Keijo Ruohonen

Developing Itô stochastic differential equation models for neuronal signal transduction pathways

Mathematical modeling and simulation of dynamic biochemical systems are receiving considerable attention due to the increasing availability of experimental knowledge of complex intracellular functions. In addition to deterministic approaches, several stochastic approaches have been developed for simulating the time-series behavior of biochemical systems. The problem with stochastic approaches, however, is the larger computational time compared to deterministic approaches. It is therefore necessary to study alternative ways to incorporate stochasticity and to seek approaches that reduce the computational time needed for simulations, yet preserve the characteristic behavior of the system in question. In this work, we develop a computational framework based on the Itô stochastic differential equations for neuronal signal transduction networks. There are several different ways to incorporate stochasticity into deterministic differential equation models and to obtain Itô stochastic differential equations. Two of the developed models are found most suitable for stochastic modeling of neuronal signal transduction. The best models give stable responses which means that the variances of the responses with time are not increasing and negative concentrations are avoided. We also make a comparative analysis of different kinds of stochastic approaches, that is the Itô stochastic differential equations, the chemical Langevin equation, and the Gillespie stochastic simulation algorithm. Different kinds of stochastic approaches can be used to produce similar responses for the neuronal protein kinase C signal transduction pathway. The fine details of the responses vary slightly, depending on the approach and the parameter values. However, when simulating great numbers of chemical species, the Gillespie algorithm is computationally several orders of magnitude slower than the Itô stochastic differential equations and the chemical Langevin equation. Furthermore, the chemical Langevin equation produces negative concentrations. The Itô stochastic differential equations developed in this work are shown to overcome the problem of obtaining negative values.

A cost study of teleconsultation for primary-care ophthalmology and dermatology.

Teleconsultations were performed between a health centre in a small Finnish town and a university hospital 55 km away. Telemedicine consultations were carried out with a total of 42 patients suffering from various eye and skin disorders. We evaluated the costs of the teleconsultations in the health centre and the conventional alternative of the patient travelling to the hospital. The cost of conventional consultations, which was not affected by the patient workload, was EU126 per patient for ophthalmology and EU143 per patient for dermatology. The cost of the teleconsultations per patient decreased as the number of patients increased. There were cost savings in relation to teleconsultations when the annual numbers of patients were more than 110 in ophthalmology and 92 in dermatology. Benefits and savings achieved through teleconsultations mainly consisted of reduced transportation costs and reduced paperwork both at the health centre and at the university hospital, as well as time savings for the patient. Another important benefit was improved medical education. The present study shows that teleconsultations can be performed in a cost-effective way in a relatively small health centre.

Equivalence Problems for Regular sets of Word Morphisms

Despite its firm basis in theoretical biology L systems theory has had some far reaching repercussions in mathematics and theoretical computer science. One of these is the emphasis on iterated composition of morphisms on a free monoid (word morphisms). This leads naturally to set equivalence problems, familiar from formal language theory, and sequence equivalence problems (variously known also as strong equivalence, graph equivalence or tree equivalence problems in deterministic L systems theory).

AN EFFECTIVE CAUCHY-PEANO EXISTENCE THEOREM FOR UNIQUE SOLUTIONS

It is shown in this paper that the solution of the initial value problem for a system of ordinary differential equations is computable if the following assumptions are satisfied: The time interval considered is computable, the system is continuous and computable, the initial values are computable, the system is effectively bounded, and the solution is unique. It should be mentioned that for a single ODE this follows immediately from the standard proof of Osgood’s existence theorem, but this approach is not available for systems of ODEs. The key assumption here is uniqueness of solution: a result of Pour-El’s and Richards’ shows that nonunique solutions may be noncomputable, even for a single ODE.

Developmental systems with fragmentation

The paper introduces a new class of L systems, where it is possible to continue derivations from certain specified subwords of the words obtained. Such L systems (called L systems with fragmentation or just JL systems) are of interest both from biological and formal language theory point of view. The paper deals with JL systems without interactions, discusses the basic properties of the language families obtained, as well as their position in the L hierarchy. Finally, two infinite hierarchies of language families are obtained by limited fragmentation, the notions being analogous to those of ultralineanty and finiteness of index for context-free languages.

