graph theory.

Preclinical Validation of the Located Hyperthermia Using Gold Macro-Rods and Ultrasound as an Effective Treatment for Solid Tumors.

Hyperthermia, the procedure of raising the temperature of a part of or the whole body above normal for a defined period of time, is applied alone or as an adjunctive with various established cancer treatment modalities such as radiotherapy and chemotherapy. In this study used a method for inducing hyperthermia in solid tumors with a combination of gold macro rod (GR) and ultrasound, the feasibility of this technique was described only with computational models and in vitro. The Ehrlich tumor, derived from a mouse adenocarcinoma, has been used to investigate the bio-heat transfer and the effect of gold rods irradiated with ultrasound. The in vivo measurements demonstrated that the technique inhibited more 80% of the tumor growth in both experimental models tested. These results not only confirm the bio heat transfer to tissue as predicted by analytical calculation and in vitro measurements, but are also proved to be a potential alternative to kill cancer cells.

Neuronal Correlation Parameter and the Idea of Thermodynamic Entropy of an N-Body Gravitationally Bounded System.

Understanding how the brain encodes information and performs computation requires statistical and functional analysis. Given the complexity of the human brain, simple methods that facilitate the interpretation of statistical correlations among different brain regions can be very useful. In this report we introduce a numerical correlation measure that may serve the interpretation of correlational neuronal data, and may assist in the evaluation of different brain states. The description of the dynamical brain system, through a global numerical measure may indicate the presence of an action principle which may facilitate a application of physics principles in the study of the human brain and cognition.

Gold Rods Irradiated with Ultrasound for Combination of Hyperthermia and Cancer Chemotherapy.

PURPOSE: The aim of this study was to analyze feasibility (in vitro and in vivo) the use of hyperthermia produced by gold rods irradiated with ultrasound and their combination with chemotherapy with doxorubicin. MATERIALS AND METHODS: initially was determined the cell viability and Hsp70 levels after treatment by gold rods irradiated with ultrasound (GR+U) in cell culture. The pretreatment with GR+U combined with doxorubicin (DOX) was evaluated from IC50, caspase-3 expression and mechanisms of cell death by electron microscopy. For evaluate the in vivo effects was used solid Ehrlich carcinoma (SEC) Tumor. The animals received three treatments with the combination of GR+U+DOX over 16 days. RESULTS: The cell viability was completely inhibited after 40 min of treatment with GR+U and significant increases the expression of HSP70 was only observed after 10 min of treatment. GR+U+DOX presented significant reduction of IC50 representing 50.7%, 76.5% 45.2% and 46.6% for cell lines K562, NCI-H292, Hep-2 and MCF-7 respectively. GR+U+DOX presented significant reduction of IC50 representing 50.7%, 76.5% 45.2% and 46.6% for cell lines K562, NCI-H292, Hep-2 and MCF-7 respectively. The caspase-3 level and ultraestructural analysis showed that treatment with GR+U+DOX enhances induction of apoptosis. Pretreatment with GR+U combined with doxorubicin (1 mg) showed 87% inhibition against SEC. and no showed cardiotoxic effect. CONCLUSIONS: The combined treatment of GR+U and DOX exhibit synergistic characteristics observed by increasing the efficiency of doxorubicin.

Analytic considerations and axiomatic approaches to the concept cell death and cell survival functions in biology and cancer treatment.

This study contains a discussion on the connection between current mathematical and biological modeling systems in response to the main research need for the development of a new mathematical theory for study of cell survival after medical treatment and cell biological behavior in general. This is a discussion of suggested future research directions and relations with interdisciplinary science. In an effort to establish the foundations for a possible framework that may be adopted to study and analyze the process of cell survival during treatment, we investigate the organic connection among an axiomatic system foundation, a predator-prey rate equation, and information theoretic signal processing. A new set theoretic approach is also introduced through the definition of cell survival units or cell survival units indicating the use of "proper classes" according to the Zermelo-Fraenkel set theory and the axiom of choice, as the mathematics appropriate for the development of biological theory of cell survival.

Respiratory particle deposition probability due to sedimentation with variable gravity and electrostatic forces.

In this chapter, we study the effects of the acceleration gravity on the sedimentation deposition probability, as well as the aerosol deposition rate on the surface of the Earth and Mars, but also aboard a spacecraft in orbit around Earth and Mars as well for particles with density ρ p = 1,300 kg/m³, diameters d p = 1, 3, 5 µm, and residence times t = 0.0272, 0.2 , respectively. For particles of diameter 1 µm we find that, on the surface of Earth and Mars the deposition probabilities are higher at the poles when compared to the ones at the equator. Similarly, on the surface of the Earth we find that the deposition probabilities exhibit 0.5 and 0.4 % higher percentage difference at the poles when compared to that of the equator, for the corresponding residence times. Moreover in orbit equatorial orbits result to higher deposition probabilities when compared to polar ones. For both residence times particles with the diameters considered above in circular and elliptical orbits around Mars, the deposition probabilities appear to be the same for all orbital inclinations. Sedimentation probability increases drastically with particle diameter and orbital eccentricity of the orbiting spacecraft. Finally, as an alternative framework for the study of interaction and the effect of gravity in biology, and in particular gravity and the respiratory system we introduce is the term information in a way Shannon has introduced it, considering the sedimentation probability as a random variable. This can be thought as a way in which gravity enters the cognitive processes of the system (processing of information) in the cybernetic sense.

The effect of the shape and size of gold seeds irradiated with ultrasound on the bio-heat transfer in tissue.

