Computer simulation of glioma growth and morphology.

Despite major advances in the study of glioma, the quantitative links between intra-tumor molecular/cellular properties, clinically observable properties such as morphology, and critical tumor behaviors such as growth and invasiveness remain unclear, hampering more effective coupling of tumor physical characteristics with implications for prognosis and therapy. Although molecular biology, histopathology, and radiological imaging are employed in this endeavor, studies are severely challenged by the multitude of different physical scales involved in tumor growth, i.e., from molecular nanoscale to cell microscale and finally to tissue centimeter scale. Consequently, it is often difficult to determine the underlying dynamics across dimensions. New techniques are needed to tackle these issues. Here, we address this multi-scalar problem by employing a novel predictive three-dimensional mathematical and computational model based on first-principle equations (conservation laws of physics) that describe mathematically the diffusion of cell substrates and other processes determining tumor mass growth and invasion. The model uses conserved variables to represent known determinants of glioma behavior, e.g., cell density and oxygen concentration, as well as biological functional relationships and parameters linking phenomena at different scales whose specific forms and values are hypothesized and calculated based on in vitro and in vivo experiments and from histopathology of tissue specimens from human gliomas. This model enables correlation of glioma morphology to tumor growth by quantifying interdependence of tumor mass on the microenvironment (e.g., hypoxia, tissue disruption) and on the cellular phenotypes (e.g., mitosis and apoptosis rates, cell adhesion strength). Once functional relationships between variables and associated parameter values have been informed, e.g., from histopathology or intra-operative analysis, this model can be used for disease diagnosis/prognosis, hypothesis testing, and to guide surgery and therapy. In particular, this tool identifies and quantifies the effects of vascularization and other cell-scale glioma morphological characteristics as predictors of tumor-scale growth and invasion.

Computer simulation of glioma growth and morphology.

Despite major advances in the study of glioma, the quantitative links between intra-tumor molecular/cellular properties, clinically observable properties such as morphology, and critical tumor behaviors such as growth and invasiveness remain unclear, hampering more effective coupling of tumor physical characteristics with implications for prognosis and therapy. Although molecular biology, histopathology, and radiological imaging are employed in this endeavor, studies are severely challenged by the multitude of different physical scales involved in tumor growth, i.e., from molecular nanoscale to cell microscale and finally to tissue centimeter scale. Consequently, it is often difficult to determine the underlying dynamics across dimensions. New techniques are needed to tackle these issues. Here, we address this multi-scalar problem by employing a novel predictive three-dimensional mathematical and computational model based on first-principle equations (conservation laws of physics) that describe mathematically the diffusion of cell substrates and other processes determining tumor mass growth and invasion. The model uses conserved variables to represent known determinants of glioma behavior, e.g., cell density and oxygen concentration, as well as biological functional relationships and parameters linking phenomena at different scales whose specific forms and values are hypothesized and calculated based on in vitro and in vivo experiments and from histopathology of tissue specimens from human gliomas. This model enables correlation of glioma morphology to tumor growth by quantifying interdependence of tumor mass on the microenvironment (e.g., hypoxia, tissue disruption) and on the cellular phenotypes (e.g., mitosis and apoptosis rates, cell adhesion strength). Once functional relationships between variables and associated parameter values have been informed, e.g., from histopathology or intra-operative analysis, this model can be used for disease diagnosis/prognosis, hypothesis testing, and to guide surgery and therapy. In particular, this tool identifies and quantifies the effects of vascularization and other cell-scale glioma morphological characteristics as predictors of tumor-scale growth and invasion.

THEORETICAL STUDIES ON THE METHODS OF RECONSTRUCTING PHYLOGENETIC TREES FROM DNA SEQUENCE DATA (MOLECULAR EVOLUTION, HOMINOID EVOLUTION, COMPUTER SIMULATION)