Preoperative leg-length inequality and hip osteoarthrosis: a radiographic study of 100 consecutive arthroplasty patients

ObjectiveTo assess the leg-length inequality in patients with hip osteoarthrosis (OA) and to evaluate a possible association between the length disparity and side of OA.Design and patientsWeight-bearing radiographs of 100 consecutive patients undergoing arthroplasty for primary OA were examined and measured for inequality of leg length, pelvic tilt and severity of OA.ResultsThe radiographic results showed that preoperatively OA occurred more frequently in the hip of the longer (84%) than the shorter (16%) leg. However, the development of OA did not show a linear relationship with the magnitude of leg-length inequality.ConclusionAs hip OA occurred more frequently in the longer leg the authors speculate whether leg-length inequality might predispose to OA in the hip of the longer leg.

Visual tests for measuring the picture quality of teleconsultations for medical purposes.

Telemedicine provides a new way of delivering medical services. The good quality of the picture is, however, essential for a proper and reliable teleconsultation, especially in the cases when visual information about the patients physical condition is of great importance as in ophthalmology and dermatology. Therefore real-time telemedical applications need standards for these procedures, e.g. minimum requirements for resolution, as well as contrast and color discrimination. The present study was carried out to test these parameters in a real environment. A panel of different resolution, contrast sensitivity and color discrimination tests was carried out for five test persons via PictureTel videoconference system by ISDN 128 kbit/s line speed and in a normal way. The good color discrimination of the teleconsultation system makes it possible to use the system in the evaluation of different skin lesions and exemas. However, the poor resolution and especially poor contrast sensitivity makes the use of the equipment valueless in the evaluation of diseases where the diagnoses are based on the discrimination of small details, like the biomicroscopical analysis of inflammatory cells in the aquas humor in cases of intraocular inflammation. The authors are suggesting a simple panel of tests to optimize and standardize these parameters.

On some variants of Post's correspondence problem

SummaryA variant of Posts Correspondence Problem is considered where two different index words are allowed provided that one of them can be obtained from the other by permuting a fixed number of subwords. It is shown that this variant is undecidable. Posts Correspondence Problem is also extended to circular words, doubly infinite words and doubly infinite powers of words, and shown to be undecidable in all these extensions.

Computational study of noise in a large signal transduction network

BackgroundBiochemical systems are inherently noisy due to the discrete reaction events that occur in a random manner. Although noise is often perceived as a disturbing factor, the system might actually benefit from it. In order to understand the role of noise better, its quality must be studied in a quantitative manner. Computational analysis and modeling play an essential role in this demanding endeavor.ResultsWe implemented a large nonlinear signal transduction network combining protein kinase C, mitogen-activated protein kinase, phospholipase A2, and β isoform of phospholipase C networks. We simulated the network in 300 different cellular volumes using the exact Gillespie stochastic simulation algorithm and analyzed the results in both the time and frequency domain. In order to perform simulations in a reasonable time, we used modern parallel computing techniques. The analysis revealed that time and frequency domain characteristics depend on the system volume. The simulation results also indicated that there are several kinds of noise processes in the network, all of them representing different kinds of low-frequency fluctuations. In the simulations, the power of noise decreased on all frequencies when the system volume was increased.ConclusionsWe concluded that basic frequency domain techniques can be applied to the analysis of simulation results produced by the Gillespie stochastic simulation algorithm. This approach is suited not only to the study of fluctuations but also to the study of pure noise processes. Noise seems to have an important role in biochemical systems and its properties can be numerically studied by simulating the reacting system in different cellular volumes. Parallel computing techniques make it possible to run massive simulations in hundreds of volumes and, as a result, accurate statistics can be obtained from computational studies.

Teleconsultation: changes in technology and costs over a 12-year period.

In our previous study, in 1997, we evaluated the cost of teleconsultations in a primary care centre compared with the cost of the conventional alternative, travelling to the hospital. The results showed that teleconsultations were cheaper than patient travel when the annual workload was more than 110 patients in ophthalmology and 115 patients in dermatology. Using the same method of analysis for 2009 data showed that cost savings would occur if the annual workload was 20 patients in ophthalmology and 17 patients in dermatology. The main differences between the two studies are the reduced cost of the technology (which was based on PCs in 2009) and the increased cost of staff. Both studies show that teleconsultations can be cost-effective in a relatively small health centre. The cost of technology continues to decrease, although the other costs in our break-even analysis continue to increase. However, the usability of technology continues to improve, and this will make telemedicine a more attractive alternative in the future.