The aim of this report is to propose a new methodology to treat prostate cancer with macro-rod-shaped gold seeds irradiated with ultrasound and develop a new computational method for temperature and thermal dose control of hyperthermia therapy induced by the proposed procedure. A computer code representation, based on the bio-heat diffusion equation, was developed to calculate the heat deposition and temperature elevation patterns in a gold rod and in the tissue surrounding it as a result of different therapy durations and ultrasound power simulations. The numerical results computed provide quantitative information on the interaction between high-energy ultrasound, gold seeds and biological tissues and can replicate the pattern observed in experimental studies. The effect of differences in shapes and sizes of gold rod targets irradiated with ultrasound is calculated and the heat enhancement and the bio-heat transfer in tissue are analyzed.

The Mass of Graviton and Its Relation to the Number of Information according to the Holographic Principle.

We investigate the relation of the mass of the graviton to the number of information N in a flat universe. As a result we find that the mass of the graviton scales as [Formula: see text]. Furthermore, we find that the number of gravitons contained inside the observable horizon is directly proportional to the number of information N; that is, N gr ∝ N. Similarly, the total mass of gravitons that exist in the universe is proportional to the number of information N; that is, [Formula: see text]. In an effort to establish a relation between the graviton mass and the basic parameters of the universe, we find that the mass of the graviton is simply twice the Hubble mass m H as it is defined by Gerstein et al. (2003), times the square root of the quantity q - 1/2, where q is the deceleration parameter of the universe. In relation to the geometry of the universe we find that the mass of the graviton varies according to the relation [Formula: see text], and therefore m gr obviously controls the geometry of the space time through a deviation of the geodesic spheres from the spheres of Euclidean metric.

Study of low speed flow cytometry for diffraction imaging with different chamber and nozzle designs.

Achieving effective hydrodynamic focusing and flow stability at low speed presents a challenging design task in flow cytometry for studying phenomena such as cell adhesion and diffraction imaging of cells with low-cost cameras. We have developed different designs of flow chamber and sheath nozzle to accomplish the above goal. A 3D computational model of the chambers has been established to simulate the fluid dynamics in different chamber designs and measurements have been performed to determine the velocity and size distributions of the core fluid from the nozzle. Comparison of the simulation data with experimental results shows good agreement. With the computational model significant insights were gained for optimization of the chamber design and improvement of the cell positioning accuracy for study of slow moving cells. The benefit of low flow speed has been demonstrated also by reduced blurring in the diffraction images of single cells. Based on these results, we concluded that the new designs of chamber and sheath nozzle produce stable hydrodynamic focusing of the core fluid at low speed and allow detailed study of cellular morphology under various rheological conditions using the diffraction imaging method.

Theoretical aspects and modelling of cellular decision making, cell killing and information-processing in photodynamic therapy of cancer.

BACKGROUND: The aim of this report is to provide a mathematical model of the mechanism for making binary fate decisions about cell death or survival, during and after Photodynamic Therapy (PDT) treatment, and to supply the logical design for this decision mechanism as an application of rate distortion theory to the biochemical processing of information by the physical system of a cell. METHODS: Based on system biology models of the molecular interactions involved in the PDT processes previously established, and regarding a cellular decision-making system as a noisy communication channel, we use rate distortion theory to design a time dependent Blahut-Arimoto algorithm where the input is a stimulus vector composed of the time dependent concentrations of three PDT related cell death signaling molecules and the output is a cell fate decision. The molecular concentrations are determined by a group of rate equations. The basic steps are: initialize the probability of the cell fate decision, compute the conditional probability distribution that minimizes the mutual information between input and output, compute the cell probability of cell fate decision that minimizes the mutual information and repeat the last two steps until the probabilities converge. Advance to the next discrete time point and repeat the process. RESULTS: Based on the model from communication theory described in this work, and assuming that the activation of the death signal processing occurs when any of the molecular stimulants increases higher than a predefined threshold (50% of the maximum concentrations), for 1800s of treatment, the cell undergoes necrosis within the first 30 minutes with probability range 90.0%-99.99% and in the case of repair/survival, it goes through apoptosis within 3-4 hours with probability range 90.00%-99.00%. Although, there is no experimental validation of the model at this moment, it reproduces some patterns of survival ratios of predicted experimental data. CONCLUSIONS: Analytical modeling based on cell death signaling molecules has been shown to be an independent and useful tool for prediction of cell surviving response to PDT. The model can be adjusted to provide important insights for cellular response to other treatments such as hyperthermia, and diseases such as neurodegeneration.

Modeling of oxygen transport and cell killing in type-II photodynamic therapy.

Photodynamic therapy (PDT) provides an effective option for treatment of tumors and other diseases in superficial tissues and attracts attention for in vitro study with cells. In this study, we present a significantly improved model of in vitro cell killing through Type-II PDT for simulation of the molecular interactions and cell killing in time domain in the presence of oxygen transport within a spherical cell. The self-consistency of the approach is examined by determination of conditions for obtaining positive definitive solutions of molecular concentrations. Decay constants of photosensitizers and unoxidized receptors are extracted as the key indices of molecular kinetics with different oxygen diffusion constants and permeability at the cell membrane. By coupling the molecular kinetics to cell killing, we develop a modeling method of PDT cytotoxicity caused by singlet oxygen and obtain the cell survival ratio as a function of light fluence or initial photosensitizer concentration with different photon density or irradiance of incident light and other parameters of oxygen transport. The results show that the present model of Type-II PDT yields a powerful tool to quantitate various events underlying PDT at the molecular and cellular levels and to interpret experimental results of in vitro cell studies.