Skin stem cell hypotheses and long term clone survival--explored using agent-based modelling.

Epithelial renewal in skin is achieved by the constant turnover and differentiation of keratinocytes. Three popular hypotheses have been proposed to explain basal keratinocyte regeneration and epidermal homeostasis: 1) asymmetric division (stem-transit amplifying cell); 2) populational asymmetry (progenitor cell with stochastic fate); and 3) populational asymmetry with stem cells. In this study, we investigated lineage dynamics using these hypotheses with a 3D agent-based model of the epidermis. The model simulated the growth and maintenance of the epidermis over three years. The offspring of each proliferative cell was traced. While all lineages were preserved in asymmetric division, the vast majority were lost when assuming populational asymmetry. The third hypothesis provided the most reliable mechanism for self-renewal by preserving genetic heterogeneity in quiescent stem cells, and also inherent mechanisms for skin ageing and the accumulation of genetic mutation.

The application of multiscale modelling to the process of development and prevention of stenosis in a stented coronary artery.

The inherent complexity of biomedical systems is well recognized; they are multiscale, multiscience systems, bridging a wide range of temporal and spatial scales. While the importance of multiscale modelling in this context is increasingly recognized, there is little underpinning literature on the methodology and generic description of the process. The COAST (complex autonoma simulation technique) project aims to address this by developing a multiscale, multiscience framework, coined complex autonoma (CxA), based on a hierarchical aggregation of coupled cellular automata (CA) and agent-based models (ABMs). The key tenet of COAST is that a multiscale system can be decomposed into N single-scale CA or ABMs that mutually interact across the scales. Decomposition is facilitated by building a scale separation map on which each single-scale system is represented according to its spatial and temporal characteristics. Processes having well-separated scales are thus easily identified as the components of the multiscale model. This paper focuses on methodology, introduces the concept of the CxA and demonstrates its use in the generation of a multiscale model of the physical and biological processes implicated in a challenging and clinically relevant problem, namely coronary artery in-stent restenosis.

Study of the optimum level of electrode placement for the evaluation of absolute lung resistivity with the Mk3.5 EIT system.

Inter-subject variability has caused the majority of previous electrical impedance tomography (EIT) techniques to focus on the derivation of relative or difference measures of in vivo tissue resistivity. Implicit in these techniques is the requirement for a reference or previously defined data set. This study assesses the accuracy and optimum electrode placement strategy for a recently developed method which estimates an absolute value of organ resistivity without recourse to a reference data set. Since this measurement of tissue resistivity is absolute, in Ohm metres, it should be possible to use EIT measurements for the objective diagnosis of lung diseases such as pulmonary oedema and emphysema. However, the stability and reproducibility of the method have not yet been investigated fully. To investigate these problems, this study used a Sheffield Mk3.5 system which was configured to operate with eight measurement electrodes. As a result of this study, the absolute resistivity measurement was found to be insensitive to the electrode level between 4 and 5 cm above the xiphoid process. The level of the electrode plane was varied between 2 cm and 7 cm above the xiphoid process. Absolute lung resistivity in 18 normal subjects (age 22.6 +/- 4.9, height 169.1 +/- 5.7 cm, weight 60.6 +/- 4.5 kg, body mass index 21.2 +/- 1.6: mean +/- standard deviation) was measured during both normal and deep breathing for 1 min. Three sets of measurements were made over a period of several days on each of nine of the normal male subjects. No significant differences in absolute lung resistivity were found, either during normal tidal breathing between the electrode levels of 4 and 5 cm (9.3 +/- 2.4 Omega m, 9.6 +/- 1.9 Omega m at 4 and 5 cm, respectively: mean +/- standard deviation) or during deep breathing between the electrode levels of 4 and 5 cm (10.9 +/- 2.9 Omega m and 11.1 +/- 2.3 Omega m, respectively: mean +/- standard deviation). However, the differences in absolute lung resistivity between normal and deep tidal breathing at the same electrode level are significant. No significant difference was found in the coefficient of variation between the electrode levels of 4 and 5 cm (9.5 +/- 3.6%, 8.5 +/- 3.2% at 4 and 5 cm, respectively: mean +/- standard deviation in individual subjects). Therefore, the electrode levels of 4 and 5 cm above the xiphoid process showed reasonable reliability in the measurement of absolute lung resistivity both among individuals and over time.