(1) A mathematical theory for computing the probabilities of various nucleotide configurations is developed, and the probability of obtaining the correct phylogenetic tree (model tree) from sequence data is evaluated for six phylogenetic tree-making methods (UPGMA, distance Wagner method, transformed distance method, Fitch-Margoliash's method, maximum parsimony method, and compatibility method). The number of nucleotides (m*) necessary to obtain the correct tree with a probability of 95% is estimated with special reference to the human, chimpanzee, and gorilla divergence. m* is at least 4,200, but the availability of outgroup species greatly reduces m* for all methods except UPGMA. m* increases if transitions occur more frequently than transversions as in the case of mitochondrial DNA. (2) A new tree-making method called the neighbor-joining method is proposed. This method is applicable either for distance data or character state data. Computer simulation has shown that the neighbor-joining method is generally better than UPGMA, Farris' method, Li's method, and modified Farris method on recovering the true topology when distance data are used. A related method, the simultaneous partitioning method, is also discussed. (3) The maximum likelihood (ML) method for phylogeny reconstruction under the assumption of both constant and varying evolutionary rates is studied, and a new algorithm for obtaining the ML tree is presented. This method gives a tree similar to that obtained by UPGMA when constant evolutionary rate is assumed, whereas it gives a tree similar to that obtained by the maximum parsimony tree and the neighbor-joining method when varying evolutionary rate is assumed. ^

High-resolution dynamic computer simulation analysis of the behavior of sample components with pI values outside the pH gradient established by carrier ampholyte CIEF

The behavior of sample components whose pI values are outside the pH gradient established by 101 hypothetical biprotic carrier ampholytes covering a pH 6-8 range was investigated by computer simulation under constant current conditions with concomitant constant electroosmosis toward the cathode. Data obtained with the sample being applied between zones of carrier ampholytes and on the anodic side of the carrier ampholytes were studied and found to evolve into zone structures comprising three regions between anolyte and catholyte. The focusing region with the pH gradient is bracketed by two isotachopheretic zone structures comprising selected sample and carrier components as isotachophoretic zones. The isotachophoretic structures electrophoretically migrate in opposite direction and their lengths increase with time due to the gradual isotachophoretic decay at the pH gradient edges. Due to electroosmosis, however, the overall pattern is being transported toward the cathode. Sample components whose pI values are outside the established pH gradient are demonstrated to form isotachophoretic zones behind the leading cation of the catholyte (components with pI values larger than 8) and the leading anion of the anolyte (components with pI values smaller than 6). Amphoteric compounds with appropriate pI values or nonamphoteric components can act as isotachophoretic spacer compounds between sample compounds or between the leader and the sample with the highest mobility. The simulation data obtained provide for the first time insight into the dynamics of amphoteric sample components that do not focus within the established pH gradient.

Dynamic high-resolution computer simulation of isotachophoretic enantiomer separation and zone stability

The development of electrophoretic computer models and their use for simulation of electrophoretic processes has increased significantly during the last few years. Recently, GENTRANS and SIMUL5 were extended with algorithms that describe chemical equilibria between solutes and a buffer additive in a fast 1:1 interaction process, an approach that enables simulation of the electrophoretic separation of enantiomers. For acidic cationic systems with sodium and H3 0(+) as leading and terminating components, respectively, acetic acid as counter component, charged weak bases as samples, and a neutral CD as chiral selector, the new codes were used to investigate the dynamics of isotachophoretic adjustment of enantiomers, enantiomer separation, boundaries between enantiomers and between an enantiomer and a buffer constituent of like charge, and zone stability. The impact of leader pH, selector concentration, free mobility of the weak base, mobilities of the formed complexes and complexation constants could thereby be elucidated. For selected examples with methadone enantiomers as analytes and (2-hydroxypropyl)-β-CD as selector, simulated zone patterns were found to compare well with those monitored experimentally in capillary setups with two conductivity detectors or an absorbance and a conductivity detector. Simulation represents an elegant way to provide insight into the formation of isotachophoretic boundaries and zone stability in presence of complexation equilibria in a hitherto inaccessible way.

Sampling strategies for capillary isoelectric focusing with electroosmotic zone mobilization assessed by high-resolution dynamic computer simulation

The impact of initial sample distribution on separation and focusing of analytes in a pH 3–11 gradient formed by 101 biprotic carrier ampholytes under concomitant electroosmotic displacement was studied by dynamic high-resolution computer simulation. Data obtained with application of the analytes mixed with the carrier ampholytes (as is customarily done), as a short zone within the initial carrier ampholyte zone, sandwiched between zones of carrier ampholytes, or introduced before or after the initial carrier ampholyte zone were compared. With sampling as a short zone within or adjacent to the carrier ampholytes, separation and focusing of analytes is shown to proceed as a cationic, anionic, or mixed process and separation of the analytes is predicted to be much faster than the separation of the carrier components. Thus, after the initial separation, analytes continue to separate and eventually reach their focusing locations. This is different to the double-peak approach to equilibrium that takes place when analytes and carrier ampholytes are applied as a homogenous mixture. Simulation data reveal that sample application between two zones of carrier ampholytes results in the formation of a pH gradient disturbance as the concentration of the carrier ampholytes within the fluid element initially occupied by the sample will be lower compared to the other parts of the gradient. As a consequence thereof, the properties of this region are sample matrix dependent, the pH gradient is flatter, and the region is likely to represent a conductance gap (hot spot). Simulation data suggest that sample placed at the anodic side or at the anodic end of the initial carrier ampholyte zone are the favorable configurations for capillary isoelectric focusing with electroosmotic zone mobilization.

