Institute of Fundamental Technological Research

In this presentation we consider hyperthermia, a procedure of raising the temperature above 43 C, as a treatment modality. To this purpose, a numerical model of in vivo soft tissue ultrasound heating is proposed by extending a previously presented in vitro model. Based on the numerical simulations, a heating scheme satisfying some constraints related to potential clinical applications is established, and the resulting temperature time-course profile is composed with the temperature-dependent protein denaturation formula of a recently published mathematical model for the eukaryotic heat shock response. The obtained simulation results of the combined models are discussed in view of potential application of ultrasound soft tissue heating in clinical treatment.

Hyperthermia, Heat Shock Response dynamics, Ultrasound therapeutic treatment, mathematical modelling

The heat shock response (HSR) is a highly evolutionarily conserved defence mechanism allowing the cell to promptly react to elevated temperature conditions and other forms of stress. It has been subject to intense research for at least two main reasons. First, it is considered a promising candidate for deciphering the engineering principles underlying regulatory networks. Second, heat shock proteins (main actors of the HSR) play crucial role in many fundamental cellular processes. Therefore, profound understanding of the heat shock response would have far-reaching ramifications for the cell biology.

Recently, a new deterministic model of the eukaryotic heat shock response has been proposed in the literature. It is very attractive since it consists of only the minimum number of components required by any functional regulatory network, while yet being capable of biological validation. However, it admits small molecule populations of some of the considered metabolites. In this paper a stochastic model corresponding to the deterministic one is constructed and the outcomes of these two models are confronted. The aim with this comparison is to show that, in the case of the heat shock response, the approximation of a discrete system with a continuous model is a reasonable approach. This is not always the truth, especially when the numbers of molecules of the considered species are small. By making the effort of performing and analysing 1000 stochastic simulations, we investigate the range of behaviour the stochastic model is likely to exhibit. We demonstrate that the obtained results agree well with the dynamics displayed by the continuous model, which strengthens the trust in the deterministic description. A proof of the existence and uniqueness of the stationary distribution of the Markov chain underlying the stochastic model is given. Moreover, the obtained view of the stochastic dynamics and the performed comparison to the outcome of the continuous formulation provide more insight into the dynamics of the heat shock response mechanism.

Stochastic model, Computer simulations, Markov chain, Gillespie algorithm, Stationary distribution

The aim of this work is twofold. Firstly, to verify a theoretical model which is capable of predicting temperature fields appearing in soft tissues during their ultrasound treatment. Secondly, to analyze some aspects of the dynamics of Heat Shock Response induced by the heating process in the context of therapeutic treatment. The theoretical investigations and quantitive analysis of temperature increments at any field point versus time of heating process, depending on the heat source power, spatial distribution and duration as well as on the tissue thermal properties, has been carried out by Finite Element Method (FEM). The validation of the numerical model has been performed by comparison of the calculation results with the experimental data obtained by measuring in vitro of the 3D temperature increments induced in samples of the turkey and veal liver by the circular focused transducer with the diameter of 15 mm, focal length of 25 mm and resonance frequency of 2 MHz. Various ultrasonic regimes were considered. They were controlled by adjusting ultrasound power and exposure time. The heat shock proteins (HSP) and misfolded proteins (MFP) levels during the proposed cyclic sonification are presented.

heat-responsive gene therapy, temperature field, low-power focused ultrasound, soft tissues, ultrasonic regime control, heat sources distribution, heat shock proteins

Background
A central goal of molecular biology is to understand the regulatory mechanisms of gene transcription and protein synthesis. Because of their solid basis in statistics, allowing to deal with the stochastic aspects of gene expressions and noisy measurements in a natural way, Bayesian networks appear attractive in the field of inferring gene interactions structure from microarray experiments data. However, the basic formalism has some disadvantages, e.g. it is sometimes hard to distinguish between the origin and the target of an interaction. Two kinds of microarray experiments yield data particularly rich in information regarding the direction of interactions: time series and perturbation experiments. In order to correctly handle them, the basic formalism must be modified. For example, dynamic Bayesian networks (DBN) apply to time series microarray data. To our knowledge the DBN technique has not been applied in the context of perturbation experiments.

Results
We extend the framework of dynamic Bayesian networks in order to incorporate perturbations. Moreover, an exact algorithm for inferring an optimal network is proposed and a discretization method specialized for time series data from perturbation experiments is introduced. We apply our procedure to realistic simulations data. The results are compared with those obtained by standard DBN learning techniques. Moreover, the advantages of using exact learning algorithm instead of heuristic methods are analyzed.

Conclusion
We show that the quality of inferred networks dramatically improves when using data from perturbation experiments. We also conclude that the exact algorithm should be used when it is possible, i.e. when considered set of genes is small enough.

W pracy przedstawiono wstępne wyniki pomiaru pola temperatury wewnątrz tkanki in vitro w czasie procesu nagrzewania wiązką ultradźwiękową o słabej mocy oraz pomiaru właściwości akustycznych wzorców tkanek miękkich. Wzorce te zbudowano w celu dalszych badań nad powiązaniem wzrostu temperatury z właściwościami akustycznymi, gdyż próbki tkankowe in vitro okazały się niepowtarzalne i nietrwałe. Na wykonanych 3 wzorcach tkankowych dokonano pomiaru sygnału przejścia i wyznaczono prędkość propagacji impulsu, współczynnik tłumienia oraz zbadano statystykę rozproszenia. Przedyskutowano wpływ liczby elementów rozpraszających na te wielkości.

wzorce tkanek, sygnał ultradźwiękowy, prędkość dźwięku, tłumienie, statystyka rozproszenia