Detection of emboli in vessels using electrical impedance measurements--phantom and electrodes.

A phantom was constructed to simulate the electrical properties of the neck. A range of possible electrode configurations was then examined in order to improve the sensitivity of the impedance measurement method for the in vivo detection of air emboli. The neck phantom consisted of simulated skin, fat and muscle layers made of agar and a conductive rubber tube mimicking the common carotid artery. The ring-shaped electrodes with a guard electrode showed the highest sensitivity to emboli at short distances.

Electrical bioimpedance readings increase with higher pressure applied to the measuring probe.

Electrical bioimpedance spectroscopy (EBIS) is a technique that uses a probe to calculate the transfer impedance from tissues. This transfer impedance can give information about the normal or pathological condition of the tissue. To take readings, pressure has to be applied to the probe in order to get a good contact between the electrodes and the tissue. We have been using EBIS to investigate the early diagnosis of dysplasia and cancer in the human cervix, oesophagus and bladder. We have found that, with increasing pressure (range used here was approximately 1 kPa to approximately 50 kPa), the resistivity readings increase in a consistent way up to 80%. In this paper, we show how this is a case in three different tissue types (oesophageal, gastric and vesical samples). These increases can be higher than those associated with the pathological changes that we are investigating (non-inflamed columnar tissue, for instance, shows values 50% higher than dysplastic columnar tissue). Finite-element modelling was also used to investigate the effect of volume reduction in the connective tissue or stroma. This simulation suggests no strong correlation between reduction of this structure and increase in resistivity. We hypothesize therefore that these changes may be mainly associated with the squeezing of water from the extracellular space. Finally, as pressure is difficult to control by hand, we raise the issue of the necessity of considering this variable when making EIS measurements.

Modelling the electrical properties of bladder tissue--quantifying impedance changes due to inflammation and oedema.

Electrical impedance spectroscopy has been developed as a potential method for the diagnosis of carcinoma in epithelial tissues. An understanding of the influence of structural changes in the tissue on the properties measured using this technique is essential for interpreting measured data and optimization of probe design. In contrast to other tissue types, carcinoma in situ of the bladder gives rise to an increase in electrical impedance over the kHz-MHz frequency range in comparison to normal tissue. Finite element models of the urothelium and the underlying superficial lamina propria have been constructed and solved in order to ascertain the influence of structural changes associated with malignancy, oedema and inflammation on the measured electrical properties of the tissue. Sensitivity analysis of results from a composite tissue model suggests that the increase in lymphocyte density in the lamina propria associated with an inflammatory response to the infiltration of urine into the tissue may explain these unusual electrical properties.

Development and validation of computational models of cellular interaction.

In this paper we take the view that computational models of biological systems should satisfy two conditions - they should be able to predict function at a systems biology level, and robust techniques of validation against biological models must be available. A modelling paradigm for developing a predictive computational model of cellular interaction is described, and methods of providing robust validation against biological models are explored, followed by a consideration of software issues.

Agent-based computational modeling of wounded epithelial cell monolayers.