Dynamic high-resolution computer simulation of electrophoretic enantiomer separations with neutral cyclodextrins as chiral selectors.

GENTRANS, a comprehensive one-dimensional dynamic simulator for electrophoretic separations and transport, was extended for handling electrokinetic chiral separations with a neutral ligand. The code can be employed to study the 1:1 interaction of monovalent weak and strong acids and bases with a single monovalent weak or strong acid or base additive, including a neutral cyclodextrin, under real experimental conditions. It is a tool to investigate the dynamics of chiral separations and to provide insight into the buffer systems used in chiral capillary zone electrophoresis (CZE) and chiral isotachophoresis. Analyte stacking across conductivity and buffer additive gradients, changes of additive concentration, buffer component concentration, pH, and conductivity across migrating sample zones and peaks, and the formation and migration of system peaks can thereby be investigated in a hitherto inaccessible way. For model systems with charged weak bases and neutral modified β-cyclodextrins at acidic pH, for which complexation constants, ionic mobilities, and mobilities of selector-analyte complexes have been determined by CZE, simulated and experimentally determined electropherograms and isotachopherograms are shown to be in good agreement. Simulation data reveal that CZE separations of cationic enantiomers performed in phosphate buffers at low pH occur behind a fast cationic migrating system peak that has a small impact on the buffer composition under which enantiomeric separation takes place.

Dynamic computer simulation of electrophoretic enantiomer migration order and separation in presence of a neutral cyclodextrin

One-dimensional dynamic computer simulation was employed to investigate the separation and migration order change of ketoconazole enantiomers at low pH in presence of increasing amounts of (2-hydroxypropyl)-β-cyclodextrin (OHP-β-CD). The 1:1 interaction of ketoconazole with the neutral cyclodextrin was simulated under real experimental conditions and by varying input parameters for complex mobilities and complexation constants. Simulation results obtained with experimentally determined apparent ionic mobilities, complex mobilities, and complexation constants were found to compare well with the calculated separation selectivity and experimental data. Simulation data revealed that the migration order of the ketoconazole enantiomers at low (OHP-β-CD) concentrations (i.e. below migration order inversion) is essentially determined by the difference in complexation constants and at high (OHP-β-CD) concentrations (i.e. above migration order inversion) by the difference in complex mobilities. Furthermore, simulations with complex mobilities set to zero provided data that mimic migration order and separation with the chiral selector being immobilized. For the studied CEC configuration, no migration order inversion is predicted and separations are shown to be quicker and electrophoretic transport reduced in comparison to migration in free solution. The presented data illustrate that dynamic computer simulation is a valuable tool to study electrokinetic migration and separations of enantiomers in presence of a complexing agent.

Computer simulation of electrophoretic aspects of enantiomer migration and separation in capillary electrochromatography with a neutral selector.

A computer simulation study describing the electrophoretic separation and migration of methadone enantiomers in presence of free and immobilized (2-hydroxypropyl)-β-CD is presented. The 1:1 interaction of methadone with the neutral CD was simulated by using experimentally determined mobilities and complexation constants for the complexes in a low-pH BGE comprising phosphoric acid and KOH. The use of complex mobilities represents free solution conditions with the chiral selector being a buffer additive, whereas complex mobilities set to zero provide data that mimic migration and separation with the chiral selector being immobilized, that is CEC conditions in absence of unspecific interaction between analytes and the chiral stationary phase. Simulation data reveal that separations are quicker, electrophoretic displacement rates are reduced, and sensitivity is enhanced in CEC with on-column detection in comparison to free solution conditions. Simulation is used to study electrophoretic analyte behavior at the interface between sample and the CEC column with the chiral selector (analyte stacking) and at the rear end when analytes leave the environment with complexation (analyte destacking). The latter aspect is relevant for off-column analyte detection in CEC and is described here for the first time via the dynamics of migrating analyte zones. Simulation provides insight into means to counteract analyte dilution at the column end via use of a BGE with higher conductivity. Furthermore, the impact of EOF on analyte migration, separation, and detection for configurations with the selector zone being displaced or remaining immobilized under buffer flow is simulated. In all cases, the data reveal that detection should occur within or immediately after the selector zone.

