David Cukjati

Sequential finite element model of tissue electropermeabilization

Permeabilization, when observed on a tissue level, is a dynamic process resulting from changes in membrane permeability when exposing biological cells to external electric field (E). In this paper we present a sequential finite element model of E distribution in tissue which considers local changes in tissue conductivity due to permeabilization. These changes affect the pattern of the field distribution during the high voltage pulse application. The presented model consists of a sequence of static models (steps), which describe E distribution at discrete time intervals during tissue permeabilization and in this way present the dynamics of electropermeabilization. The tissue conductivity for each static model in a sequence is determined based on E distribution from the previous step by considering a sigmoid dependency between specific conductivity and E intensity. Such a dependency was determined by parameter estimation on a set of current measurements, obtained by in vivo experiments. Another set of measurements was used for model validation. All experiments were performed on rabbit liver tissue with inserted needle electrodes. Model validation was carried out in four different ways: 1) by comparing reversibly permeabilized tissue computed by the model and the reversibly permeabilized area of tissue as obtained in the experiments; 2) by comparing the area of irreversibly permeabilized tissue computed by the model and the area where tissue necrosis was observed in experiments; 3) through the comparison of total current at the end of pulse and computed current in the last step of sequential electropermeabilization model; 4) by comparing total current during the first pulse and current computed in consecutive steps of a modeling sequence. The presented permeabilization model presents the first approach of describing the course of permeabilization on tissue level. Despite some approximations (ohmic tissue behavior) the model can predict the permeabilized volume of tissue, when exposed to electrical treatment. Therefore, the most important contribution and novelty of the model is its potentiality to be used as a tool for determining parameters for effective tissue permeabilization.

The course of tissue permeabilization studied on a mathematical model of a subcutaneous tumor in small animals

One of the ways to potentiate antitumor effectiveness of chemotherapeutic drugs is by local application of short intense electric pulses. This causes an increase of the cell membrane permeability and is called electropermeabilization. In order to study the course of tissue permeabilization of a subcutaneous tumor in small animals, a mathematical model was built with the commercial program EMAS, which uses the finite element method. The model is based on the tissue specific conductivity values found in literature, experimentally determined electric field threshold values of reversible and irreversible tissue permeabilization, and conductivity changes in the tissues. The results obtained with the model were then compared to experimental results from the treatment of subcutaneous tumors in mice and a good agreement was obtained. Our results and the reversible and irreversible thresholds used coincide well with the effectiveness of the electrochemotherapy in real tumors where experiments show antitumor effectiveness for amplitudes higher than 900 V/cm ratio and pronounced antitumor effects at 1300 V/cm ratio.

A reliable method of determining wound healing rate

Several wound healing rate measures have been introduced with the main goal of enabling quantification of the effects of various therapeutic modalities on the healing of open wounds. Different definitions of wound healing rate render comparison of clinical results difficult. The goal of the present study was to propose a measure of wound healing rate that is independent of initial wound extent and to present a method of wound healing rate prediction. Comparisons were made of wound healing rate defined as absolute area healed per day, percentage of initial area healed per day and advance of the wound margin towards the wound centre per day. Analysis was performed on 300 wound cases. A disadvantage of wound healing measures that either use absolute area healed per day or percentage of initial area healed per day is their very limited use for comparing healing rates of wounds with different initial sizes. This disadvantage was overcome by incorporating a wound perimeter; thus obtaining a measure of the advance of the wound margin towards the wound centre. A definition of healing rate expressed as the greatest average wound margin distance from the wound centre divided by the time to complete wound closure is proposed. Because not all wounds are closed in the observation period, the time to complete wound closure has to be predicted. A method of wound healing rate prediction is presented based on a delayed exponential model the parameters of which are obtained from at least five weekly wound area measurements. Paired t-tests between actual time needed to complete wound closure and the predicted time resulted in p=0.062 after four, 0.484 after five and 0.900 after six weeks of observation.