Computational modeling of biological systems, or in silico biology, is an emerging tool for understanding structure and order in biological tissues. Computational models of the behavior of epithelial cells in monolayer cell culture have been developed and used to predict the healing characteristics of scratch wounds made to urothelial cell cultures maintained in low- and physiological [Ca2+] environments. Both computational models and in vitro experiments demonstrated that in low exogenous [Ca2+], the closure of 500-microm scratch wounds was achieved primarily by cell migration into the denuded area. The wound healing rate in low (0.09 mM) [Ca2+] was approximately twice as rapid as in physiological (2 mM) [Ca2+]. Computational modeling predicted that in cell cultures that are actively proliferating, no increase in the fraction of cells in the S-phase would be expected, and this conclusion was supported experimentally in vitro by bromodeoxyuridine incorporation assay. We have demonstrated that a simple rule-based model of cell behavior, incorporating rules relating to contact inhibition of proliferation and migration, is sufficient to qualitatively predict the calcium-dependent pattern of wound closure observed in vitro. Differences between the in vitro and in silico models suggest a role for wound-induced signaling events in urothelial cell cultures.

The epitheliome: agent-based modelling of the social behaviour of cells.

We have developed a new computational modelling paradigm for predicting the emergent behaviour resulting from the interaction of cells in epithelial tissue. As proof-of-concept, an agent-based model, in which there is a one-to-one correspondence between biological cells and software agents, has been coupled to a simple physical model. Behaviour of the computational model is compared with the growth characteristics of epithelial cells in monolayer culture, using growth media with low and physiological calcium concentrations. Results show a qualitative fit between the growth characteristics produced by the simulation and the in vitro cell models.

Estimation of the size of air emboli detectable by electrical impedance measurement.

Non-invasive detection of air emboli in blood is investigated in vitro using a tetrapolar electrical impedance measurement. A cubic tank with a linear array of four electrodes, spaced approximately 1 cm apart down one side, was filled with 0.2 Sm(-1) saline. Bubbles were generated by carbon dioxide gas. Electrical transfer impedance was measured every 8.2 ms at 1.25 MHz. The movement of bubbles was recorded by a video camera, and their sizes and depths from the middle of the array were measured using captured video images. Changes in transfer impedance caused by passage of bubbles were clearly observed and almost identical with those calculated theoretically. Using lead field theory and experimental results, the fundamental limit on the detectable size of bubbles was estimated at the carotid artery, the great saphenous vein and the cephalic vein. The theoretical results showed that a 0.5 mm diameter bubble is detectable at a depth of 5.3 mm, similar to the depth of the great saphenous and the cephalic veins, and a 2.3 mm diameter bubble is detectable at a depth of 21 mm, similar to the depth of the common carotid artery.

Low frequency electrical bioimpedance for the detection of inflammation and dysplasia in Barrett's oesophagus.

Biological tissues undergoing inflammation and dysplasia seem to exhibit changes in the intercellular space that can be sensed using low frequency electrical impedance methods. Basically, low frequency electric current flows through this space and its widening as well as the disruption of the tight junction decrease the resistance, facilitating current flow. The electrical changes accompanying structural changes from columnar tissue to adenocarcinoma in Barrett's metaplastic mucosa and gastric tissue are illustrated using resected tissue from 32 patients. Two hundred and fifty-eight biopsies were analysed, correlating their electrical resistivity (R) at 9.6 kHz and their histopathological interpretation. Compared to non-inflamed non-dysplastic columnar tissue (R = 4.9 ohms m), the results suggest a small but statistically significant decrease of electrical impedance in columnar tissue showing inflammation (R = 4.2 ohms m, p = 0.016) and a larger decrease when dysplasia is present (R = 3.4 ohms m, p = 0.040). If this method is validated further, this technique could be used to obtain guided biopsies from patients undergoing surveillance programmes for Barrett's oesophagus. We aim to refine this technique using a new system with lower frequencies and, possibly, in vitro (cultured cells) and in vivo (rats) models of Barrett's oesophagus.

Modelling of epithelial tissue impedance measured using three different designs of probe.