Impact of Taylor-Aris diffusivity on analyte and system zone dispersion in CZE assessed by computer simulation and experimental validation.

Application of pressure-driven laminar flow has an impact on zone and boundary dispersion in open tubular CE. The GENTRANS dynamic simulator for electrophoresis was extended with Taylor-Aris diffusivity which accounts for dispersion due to the parabolic flow profile associated with pressure-driven flow. Effective diffusivity of analyte and system zones as functions of the capillary diameter and the amount of flow in comparison to molecular diffusion alone were studied for configurations with concomitant action of imposed hydrodynamic flow and electroosmosis. For selected examples under realistic experimental conditions, simulation data are compared with those monitored experimentally using modular CE setups featuring both capacitively coupled contactless conductivity and UV absorbance detection along a 50 μm id fused-silica capillary of 90 cm total length. The data presented indicate that inclusion of flow profile based Taylor-Aris diffusivity provides realistic simulation data for analyte and system peaks, particularly those monitored in CE with conductivity detection.

Cerebellar mechanisms for motor learning: Testing predictions from a large-scale computer simulation

The cerebellum is the major brain structure that contributes to our ability to improve movements through learning and experience. We have combined computer simulations with behavioral and lesion studies to investigate how modification of synaptic strength at two different sites within the cerebellum contributes to a simple form of motor learning—Pavlovian conditioning of the eyelid response. These studies are based on the wealth of knowledge about the intrinsic circuitry and physiology of the cerebellum and the straightforward manner in which this circuitry is engaged during eyelid conditioning. Thus, our simulations are constrained by the well-characterized synaptic organization of the cerebellum and further, the activity of cerebellar inputs during simulated eyelid conditioning is based on existing recording data. These simulations have allowed us to make two important predictions regarding the mechanisms underlying cerebellar function, which we have tested and confirmed with behavioral studies. The first prediction describes the mechanisms by which one of the sites of synaptic modification, the granule to Purkinje cell synapses (gr → Pkj) of the cerebellar cortex, could generate two time-dependent properties of eyelid conditioning—response timing and the ISI function. An empirical test of this prediction using small, electrolytic lesions of the cerebellar cortex revealed the pattern of results predicted by the simulations. The second prediction made by the simulations is that modification of synaptic strength at the other site of plasticity, the mossy fiber to deep nuclei synapses (mf → nuc), is under the control of Purkinje cell activity. The analysis predicts that this property should confer mf → nuc synapses with resistance to extinction. Thus, while extinction processes erase plasticity at the first site, residual plasticity at mf → nuc synapses remains. The residual plasticity at the mf → nuc site confers the cerebellum with the capability for rapid relearning long after the learned behavior has been extinguished. We confirmed this prediction using a lesion technique that reversibly disconnected the cerebellar cortex at various stages during extinction and reacquisition of eyelid responses. The results of these studies represent significant progress toward a complete understanding of how the cerebellum contributes to motor learning. ^

Computer Simulation of Crowd Dynamics and Destructive Crowd Behavior

The social processes that lead to destructive behavior in celebratory crowds can be studied through an agent-based computer simulation. Riots are an increasingly common outcome of sports celebrations, and pose the potential for harm to participants, bystanders, property, and the reputation of the groups with whom participants are associated. Rioting cannot necessarily be attributed to the negative emotions of individuals, such as anger, rage, frustration and despair. For instance, the celebratory behavior (e.g., chanting, cheering, singing) during UConn’s “Spring Weekend” and after the 2004 NCAA Championships resulted in several small fires and overturned cars. Further, not every individual in the area of a riot engages in violence, and those who do, do not do so continuously. Instead, small groups carry out the majority of violent acts in relatively short-lived episodes. Agent-based computer simulations are an ideal method for modeling complex group-level social phenomena, such as celebratory gatherings and riots, which emerge from the interaction of relatively “simple” individuals. By making simple assumptions about individuals’ decision-making and behaviors and allowing actors to affect one another, behavioral patterns emerge that cannot be predicted by the characteristics of individuals. The computer simulation developed here models celebratory riot behavior by repeatedly evaluating a single algorithm for each individual, the inputs of which are affected by the characteristics of nearby actors. Specifically, the simulation assumes that (a) actors possess 1 of 5 distinct social identities (group memberships), (b) actors will congregate with actors who possess the same identity, (c) the degree of social cohesion generated in the social context determines the stability of relationships within groups, and (d) actors’ level of aggression is affected by the aggression of other group members. Not only does this simulation provide a systematic investigation of the effects of the initial distribution of aggression, social identification, and cohesiveness on riot outcomes, but also an analytic tool others may use to investigate, visualize and predict how various individual characteristics affect emergent crowd behavior.

