Phenomenological universalities: a novel tool for the analysis of dynamic contrast enhancement in magnetic resonance imaging.

Dynamic contrast enhancement in magnetic resonance imaging (DCE-MRI) is a promising tool for the clinical diagnosis of tumors, whose implementation may be improved through the use of suitable hemodynamic models. If one prefers to avoid assumptions about the tumor physiology, empirical fitting functions may be adopted. For this purpose, in this paper we discuss the exploitation of a recently proposed phenomenological universalities (PUN) formalism. In fact, we show that a novel PUN class may be used to describe the time-signal intensity curves in both healthy and tumoral tissues, discriminating between the two cases and thus potentially providing a convenient diagnostic tool. The proposed approach is applied to analysis of the DCE-MRI data relative to a study group composed of ten patients with spine tumors.

Oscillations in growth of multicellular tumour spheroids: a revisited quantitative analysis.

OBJECTIVES: Multicellular tumour spheroids (MTS) provide an important tool for study of the microscopic properties of solid tumours and their responses to therapy. Thus, observation of large-scale volume oscillations in MTS, reported several years ago by two independent groups (1,2), in our opinion represent a remarkable discovery, particularly if this could promote careful investigation of the possible occurrence of volume oscillations of tumours 'in vivo'. MATERIALS AND METHODS: Because of high background noise, quantitative analysis of properties of observed oscillations has not been possible in previous studies. Such an analysis can be now performed, thanks to a recently proposed approach, based on formalism of phenomenological universalities (PUN). RESULTS: Results have provided unambiguous confirmation of the existence of MTS volume oscillations, and quantitative evaluation of their properties, for two tumour cell lines. Proof is based not only on quality of fitting of the experimental datasets, but also on determination of well-defined values of frequency and amplitude of the oscillations for each line investigated, which would not be consistent with random fluctuation. CONCLUSIONS: Biological mechanisms, which can be directly responsible for observed oscillations, are proposed, which relates also to recent work on related topics. Further investigations, both at experimental and at modelling levels, are also suggested. Finally, from a methodological point of view, results obtained represent further confirmation of applicability and usefulness of the PUN approach.

Concurrent growth of phenotypic features: a phenomenological universalities approach.

Different physical features of an organism are often measured concurrently, because their correlations can be used as predictors of longevity, future health, or adaptability to an ecological niche. Since, in general, we do not know a priori if the temporal variations in the measured quantities are causally related, it may be useful to have a method that could help us to identify possible correlations and to obtain parameters that may vary from population to population. In this paper we develop a procedure that may detect underlying relationships. We do this by generalizing the recently introduced concept of phenomenological universalities to the complex field. In this generalization, allometric growth is described by a complex function, whose real and imaginary parts represent two phenotypic traits of the same organism. As particular solutions of the resulting problem, we obtain generalizations of the Gompertz and the von Bertalanffy-West growth equations. We then apply the procedure to two biological systems in order to show how to determine the existence of mutual interference between trait variations.

Cancer metabolism and the dynamics of metastasis.

Cancer growth dynamics, commonly simulated with a Gompertzian model, is analyzed in the framework of a more recent and realistic model. In particular, we consider the setting of a tumor embedded in a host organ and investigate their interaction. We assume that, at least in some cases, tumor metastasis may be triggered by an 'energetic crisis', when the tumor exceeds the 'carrying capacity' of the host organ. As a consequence, dissemination of clusters of cancer cells is set in motion, with a statistical probability given by a Poisson distribution. The model, although still at a preclinical level, is fully quantitative and is applied, as an example, to the case of prostate cancer. The results confirm that, at least for the more aggressive cancers, metastasis starts very early during tumorigenesis and a quantitative link is found between the tumor's doubling time, its 'aggressiveness' and the metastatic potential.

A multilevel approach to cancer growth modeling.

Cancer growth models may be divided into macroscopic models, which describe the tumor as a single entity, and microscopic ones, which consider the tumor as a complex system whose behavior emerges from the local dynamics of its basic components, the neoplastic cells. Mesoscopic models (e.g. as based on the Local Interaction Simulation Approach [Delsanto, P.P., Mignogna, R., Scalerandi, M., Schechter, R., 1998. In: Delsanto, P.P. Saenz, A.W. (Eds.), New Perspectives on Problems in Classical and Quantum Physics, vol. 2. Gordon & Breach, New Delhi, p. 5174]), which explicitly consider the behavior of cell clusters and their interactions, may be used instead of the microscopic ones, in order to study the properties of cancer biology that strongly depend on the interactions of small groups of cells at intermediate spatial and temporal scales. All these approaches have been developed independently, which limits their usefulness, since they all include relevant features and information that should be cross-correlated for a deeper understanding of the mechanisms involved. In this contribution we consider multicellular tumor spheroids as biological reference systems and propose an intermediate model to bridge the gap between a macroscopic formulation of tumor growth and a mesoscopic one. Thus we are able to establish, as an important result of our formalism, a direct correspondence between parameters characterizing processes occurring at different scales. In particular, we analyze their dependence on an important limiting factor to tumor growth, i.e. the extra-cellular matrix pressure. Since the macro and meso-models stem from totally different roots (energy conservation and clinical observations vs. cell groups dynamics), their consistency may be used to validate both approaches. It may also be interesting to note that the proposed formalism fits well into a recently proposed conjecture of growth laws universality.