Impedance measurement is a promising technique for detecting pre-malignant changes in epithelial tissue. This paper considers how the design of the impedance probe affects the ability to discriminate between tissue types. To do this, finite element models of the electrical properties of squamous and glandular columnar epithelia have been used. The glandular tissue model is described here for the first time. Glandular mucosa is found in many regions of the gastrointestinal tract, such as the stomach and intestine, and has a large effective surface area. Firstly, the electrical properties of a small section of gland, with epithelial cells and supportive tissue, are determined. These properties are then used to build up a three-dimensional model of a whole section of mucosa containing many thousands of glands. Measurements using different types of impedance probe were simulated by applying different boundary conditions to the models. Transepithelial impedance, and tetrapolar measurement with a probe placed on the tissue surface have been modelled. In the latter case, the impedance can be affected by conductive fluid, such as mucus, on the tissue surface. This effect has been investigated, and a new design of probe, which uses a guard electrode to counteract this potential source of variability, is proposed.

A study of the morphological parameters of cervical squamous epithelium.

Electrical impedance spectroscopy is a technique that has been investigated as a potential method for the diagnosis of epithelial carcinomas. Finite element modelling can provide an insight into the patterns of current flow in normal and pathological epithelium and hence aid in the process of probe design optimization. In order to develop a finite element model of the structure of normal and precancerous cervical squamous epithelium, it was first necessary to obtain the mean values and ranges of a number of morphological tissue parameters. The most important parameters in discriminating normal from neoplastic tissue were identified as being cell size and shape distribution, nuclear-to-cytoplasmic volume ratio and volume of extracellular space. A survey of the literature revealed an absence of reliable quantitative data for these parameters. We therefore present the results of our own basic image analysis on normal and pathological tissue sections, which we hope will be of use to other workers wishing to model cervical squamous epithelium, or other similar tissue structures.

Neonatal lungs: maturational changes in lung resistivity spectra.

The electrical resistivity of lung tissue can be related to the structure and composition of the tissue and also to the air content. Electrical impedance tomographic measurements have been used on 155 normal children over the first three years of life and 25 pre-term infants, to determine the absolute resistivity of lung tissue as a function of frequency. The results show consistent changes with increasing age in both lung tissue resistivity (5.8 ohm m at birth to 20.9 ohm m at 3 years of age) and in the changes of resistivity with frequency (Cole parameter ratio R/S=0.41 at birth and 0.84 at 3 years of age). Comparison with a lung model showed that the measurements are consistent with maturational changes in the number and size of alveoli, the extracapillary blood volume and the size of the extracapillary vessels. However, the results show that the process of maturation is not complete at the age of three years.

Neonatal lungs--can absolute lung resistivity be determined non-invasively?

The electrical resistivity of lung tissue can be related to the structure and composition of the tissue and also to the air content. Conditions such as pulmonary oedema and emphysema have been shown to change lung resistivity. However, direct access to the lungs to enable resistivity to be measured is very difficult. We have developed a new method of using electrical impedance tomographic (EIT) measurements on a group of 142 normal neonates to determine the absolute resistivity of lung tissue. The methodology involves comparing the measured EIT data with that from a finite difference model of the thorax in which lung tissue resistivity can be changed. A mean value of 5.7 +/- 1.7 omega(m) was found over the frequency range 4 kHz to 813 kHz. This value is lower than that usually given for adult lung tissue but consistent with the literature on the composition of the neonatal lung and with structural modelling.

Electrical impedance spectroscopy and the diagnosis of bladder pathology: a pilot study.