Prognostic factors in the prediction of chronic wound healing by electrical stimulation

The aim of the study is to determine the effects of wound, patient and treatment attributes on the wound healing rate and to propose a system for wound healing rate prediction. Predicting the wound healing rate from the initial wound, patient and treatment data collected in a database of 300 chronic wounds is not possible. After considering weekly follow-ups, it was determined that the best prognostic factors are weekly follow-ups of the wound healing process, which alone were found to predict accurately the wound healing rate after a minimum follow-up period of four weeks (at least five measurements of wound area). After combining the follow-ups with wound, patient and treatment attributes, the minimum follow-up period was reduced to two weeks (at least three measurements of wound area). After a follow-up period of two weeks, it was possible to predict the wound healing rate of an independent test set of chronic wounds with a relative squared error of 0.347, and after three weeks, with a relative squared error of 0.181 (using regression trees with linear equations in its leaves). Regression trees with a relative squared error close to 0 produce better prediction than with an error closer to 1. Results show that the type of treatment is just one of many prognostic factors. Arranged in order of decreasing prediction capability, prognostic factors are: wound size, patients age, elapsed time from wound appearance to the beginning of the treatment, width-to-length ratio, location and type of treatment. The data collected support former findings that the biphasic- and direct-current stimulation contributes to faster healing of chronic wounds. The model of wound healing dynamics aids the prediction of chronic wound healing rate, and hence helps with the formulation of appropriate treatment decisions.

Modelling of chronic wound healing dynamics

Following chronic wound area over time can give a general overview of wound healing dynamics. Decrease or increase in wound area over time has been modelled using either exponential or linear models, which are two-parameter mathematical models. In many cases of chronic wound healing, a delay of healing process was noticed. Such dynamics cannot be described solely with two parameters. The reported study deals with two-, three-, and four-parameter models. Assessment of the models was based on weekly measurements of 226 chronic wounds of various aetiologies. Several quantitative fitting criteria, i.e. goodness of fit, handling missing data and prediction capability, and qualitative criteria, i.e. number of parameters and their biophysical meaning were considered. The median of goodness of fit of three- and four-parameter models was between 0.937 and 0.958, and the median of two-parameter moels was 0.821 to 0.883. Two-parameter models fitted wound area over time significantly (p=0.001) worse than three- and four-parameter models. The criterion handling missing data provided similar results, with no significant difference between three- and four-parameter models. Median prediction error of two-parameter models was between 111 and 746; three-parameter models resulted in an error of 64 to 128, and finally four-parameter models resulted in the highest prediction error of 407 and 238. Based on the values of quantitative fitting criteria obtained, three parameters were chosen as the most appropriate. Based on qualitative criteria, the delayed exponential model was selected as the most general three-parameter model. It was found to have good prediction capability and in this capacity it could be used to help physicians choose the most appropriate treatment for patients with chronic wounds after an initial three-week observation period, when the median error increase of fitting is 74%.

Sequential Finite Element Model of Tissue Electropermeabilisation

Sequential model of liver tissue electropermeabilisation around two needle electrodes was designed by computing electric field (E) distribution by means of the finite element (FE) method. Sequential model consists of a sequence of static FE models which represent E distribution during tissue permeabilisation. In the model an S-shaped dependency between specific conductivity and E was assumed. Parameter estimation of S-shaped dependency was performed on a set of current measurements obtained by in vivo experiments. Another set of in vivo measurements was used for model validation. Model validation was carried out in three different ways by comparing experimental measurements and modelled results. The model validation showed good agreement between modelled and measured results. The model also provided means for better understanding processes that occur during permeabilisation. Based on the model, the permeabilised volume of tissue exposed to electrical treatment can be predicted. Therefore, the most important contribution of the model is its potential to be used as a tool for determining the electrode position and pulse amplitude needed for effective tissue permeabilisation.

