Tomi Huttunen - Academia.edu (original) (raw)

Papers by Tomi Huttunen

Physics in Medicine and Biology, 2005

One of the problems in ultrasound surgery are the long treatment times when large tumor volumes a... more One of the problems in ultrasound surgery are the long treatment times when large tumor volumes are sonicated. Large tumors are usually treated by scanning the tumor volume using a sequence of individual focus points. During the scanning, it is possible that surrounding healthy tissue suffers from undesired temperature rise. The selection of the scanning path so that the tumor volume is treated as fast as possible while temperature rise in healthy tissue is minimized would increase the efficiency of ultrasound surgery. The main purpose of this paper is to develop a computationally efficient method which optimizes scanning path. The optimization algorithm is based on the minimum time formulation of the optimal control theory. The developed algorithm uses quadratic cost criteria to obtain the desired thermal dose in the tumor region. The derived method is evaluated with numerical simulations in 3D which are applied to ultrasound surgery of the breast in simplified geometry. Results from the simulations show that the treatment time as well as the total applied energy can be decreased from 16% to 43% as compared to standard sonication. The robustness of the optimized scanning path is studied by varying the perfusion and absorption in tumor region.

Ieee Transactions on Ultrasonics Ferroelectrics and Frequency Control, Oct 1, 2014

In ultrasound tomography, the spatial distribution of the speed of sound in a region of interest ... more In ultrasound tomography, the spatial distribution of the speed of sound in a region of interest is reconstructed based on transient measurements made around the object. The computation of the forward problem (the full-wave solution) within the object is a computationally intensive task and can often be prohibitive for practical purposes. The purpose of this paper is to investigate the feasibility of using approximate forward solvers and the partial recovery from the related errors by employing the Bayesian approximation error approach. In addition to discretization error, we also investigate whether the approach can be used to reduce the reconstruction errors that are due to the adoption of approximate absorbing boundary models. We carry out two numerical studies in which the objective is to reduce the computational times to around 3% of the time that would be required by a numerically accurate forward solver. The results show that the Bayesian approximation error approach improves the reconstructions.

Int J Numer Method Eng, 2010

Several numerical methods using non-polynomial interpolation have been proposed for wave propagat... more Several numerical methods using non-polynomial interpolation have been proposed for wave propagation problems at high frequencies. The common feature of these methods is that in each element, the solution is approximated by a set of local solutions. They can provide very accurate solutions with a much smaller number of degrees of freedom compared to polynomial interpolation. There are however significant differences in the way the matching conditions enforcing the continuity of the solution between elements can be formulated. The similarities and discrepancies between several non-polynomial numerical methods are discussed in the context of the Helmholtz equation. The present comparison is concerned with the ultraweak variational formulation (UWVF), the least-squares method (LSM) and the discontinuous Galerkin method with numerical flux (DGM). An analysis in terms of Trefftz methods provides an interesting insight into the properties of these methods. Second, the UWVF and the LSM are reformulated in a similar fashion to that of the DGM. This offers a unified framework to understand the properties of several non-polynomial methods. Numerical results are also presented to put in perspective the relative accuracy of the methods. The numerical accuracies of the methods are compared with the interpolation errors of the wave bases.

J Comput Acoust, 2007

In this study, a method for simulating the transfer function of a head-and-torso model over the e... more In this study, a method for simulating the transfer function of a head-and-torso model over the entire audible frequency range is introduced. The simulation method uses the ultra-weak variational formulation (UWVF) which is a finite element type method tailored for wave problems. In particular, the UWVF uses plane wave basis functions which better approximate the oscillatory field than a polynomial basis used in the standard finite element methods (FEM). This leads to reduction in the computational complexity at the high frequencies which, accompanied with parallel computing, extends the feasible frequency range of the UWVF method. The accuracy of the new simulation tool is investigated using a simple spherical geometry after which the method used for preliminary HRTF simulations in the geometry of a widely used head-and-torso mannequin.

