J. C. Antoranz

Behavior of tumors under nonstationary therapy

We present a model for the interaction dynamics of lymphocytes-tumor cells population. This model reproduces all known states for the tumor. Further, we develop it taking into account periodical immunotherapy treatment with cytokines alone. A detailed analysis for the evolution of tumor cells as a function of frequency and therapy burden applied for the periodical treatment is carried out. Certain threshold values for the frequency and applied doses are derived from this analysis. So it seems possible to control and reduce the growth of the tumor. Also, constant values for cytokines doses seems to be a successful treatment.

Lévy flights and earthquakes

Levy flights representation is proposed to describe earthquake characteristics like the distribution of waiting times and position of hypocenters in a seismic region. Over 7500 microearthquakes and earthquakes from 1985 to 1994 were analyzed to test that its spatial and temporal distributions are such that can be described by a Levy flight with anomalous diffusion (in this case in a subdiffusive regime). Earthquake behavior is well described through Levy flights and Levy distribution functions such as results show.

Continuous time random walks and south Spain seismic series

Lévy flights were introduced through the mathematical research of thealgebra or random variables with infinite moments. Mandelbrot recognizedthat the Lévy flight prescription had a deep connection toscale-invariant fractal random walk trajectories. The theory of ContinuousTime Random Walks (CTRW) can be described in terms of Lévydistribution functions and it can be used to explain some earthquakecharacteristics like the distribution of waiting times and hypocenter locationsin a seismic region. This paper checks the validity of this assumptionanalyzing three seismic series localized in South Spain. The three seismicseries (Alborán, Antequera and Loja) show qualitatively the samebehavior, although there are quantitative differences between them.

Impact of image spatial, temporal, and velocity resolutions on cardiovascular indices derived from color-Doppler echocardiography

Quantitative processing of color-Doppler echocardiographic images has substantially improved noninvasive assessment of cardiac physiology. Many indices are computed from the velocity fields derived either from color-Doppler tissue imaging (DTI), such as acceleration, strain and strain-rate, or from blood-flow color-Doppler, such as intracardiac pressure gradients (ICPG). All of these indices are dependent on the finite resolution of the ultrasound scanner. Therefore, we developed an image-dependent method for assessing the influence of temporal, spatial, and velocity resolutions, on cardiovascular parameters derived from velocity images. In order to focus our study on the spatial, temporal, and velocity resolutions of the digital image, we did not consider the effect of other sources of noise such as the interaction between ultrasound and tissue. A simple first-order Taylors expansion was used to establish the functional relationship between the acquired image velocity and the calculated cardiac index. Resolutions were studied on: (a) myocardial acceleration, strain, and strain-rate from DTI, and (b) ICPG from blood-flow color-Doppler. The performance of Taylors-based error bounds (TBEB) was demonstrated on simulated models and illustrated on clinical images. Velocity and temporal resolution were highly relevant for the accuracy of DTI-derived parameters and ICPGs. TBEB allow to assess the effects of ideal digital image resolution on quantitative cardiovascular indices derived from velocity measurements obtained by cardiac imaging techniques.

Support vector analysis of color-Doppler images: a new approach for estimating indices of left ventricular function

Reliable noninvasive estimators of global left ventricular (LV) chamber function remain unavailable. We have previously demonstrated a potential relationship between color-Doppler M-mode (CDMM) images and two basic indices of LV function: peak-systolic elastance (Emax ) and the time-constant of LV relaxation (tau). Thus, we hypothesized that these two indices could be estimated noninvasively by adequate postprocessing of CDMM recordings. A semiparametric regression (SR) version of support vector machine (SVM) is here proposed for building a blind model, capable of analyzing CDMM images automatically, as well as complementary clinical information. Simultaneous invasive and Doppler tracings were obtained in nine mini-pigs in a high-fidelity experimental setup. The model was developed using a test and validation leave-one-out design. Reasonably acceptable prediction accuracy was obtained for both Emax (intraclass correlation coefficient R ic=0.81) and tau (Ric=0.61). For the first time, a quantitative, noninvasive estimation of cardiovascular indices is addressed by processing Doppler-echocardiography recordings using a learning-from-samples method

Accuracy of heart strain rate calculation derived from Doppler tissue velocity data