Evaluation of angle-dependent absorption: Computer simulation and listening test for an objective and subjective evaluation

The aim of this thesis is the subjective and objective evaluation of angledependent absorption coefficients. As the assumption of a constant absorption coefficient over the angle of incidence is not always held, a new model acknowledging an angle-dependent reflection must be considered, to get a more accurate prediction in the sound field. The study provides information about the behavior of different materials in several rooms, depending on the reflection modeling of incident sound waves. An objective evaluation was run for an implementation of angle-dependent reflection factors in the image source and ray tracing simulation models. Results obtained were analysed after comparison to diffuse-field averaged data. However, changes in acoustic characteristics of a room do not always mean a variation in the listener’s perception. Thus, additional subjective evaluation allowed a comparison between the different results obtained with the computer simulation and the response from the individuals who participated in the listening test. The listening test was designed following a three-alternative forced-choice (3AFC) paradigm. In each interaction asked to the subjects a sequence of either three pink noise bursts or three natural signals was alternated. These results were supposed to show the influence and perception of the two different ways to implement surface reflection –either with diffuse or angle-dependent absorption properties. Results show slightly audible effects when material properties were exaggerated. El objetivo de este trabajo es la evaluación objetiva y subjetiva del coeficiente de absorción en función del ángulo de incidencia de la onda de sonido. La suposición de un coeficiente de absorción constante con respecto al ángulo de incidencia no siempre se sostiene. Por ello, un nuevo modelo considerando la reflexión dependiente del ángulo se debe tener en cuenta para obtener predicciones más certeras en el campo del sonido. El estudio proporciona información sobre el comportamiento de diferentes materiales en distintos recintos, dependientes del modelo de reflexión de las ondas de sonido incidentes. Debido a las dificultades a la hora de realizar las medidas y, por lo tanto, a la falta de datos, los coeficientes de absorción dependientes del ángulo a menudo no se tienen en cuenta a la hora de realizar las simulaciones. Hoy en día, aún no hay una tendencia de aplicar el coeficiente de absorción dependiente del ángulo para mejorar los modelos de reflexión. Por otra parte, para una medición satisfactoria de la absorción dependiente del ángulo, sólo hay unos pocos métodos. Las técnicas de medición actuales llevan mucho tiempo y hay algunos materiales, condiciones y ángulos que no pueden ser reproducidos y, por lo tanto, no es posible su medición. Sin embargo, en el presente estudio, los ángulos de incidencia de las ondas de sonido son conocidos y almacenados en una de base de datos para cada uno de los materiales, de modo que los coeficientes de absorción para el ángulo dado pueden ser devueltos siempre que sean requeridos por el usuario. Para realizar el estudio se llevó a cabo una evaluación objetiva, por medio de la implementación del factor de reflexión dependiente del ángulo en los modelos de fuentes imagen y trazado de rayos. Los resultados fueron analizados después de ser comparados con el promedio de los datos obtenidos en medidas en el campo difuso. La simulación se hizo una vez se configuraron un número de materiales creados por el autor, a partir de los datos existentes en la literatura y los catálogos de fabricantes. Los modelos de Komatsu y Mechel sirvieron como referencia para los materiales porosos, configurando la resistividad al aire o el grosor, y para los paneles perforados, introduciendo el radio de los orificios y la distancia entre centros, respectivamente. Estos materiales se situaban en la pared opuesta a la que se consideraba que debía alojar a la fuente sonora. El resto de superficies se modelaban con el mismo material, variando su coeficiente de absorción y/o de dispersión. Al mismo tiempo, una serie de recintos fueron modelados para poder reproducir distintos escenarios de los que obtener los resultados. Sin embargo, los cambios en las características acústicas de un recinto no significan variaciones en la percepción por parte del oyente. Por ello, una evaluación subjetiva adicional permitió una comparación entre los diferentes resultados obtenidos mediante la simulación informática y la respuesta de los individuos que participaron en la prueba de escucha. Ésta fue