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We investigate the parallelized ultra weak variational formulation (UWVF) method for large-scale ... more We investigate the parallelized ultra weak variational formulation (UWVF) method for large-scale 3D Helmholtz problems. The unbounded Helmholtz problem is truncated using the perfectly matched layers (PML). We propose a method to partition the problem in a balanced way and examine the scalability of the parallel UWVF method. The method is evaluated with numerical simulations that are performed on a PC cluster.

In this paper we extend the standard Ultra Weak Variational Formulation (UWVF) of Maxwell's equat... more In this paper we extend the standard Ultra Weak Variational Formulation (UWVF) of Maxwell's equations in an isotropic medium to the case of an anisotropic medium. We verify that the underlying theoretical framework carries over to anisotropic media (however error estimates are not yet available) and completely describe the new scheme. We then consider TM mode scattering, show how this results in a Helmholtz equation in two dimensions with an anisotropic coefficient and demonstrate how to formulate the UWVF for it. In one special case, convergence can be proved. We then show some numerical results that suggest that the UWVF can successfully simulate wave propagation in anisotropic media.

In this paper, a two-stage control method is proposed to control thermal dose and temperature in ... more In this paper, a two-stage control method is proposed to control thermal dose and temperature in ultrasound surgery. The first part in the proposed scheme consists of nonlinear model-based feedforward control. The focusing as well as the scanning path of the foci is chosen by the feedforward controller. The presented feedforward scheme leads to a large dimensional nonlinear control problem which is solved with gradient based algorithm. The temperature measurements during the ultrasound surgery can be adopted from the magnetic resonance imaging (MRI). In the second part of the control scheme these temperature measurements with LQG feedback control and Kalman filter are used to compensate the modeling errors which may arise in the feedforward part. The LQG controller and Kalman filter are derived by linearizing the original nonlinear state equation with respect to the feedforward control trajectories. The presented control scheme is tested with numerical simulations and feasible solutions can be achieved with both feedback and feedforward controllers. In addition, simulations indicate that the LQG scheme can compensate large modeling errors.

Finite element methods (FEM) are widely used for the modeling of acoustic fields characterized by... more Finite element methods (FEM) are widely used for the modeling of acoustic fields characterized by the Helmholtz equation. At high frequencies, however, the requirement of a sufficiently large number of elements per wavelength in standard FEM, may lead to an intolerable computational burden. Recently, a variety of new methods have been proposed that have the flexibility of FEM for general geometries while relax the need for dense meshes. One such method is the ultra weak variational formulation (UWVF). For the spatial discretization, the UWVF uses conventional finite element meshes but instead of polynomials used in FEM, the solution in each element is approximated using a system of plane waves. We show that a parallel UWVF method on a PC cluster can be used to simulate 3D acoustic fields that extend over tens of wavelengths.

We introduce an extension for Femlab's acoustic mode which uses the ultra-weak variational formul... more We introduce an extension for Femlab's acoustic mode which uses the ultra-weak variational formulation (UWVF) method for solving 3D Helmholtz problems. The solver, called Waveller, uses Femlab's graphical interface for creating geometries, generating meshes, post-processing and visualization. However, the solution of acoustic wave problems using the UWVF significantly reduces the computational burden associated with standard finite element methods (FEM) applied to the wave problems at high frequencies. In addition, Waveller can be run on multi-processors computers or PC-clusters. The feasibility of Waveller for large-scale acoustic simulations is shown via numerical examples.