Strain Rate (SR) Imaging is a recent imaging technique that provides information about regional myocardial deformation by measuring local compression and expansion rates. SR can be obtained by calculating the local in-plane velocity gradients along the ultrasound beam from Doppler Tissue velocity data. However, SR calculations are very dependent on the image noise and artifacts, and different calculation algorithms may provide inconsistent results. This paper compares techniques to calculate SR. 2D Doppler Tissue Images (DTI) are acquired with an Acuson Sequoia scanner. Noise was measured with the aid of a rotating phantom. Processing is performed on polar coordinates. For each image, after removal of black spot artifacts by a selective median filter, two different SR calculation methods have been implemented. In the first one, SR is computed as the discrete velocity derivative, and noise is reduced with a variable-width gaussian filter. In the second method a smoothing cubic spine is calculated for every scan line according to the noise level and the derivative is obtained from an analytical expression. Both methods have been tested with DTI data from synthetic phantoms and normal volunteers. Results show that noise characteristics, border effects and the adequate scale are critical to obtain meaningful results.

Tsallis entropy approach to radiotherapy treatments

The biological effect of one single radiation dose on a living tissue has been described by several radiobiological models. However, the fractionated radiotherapy requires to account for a new magnitude: time. In this paper we explore the biological consequences posed by the mathematical prolongation of a previous model to fractionated treatment. Nonextensive composition rules are introduced to obtain the survival fraction and equivalent physical dose in terms of a time dependent factor describing the tissue trend towards recovering its radioresistance (a kind of repair coefficient). Interesting (known and new) behaviors are described regarding the effectiveness of the treatment which is shown to be fundamentally bound to this factor. The continuous limit, applicable to brachytherapy, is also analyzed in the framework of nonextensive calculus. Here a coefficient that rules the time behavior also arises. All the results are discussed in terms of the clinical evidence and their major implications are highlighted.

Non‐extensive radiobiology

The expression of survival factors for radiation damaged cells is based on probabilistic assumptions and experimentally fitted for each tumor, radiation and conditions. Here we show how the simplest of these radiobiological models can be derived from the maximum entropy principle of the classical Boltzmann-Gibbs expression. We extend this derivation using the Tsallis entropy and a cutoff hypothesis, motivated by clinical observations. A generalization of the exponential, the logarithm and the product to a non-extensive framework, provides a simple formula for the survival fraction corresponding to the application of several radiation doses on a living tissue. The obtained expression shows a remarkable agreement with the experimental data found in the literature, also providing a new interpretation of some of the parameters introduced anew. It is also shown how the presented formalism may has direct application in radiotherapy treatment optimization through the definition of the potential effect difference, simply calculated between the tumour and the surrounding tissue.

Comparative study of two flat-panel X-ray detectors applied to small-animal imaging cone-beam micro-CT

This work compares two different X-ray flat-panel detectors for its use in high-speed, cone-beam CT applied to small-animal imaging. The main differences between these two devices are the scintillators and the achievable frame rate. Both devices have been tested in terms of system linearity, sensitivity, resolution, stability and noise properties, taking into account the different timing schemes for each one of them and the mandatory corrections on the raw data. Tomographic scans have been carried out using both detectors to evaluate its final performance as well as the delivered dose needed to achieve similar quality scans. An experimental cone-beam CT test-bench has been designed and implemented to perform the different measurements. It uses a micro-focus X-ray source and a rotating stage where the samples are placed. A modified FDK algorithm has been used to reconstruct the acquired data. Both detectors show similar results for pixel linearity and stability measurements, and their noise levels are comparable. The resolution and sensitivity features are better for the direct grown scintillator detector (9 lpmm vs. 6 lpmm, and ∼4 times more sensitive for similar delivered dose). Since tomographic reconstructed images for the higher frame-rate detector show acceptable quality, it can be used to implement a faster system for high-speed acquisition techniques like, for example, dynamic imaging or gated protocols.

Immune system-tumour efficiency ratio as a new oncological index for radiotherapy treatment optimization

A dynamical system model for tumour-immune system interaction together with a method to mimic radiation therapy are proposed. A large population of virtual patients is simulated following an ideal radiation treatment. A characteristic parameter, the immune system-tumor efficiency ratio (ISTER) is introduced. ISTER dependence of treatment success and other features are studied. Radiotherapy treatment dose optimization, following ALARA (As Low As Reasonably Achievable) criterion, as well as a patient classification are drawn from the statistics results.