diseñada bajo las pautas del modelo de test three-alternative forced-choice (3AFC), con treinta y dos preguntas diferentes. En cada iteración los sujetos fueron preguntados por una secuencia alterna entre tres señales, siendo dos de ellas iguales. Éstas podían ser tanto ráfagas de ruido rosa como señales naturales, en este test se utilizó un fragmento de una obra clásica interpretada por un piano. Antes de contestar al cuestionario, los bloques de preguntas eran ordenados al azar. Para cada ensayo, la mezcla era diferente, así los sujetos no repetían la misma prueba, evitando un sesgo por efectos de aprendizaje. Los bloques se barajaban recordando siempre el orden inicial, para después almacenar los resultados reordenados. La prueba de escucha fue realizada por veintitrés personas, toda ellas con conocimientos dentro del campo de la acústica. Antes de llevar a cabo la prueba de escucha en un entorno adecuado, una hoja con las instrucciones fue facilitada a cada persona. Los resultados muestran la influencia y percepción de las dos maneras distintas de implementar las reflexiones de una superficie –ya sea con respecto a la propiedad de difusión o de absorción dependiente del ángulo de los materiales. Los resultados objetivos, después de ejecutar las simulaciones, muestran los datos medios obtenidos para comprender el comportamiento de distintos materiales de acuerdo con el modelo de reflexión utilizado en el caso de estudio. En las tablas proporcionadas en la memoria se muestran los valores del tiempo de reverberación, la claridad y el tiempo de caída temprana. Los datos de las características del recinto obtenidos en este análisis tienen una fuerte dependencia respecto al coeficiente de absorción de los diferentes materiales que recubren las superficies del cuarto. En los resultados subjetivos, la media de percepción, a la hora de distinguir las distintas señales, por parte de los sujetos, se situó significativamente por debajo del umbral marcado por el punto de inflexión de la función psicométrica. Sin embargo, es posible concluir que la mayoría de los individuos tienden a ser capaces de detectar alguna diferencia entre los estímulos presentados en el 3AFC test. En conclusión, la hipótesis de que los valores del coeficiente de absorción dependiente del ángulo difieren es contrastada. Pero la respuesta subjetiva de los individuos muestra que únicamente hay ligeras variaciones en la percepción si el coeficiente varía en intervalos pequeños entre los valores manejados en la simulación. Además, si los parámetros de los materiales acústicos no son exagerados, los sujetos no perciben ninguna variación. Los primeros resultados obtenidos, proporcionando información respecto a la dependencia del ángulo, llevan a una nueva consideración en el campo de la acústica, y en la realización de nuevos proyectos en el futuro. Para futuras líneas de investigación, las simulaciones se deberían realizar con distintos tipos de recintos, buscando escenarios con geometrías irregulares. También, la implementación de distintos materiales para obtener resultados más certeros. Otra de las fases de los futuros proyectos puede realizarse teniendo en cuenta el coeficiente de dispersión dependiente del ángulo de incidencia de la onda de sonido. En la parte de la evaluación subjetiva, realizar una serie de pruebas de escucha con distintos individuos, incluyendo personas sin una formación relacionada con la ingeniería acústica.

Computer simulation of the interplay between fractal structures and surrounding heterogeneous multifractal distributions. Applications

In a large number of physical, biological and environmental processes interfaces with high irregular geometry appear separating media (phases) in which the heterogeneity of constituents is present. In this work the quantification of the interplay between irregular structures and surrounding heterogeneous distributions in the plane is made For a geometric set image and a mass distribution (measure) image supported in image, being image, the mass image gives account of the interplay between the geometric structure and the surrounding distribution. A computation method is developed for the estimation and corresponding scaling analysis of image, being image a fractal plane set of Minkowski dimension image and image a multifractal measure produced by random multiplicative cascades. The method is applied to natural and mathematical fractal structures in order to study the influence of both, the irregularity of the geometric structure and the heterogeneity of the distribution, in the scaling of image. Applications to the analysis and modeling of interplay of phases in environmental scenarios are given.