Comprehensible evaluation of prognostic factors and prediction of wound healing

We analyzed the data of a controlled clinical study of the chronic wound healing acceleration as a result of electrical stimulation. The study involved a conventional conservative treatment, sham treatment, biphasic pulsed current, and direct current electrical stimulation. Data was collected over 10 years and suffices for an analysis with machine learning methods. So far, only a limited number of studies have investigated the wound and patient attributes which affect the chronic wound healing. There is none to our knowledge to include treatment attributes. The aims of our study are to determine effects of the wound, patient and treatment attributes on the wound healing process and to propose a system for prediction of the wound healing rate. First we analyzed which wound and patient attributes play a predominant role in the wound healing process and investigated a possibility to predict the wound healing rate at the beginning of the treatment based on the initial wound, patient and treatment attributes. Later we tried to enhance the wound healing rate prediction accuracy by predicting it after a few weeks of the wound healing follow-up. Using the attribute estimation algorithms ReliefF and RReliefF we obtained a ranking of the prognostic factors which was comprehensible to experts. We used regression and classification trees to build models for prediction of the wound healing rate. The obtained results are encouraging and may form a basis for an expert system for the chronic wound healing rate prediction. If the wound healing rate is known, then the provided information can help to formulate the appropriate treatment decisions and orient resources towards individuals with poor prognosis.

Evaluation of Prognostic Factors and Prediction of Chronic Wound Healing Rate by Machine Learning Tools

In more than a decade of clinical use of electrical stimulation to accelerate the chronic wound healing each patient and wound were registered and a wound healing process was weekly followed. The controlled study involved a conventional conservative treatment, sham treatment, biphasic pulsed current, and direct current electrical stimulation. A quantity of available data suffices for an analysis with machine learning methods.So far only a limited number of studies have investigated the wound and patient attributes which affect the chronic wound healing. There is none to our knowledge to include the treatment attributes. The aims of our study are to determine effects of the wound, patient and treatment attributes on the wound healing process and to propose a system for prediction of the wound healing rate.In the first step of our analysis we determined which wound and patient attributes play a predominant role in the wound healing process. Then we investigated a possibility to predict the wound healing rate at the beginning of the treatment based on the initial wound, patient and treatment attributes. Finally we discussed the possibility to enhance the wound healing rate prediction accuracy by predicting it after a few weeks of the wound healing follow-up.By using the attribute estimation algorithms ReliefF and RReliefF we obtained a ranking of the prognostic factors which was comprehensible to field experts. We also used regression and classification trees to build models for prediction of the wound healing rate. The obtained results are encouraging and may form a basis of an expert system for the chronic wound healing rate prediction. If the wound healing rate is known, then the provided information can help to formulate the appropriate treatment decisions and orient resources to those individuals with poor prognosis.

The Web-based medical record system to support clinical trials

In this paper the Web-based medical record system that supports the medical device Cliniporator is presented. The system helps transferring data collected by device during the electroporation process to the central database, and enables filling of medical records through the Web-forms. It is based on the technologies like ASP, HTML, Flash, JavaScript, XML and others. The main features of this medical information system are easy and rapid data access, scalability and independence of client computer as well as easy application debugging and upgrading.

Real time electroporation control for accurate and safe in vivo electrogene therapy

In vivo cell electroporation is the basis of DNA electrotransfer, an efficient method for non-viral gene therapy using naked DNA. The electric pulses have two roles, to permeabilize the target cell plasma membrane and to transport the DNA towards or across the permeabilized membrane by electrophoresis. For efficient electrotransfer, reversible undamaging target cell permeabilization is mandatory. We report the possibility to monitor in vivo cell electroporation during pulse delivery, and to adjust the electric field strength on real time, within a few microseconds after the beginning of the pulse, to ensure efficacy and safety of the procedure. A control algorithm was elaborated, implemented in a prototype device and tested ex vivo. Controlled pulses resulted in protection of the tissue where uncorrected excessive applied voltages lead to intense tissue damage and consecutive loss of gene transfer expression.