The Journal of the Acoustical Society of America, 2014

Springer Optimization and Its Applications, 2008

Optimization has become pervasive in medicine. The application of computing to medical applicatio... more Optimization has become pervasive in medicine. The application of computing to medical applications has opened many challenging issues and problems for both the medical computing field and the mathematical community. Mathematical techniques (continuous and discrete) are playing a key role with increasingly importance in understanding several fundamental problems in medicine. Naturally, optimization is a fundamental important tool due to the limitation of the resources involved and the need for better decision making. The book starts with two papers on Intensity Modulated Radiation Therapy (IMRT). The first paper, by R. Acosta, M. Ehrgott, A. Holder, D. Nevin, J. Reese, and B. Salter, discusses an important subproblem in the design of radiation plans, the selection of beam directions. The manuscript compares different heuristic methods for beam selection on a clinical case and studies the effect of various dose calculation grid resolutions. The next paper, by M. Ehrgott, H. W. Hamacher, and M. Nußbaum, reviews several contributions on the decomposition of matrices as a model for rearranging leaves on a multileaf collimator. Such a process is essential for block radiation in IMRT in order to achieve desirable intensity profiles. Additionally, they present a new approach for minimizing the number of decomposition segments by sequentially solving this problem in polynomial time with respect to fixed decomposition times. The book continues with a paper by G. Deng and M. Ferris on the formulation of the day-today radiation therapy treatment planning problem as a dynamic program. The authors consider errors due to variations in the positioning of the patient, and apply neuro-dynamic programming to compute approximate solutions for the dynamic optimization problems. The fourth paper, by L. Kliemann, H. Fohlin, and A. Srivastav considers the seed reconstruction problem in brachytherapy as a minimum-weight perfect matching problem in a hypergraph. The problem is modeled as an integer linear program for which the authors develop an algorithm based on a randomized rounding scheme and a greedy approach. The book covers also other types of medical applications. For instance, in the paper by S. Sabesan, N. Chakravarthy, L. Good, K. Tsakalis, P. Parda-VI Preface los, and L. Iasemidis, the authors propose an application of global optimization in the selection of critical brain sites prior to an epileptic seizure. The paper shows the advantages of using optimization (in particular nonconvex quadratic programming) in combination with measures of EEG dynamics, such as Lyapunov exponents, phase and energy, for long-term prediction of epileptic seizures. E. K. Lee presents then optimization-classification models within discriminant analysis, to develop predictive rules for large heterogeneous biological and medical data sets. As mentioned by the author, classification models are critical to medical advances as they can be used in genomic, cell molecular, and system level analysis to assist in early prediction, diagnosis and detection of diseases, as well as for intervention and monitoring. A wide range of applications are described in the paper. This book also includes two papers in inverse problems with applications to medical imaging. The paper by A. K. Louis presents an overview of several techniques that lead to robust algorithms for imaging reconstruction from the measured data, in particular the inversion of the Radon transform is considered as a model case of inversion. In this paper, a reconstruction of the inside of a surprise egg is presented as a numerical example for 3D X-Ray reconstruction from real data. In the paper by M. Malinen, T. Huttunen, and J. Kaipio, an inverse problem related to ultrasound surgery is considered in an optimization framework that aims to control the optimal thermal dose to apply, for instance, in the treatment of breast cancer. Two alternative procedures (a scanning path optimization algorithm and a feedforward-feedback control method) are discussed in detail with numerical examples in 2D and 3D. We would like to thank the authors for their contributions. It would not have been possible to reach the quality of this publication without the contributions of the many anonymous referees involved in the revision and acceptance process of the submitted manuscripts. Our gratitude is extended to them as well. This book was generated mostly from invited talks given at the Work

IEEE transactions on ultrasonics, ferroelectrics, and frequency control, 2014

ABSTRACT In this paper we consider two least-squares methods: the discontinuous Petrov-Galerkin m... more ABSTRACT In this paper we consider two least-squares methods: the discontinuous Petrov-Galerkin method and a new version of the hybridized discontinuous Petrov-Galerkin method. The aim of this paper is to compute the optimal test functions for these methods in the Babuska-Ihlenburg problem in 1D. The optimal test functions will be computed with respect to the chosen inner product spaces and bilinear forms. We shall show numerical results of h-convergence of the methods.