Classification scheme for phenomenological universalities in growth problems in physics and other sciences.

A classification in universality classes of broad categories of phenomenologies, belonging to physics and other disciplines, may be very useful for a cross fertilization among them and for the purpose of pattern recognition and interpretation of experimental data. We present here a simple scheme for the classification of nonlinear growth problems. The success of the scheme in predicting and characterizing the well known Gompertz, West, and logistic models, suggests to us the study of a hitherto unexplored class of nonlinear growth problems.

A 2D spring model for the simulation of ultrasonic wave propagation in nonlinear hysteretic media.

A two-dimensional (2D) approach to the simulation of ultrasonic wave propagation in nonclassical nonlinear (NCNL) media is presented. The approach represents the extension to 2D of a previously proposed one dimensional (1D) Spring Model, with the inclusion of a PM space treatment of the intersticial regions between grains. The extension to 2D is of great practical relevance for its potential applications in the field of quantitative nondestructive evaluation and material characterization, but it is also useful, from a theoretical point of view, to gain a better insight of the interaction mechanisms involved. The model is tested by means of virtual 2D experiments. The expected NCNL behaviors are qualitatively well reproduced.

Bridging the Gap between mesoscopic and macroscopic models: the case of multicellular tumor spheroids.

Multicellular tumor spheroids are valuable experimental tools in cancer research. By introducing an intermediate model, we have been able to successfully relate mesoscopic and macroscopic descriptions of spheroid growth. Since these descriptions stem from completely different roots (cell dynamics, and energy conservation and scaling arguments, respectively), their consistency validates both approaches and allows us to establish a direct correspondence between parameters characterizing processes occurring at different scales. Our approach may find applications as an example of bridging the gap between models at different scale levels in other contexts.

Modelling and simulation of acoustic wave propagation in locally resonant sonic materials.

Sonic crystals are artificial structures consisting of a periodic array of acoustic scatterers embedded in a homogeneous matrix material, with a usually large impedance mismatch between the two materials. They exhibit strong sound attenuation at selective frequency bands due to the interference of multiply reflected waves. However, sound attenuation bands in the audible range are only achieved by unfunctionally large sonic crystals. If local resonators are used instead of simple scatterers, the frequencies of the attenuation bands can be reduced by about two orders of magnitude. In the present paper we perform numerical simulations of acoustic wave propagation through sonic crystals consisting of local resonators using the local interaction simulation approach (LISA). Three strong attenuation bands are found at frequencies between 0.3 and 6.0 kHz, which do not depend on the periodicity of the crystal. The results are in good qualitative agreement with experimental data. We analyze the dependence of the resonance frequencies on the structural parameters of the local resonators in order to create a tool for design and optimization of any kind of sonic crystal.

Modeling the propagation of ultrasonic waves in the interface region between two bonded elements.

An important task in nondestructive materials evaluation is the development of techniques to characterize the bond quality of adherent joints. Binding forces are nonlinear and cause a nonlinear modulation of transmitted and reflected ultrasonic waves. As a consequence, the higher harmonics generated by an insonified monochromatic wave give information about the adhesive bonds. The local binding forces in thin bonded interfaces can be obtained by the amplitudes of the ultrasonic waves of the insonified frequency and its higher harmonics as transmitted through the interface. Additional phase measurements may enable one to obtain the evaluation of the full hysteretic cycle of the interaction force. In order to gain a deeper understanding of the interface region and to improve the technique, numerical simulations of the ultrasonic wave propagation through specimens of two bonded elements can be used. A simple model based on the local interaction simulation approach (LISA) is described in this contribution, and a comparison between the results of the simulations and the experimental data is presented. Besides its intrinsic relevance for NDE, the problem considered in this paper may be very useful to analyze and test models for the simulation of ultrasonic wave propagation in nonclassical nonlinear mesoscopic elastic materials.

Effects of anatomical constraints on tumor growth.

Competition for available nutrients and the presence of anatomical barriers are major determinants of tumor growth in vivo. We extend a model recently proposed to simulate the growth of neoplasms in real tissues to include geometrical constraints mimicking pressure effects on the tumor surface induced by the presence of rigid or semirigid structures. Different tissues have different diffusivities for nutrients and cells. Despite the simplicity of the approach, based on a few inherently local mechanisms, the numerical results agree qualitatively with clinical data (computed tomography scans of neoplasms) for the larynx and the oral cavity.