PURPOSE: Carcinoma in situ is an aggressive form of bladder cancer with a high propensity for invasion if left untreated. On cystoscopy these flat lesions cannot be differentiated from other erythematous, potentially benign areas and they require biopsy for definitive diagnosis. Other methods of detecting carcinoma in situ remain experimental. We assessed the effectiveness of electrical impedance spectroscopy, a method that measures the variation of electrical current flow with frequency through the mucosa, for differentiating various pathological changes in the urothelium. MATERIALS AND METHODS: We obtained 250 impedance measurements immediately after resection in 35 cystectomy specimens using a custom designed probe. Three consecutive readings were recorded per point to assess reproducibility and punch biopsy was done at the measurement site. RESULTS: Changes in the urothelium were classified histologically into 7 subgroups according to the degree of edema and inflammation. Electrical impedance spectroscopy measurements were able to separate benign and malignant changes when tested as a group (p <0.001), although some individual points overlapped. Edema also had a significant effect on tissue impedance (p <0.001). CONCLUSIONS: Using measurements we established patterns of electrical impedance in the human bladder. Early results suggest that this minimally invasive technique is able to differentiate benign and malignant bladder pathologies. However, it requires further refinement and evaluation at lower frequencies, where the greatest impedance difference in benign and malignant tissues is expected.

Electrical impedance spectroscopy (EIS) in the urinary bladder: the effect of inflammation and edema on identification of malignancy.

Previous studies have shown that tetrapolar electrical impedance spectroscopy measurements can identify cervical interstitial neoplasia with the same sensitivity and specificity as cervical smears. In the urinary bladder, the same technique yields significant differences (p < 0.05 at seven frequencies between 9.6 and 614 kHz) between normal and malignant urothelium, but is unable to classify individual measurements. Detailed histological examination demonstrates that inflammation and edema--both of which are common in abnormal urothelium--alter the impedance spectrum significantly in opposing directions. Consideration of morphological changes in abnormal urothelium suggests alternative measurement strategies.

Modelled current distribution in cervical squamous tissue.

The electrical properties of cervical squamous epithelium have been modelled in the frequency range 100 Hz to 10 MHz. The hierarchical modelling process comprises a cellular level stage, which includes detailed models of cells typical of different depths within the epithelium and a tissue model, which utilizes electrical properties obtained from the cellular models. The fit between the modelled and measured impedance spectra and the distribution of current with depth depends on the macroscopic model structure. Both the properties of the basement membrane and the presence of a surface mucus layer are shown to have a significant effect. The best fit with measured data is obtained when a 10 microm thick, high-conductivity surface layer is included in the tissue model.

Accuracy of an optically isolated tetra-polar impedance measurement system.

Accurate electrical transfer impedance measurement at the high frequencies (> 1 MHz) required to characterise blood and intracellular structures is very difficult, owing to stray capacitances between lead wires. To solve this problem, an optically isolated measurement system has been developed using a phase-locked-loop technique for synchronisation between current injection (drive) and voltage measurement (receive) circuits. The synchronisation error between drive and receive circuits was less than 1 ns. The accuracy and reproducibility of the developed system was examined using a tissue equivalent Cole model consisting of two resistors and one capacitor. The absolute value Z and phase shift theta in impedance of the Cole model was measured at 1.25 MHz by both an LCR meter and the isolated measurement system. The difference between the values measured by the isolated measurement system and those measured by the LCR meter was less than 0.27omega (2.9%) in Z and 0.79 degree in theta. The standard deviation was less than 0.09 omega in Z and 0.60 degree in theta.

Mk3.5: a modular, multi-frequency successor to the Mk3a EIS/EIT system.

This paper describes the Sheffield Mk3.5 EIT/EIS system which measures both the real and imaginary part of impedance at 30 frequencies between 2 kHz and 1.6 MHz. The system uses eight electrodes with an adjacent drive/receive electrode data acquisition protocol. The system is modular, containing eight identical data acquisition boards, which contain DSPs to generate the drive frequencies and to perform the FFT used for demodulation. The current drive is in three sequentially applied packets, where each packet contains ten summed sine waves. The data acquisition system is interfaced to a host PC through an optically isolated high speed serial link (RS485) running at 2 Mbaud (2 Mbits s(-1)). Measurements on a saline filled tank show that the average signal to noise performance of the system is 40 dB measured across all frequencies and that this figure is independent of frequency of measurement. These results suggest that the current system is 10 dB better in absolute terms than the previous Sheffield (Mk3a) system.