Local interaction simulation approach for the response of the vascular system to metabolic changes of cell behavior.

The self-regulatory interactions between cells and the vascular system are mediated by signals propagating at a finite speed. In order to build up a physical model of these processes, several features, such as storing of internal energy, nonclassical nonlinear behavior, and delay and threshold effects, have to be taken into account. Considering cells as particles in different metabolic states according to their internal energy, we have developed a model based on the local interaction simulation approach. Several numerical results, in qualitative agreement with biological observations, illustrate the applicability of the model and the method to implement it.

Analysis of a "phase transition" from tumor growth to latency.

A mathematical model, based on the local interaction simulation approach, is developed in order to allow simulations of the spatiotemporal evolution of neoplasies. The model consists of a set of rules, which govern the interaction of cancerous cells among themselves and in competition with other cell populations for the acquisition of essential nutrients. As a result of small variations in the basic parameters, it leads to four different outcomes: indefinite growth, metastasis, latency, and complete regression. In the present contribution a detailed analysis of the dormant phase is carried on and the critical parameters for the transition to other phases are computed. Interesting chaotic behaviors can also be observed, with different attractors in the parameters space. Interest in the latency phase has been aroused by therapeutical strategies aiming to reduce a growing tumor to dormancy. The effect of such strategies may be simulated with our approach.

Scattering of ultrasonic waves by void inclusions.

The Local Interaction Simulation Approach (LISA) has been applied to study the propagation of ultrasonic pulses in materials containing void inclusions. First the case of a single scatterer has been considered, with the conclusion that a void must be represented by at least four cells of the discretization lattice. Then the case of ultrasound propagation in a material with both a regular and random distribution of inclusions has been studied. Interesting interference effects have been obtained and it can be concluded that in both cases LISA allows reliable and efficient simulations to be performed.

A physical-based model for the simulation of neoplastic growth and metastasis.

BACKGROUND AND OBJECTIVES: It is possible to formulate models capable of reproducing the main details of the physical processes involved in the evolution of biological systems. The complexity of the problem requires to begin with a simple and universal model for the description of the cellular growth, to be adapted successively to the local conditions found in clinically observed neoplastic growths. METHODS: A model based on the Local Interaction Simulation Approach (LISA) has been formulated for the simulation of growth, diffusion, and metastasis of neoplasms. The vascularization is described by a blood vessel located on one edge of the specimen in which a constant and homogeneous flow is assumed. A nutrient density is defined to mimic the blood flow within the tissue. RESULTS: Photograms taken at proper times may identify the main characteristics of the tumor evolution and describe its volume variations in a transversal section. Furthermore, it is possible to monitor constantly the volume of the neoplasm and of the necrotic tissue as a function of time, as well as the portion of cells that have migrated in the blood vessel. CONCLUSIONS: In spite of strong simplifying assumptions, the model presents good qualitative agreement with clinical data, which may be further improved by more detailed information about cancer cells properties or local vascular system patterns.

Non-linear model of cancer growth and metastasis: a limiting nutrient as a major determinant of tumor shape and diffusion.

A new approach for modelling the spatio-temporal evolution of tumors is presented. To test its validity, a very basic model is considered, which, in spite of its simplicity, is capable of generating a multiplicity of morphologies and growth and migration rates. From an in-vivo scenario of basic life processes, cancer cell proliferation is described as a competition for basic nutrients. The chosen mathematical treatment and simulation techniques permit a direct implementation of the local nonlinear couplings existing between the various cell populations and the free and bound nutrient concentration. A discussion of the results and proposed improvements and applications of the model is also presented.

Effect of transport and competition on ligand binding.

We present a model to describe the physics of chemoreception in processes determined by competitive ligand binding. Our model describes the competition between various populations, such as ligands vs. blockers and receptors vs. decoys, in protein activation when diffusion is rate-determining. Full spatio-temporal solutions can be obtained numerically. The model structure is kept simple enough as to permit its easy generalization to describe a large subset of the manifold of possible situations occurring in nature. The power and simplicity of the proposed method are exhibited through the solution of several examples which are discussed in detail.

Real-time parallel computation and visualization of ultrasonic pulses in solids.

Parallel processing has changed the way much computational physics is done. Areas such as condensed matter physics, fluid dynamics, and other fields are making use of massively parallel computers to solve immense and important problems in new ways. Simulating wave propagation is another area that has benefited through the use of parallel processing. This is graphically illustrated in this article by various numerical simulations of ultrasonic pulses propagating through solids carried out on a massively parallel computer. These computations are accompanied by visualizations of the resulting wavefield. The calculations and visualizations, together, can be completed in only seconds to several minutes and compare well with experimental data. The computations and parallel processing techniques described should be important in related fields, such as geophysics, acoustics, and mechanics.