The Interaction Between Plasma Filaments in Dielectric Barrier
Total Page：16
File Type：pdf, Size：1020Kb
Journal of Physics D: Applied Physics J. Phys. D: Appl. Phys. 47 (2014) 235201 (11pp) doi:10.1088/0022-3727/47/23/235201 The interaction between plasma filaments in dielectric barrier discharges and liquid covered wounds: electric fields delivered to model platelets and cells Natalia Yu Babaeva1, Wei Tian2 and Mark J Kushner1,3 1 Department of Electrical Engineering and Computer Science, University of Michigan, 1301 Beal Ave, Ann Arbor, MI 48109-2122, USA 2 Department of Nuclear Engineering and Radiological Sciences, University of Michigan, 2355 Bonisteel Blvd, Ann Arbor, MI 48109-2104, USA E-mail: [email protected], [email protected] and [email protected] Received 14 February 2014, revised 8 April 2014 Accepted for publication 10 April 2014 Published 8 May 2014 Abstract The treatment of wounds by atmospheric pressure plasmas in the context of plasma medicine typically proceeds through a liquid layer covering exposed cells. The wounds and their liquid covering often have irregular shapes with electrical properties (i.e. conductivity and permittivities) that may differ not only from wound-to-wound but also for a single wound as healing proceeds. The differing shapes and electrical properties extend into the liquid within the wound that typically contains cellular materials such as blood platelets. The plasma, wound, liquid and intra-liquid cellular components represent an interacting system of mutual dependence. In this paper, we discuss the results from a computational investigation of the treatment of small, liquid-covered wounds by filamentary dielectric barrier discharges. The sizes of the wounds are of the order of the plasma filaments and the liquid within the wound, an approximation of blood serum, contains idealized blood platelets. We find that the electrical properties of a wound can have significant effects on the spreading of the plasma on its surface by virtue of the deformation of the vacuum electric fields due to the shape, the effective capacitance of the wound and the discontinuities in electrical permittivity. This in turn effects the penetration of the electric field to cells under the liquid. The orientation and permittivity of the platelets relative to the liquid determines the electric fields that may stimulate the platelets. Keywords: dielectric barrier discharge, plasma medicine, wound, electroporation, blood (Some figures may appear in colour only in the online journal) 1. Introduction (DBDs) in particular, may be attributed to several processes— the fluxes of radicals and charged species, the production of Non-equilibrium, atmospheric pressure plasma (APP) treat- energetic fluxes of ions and photons, the activation of overlying ment of living tissue is being used in a variety of processes liquids and the generation of surface and intracellular electric collectively called plasma medicine [1, 2]. These processes fields [1–7]. One favoured type of plasma applicator is the may involve the direct contact of non-equilibrium plasmas with floating electrode DBD where the tissue being treated acts as biological cells resulting in sterilization or the production of the unpowered electrode [8, 9]. therapeutic effects. The therapeutic and sterilizing effects of One application of DBDs in plasma medicine is wound plasmas, and those produced by dielectric barrier discharges healing in which the plasma is in physical contact with the wound. In most such treatments, the wound is covered by 3 Author to whom any correspondence should be addressed. or filled with a biological liquid, for example some variation 0022-3727/14/235201+11$33.00 1 © 2014 IOP Publishing Ltd Printed in the UK J. Phys. D: Appl. Phys. 47 (2014) 235201 N Y Babaeva et al of blood plasma (BP). BP consists of about 92% water with within the liquid. We found that the electrical properties of the remainder consisting of large organic molecules, such as the wound can have significant effects on the spreading of proteins and clotting factors and cell fragments, often referred DBD filaments on the surface of the wound by virtue of the to as platelets [10]. Human blood platelets are anucleated cells, deformation of the vacuum electric fields by the shape and by typically discoid in shape with dimensions of 2–4 µm by about the effective capacitance of the wound. This in turn effects the 0.5 µm. Platelets are multifunctional and are critical to blood penetration of the electric field into the liquid of the wound, clotting through the release of platelet-derived growth factors and to the cells below the liquid. The shape and permittivity (PDGF) which are known to play an important role in wound of the platelets then in turn determine the local electric fields healing [11–22]. It is known that APPs can induce blood to which the platelets respond. coagulation, which naturally occurs via a complex cascade The model used in this investigation is described in of events that start with platelet activation and the triggering section 2. The dynamics of the DBDs over large, medium of clotting factors to form fibrin [8]. and small wounds are discussed in section 3. In section 4,we A related and likely important effect in the plasma discuss the consequences of the wound-filling liquid on the treatment of wounds is the generation of intra-wound electric electric fields that may stimulate platelets and cells below the fields. Nanosecond pulsed electric field stimulation of a liquid. Our concluding remarks are in section 5. cell produces a variety of physiological responses, such as + apoptosis, stimulation of calcium (Ca2 ) fluxes and changes 2. Description of the model and its geometry in membrane potential. Platelets can be externally activated to release PDGF. For example, Zhang et al [11] applied The model used in the investigation, nonPDPSIM, is a two- − 300 ns pulses of 30 kV cm 1 to platelet-rich BP and observed dimensional simulator in which Poisson’s equation for the platelet aggregation, an effect attributed to the electric field electric potential and transport equations for charged and + increasing Ca2 concentrations. High intensity electric pulses neutral species are solved [23]. The electron temperature, + permit Ca2 entry into the platelet through the formation Te, is obtained by solving an electron energy conservation of nanopores [12, 19, 20]. Extremely high fields can result equation with transport and rate coefficients coming from the in irreversible platelet responses and even stimulate platelet local solutions of Boltzmann’s equation. Radiation transport apoptosis [21]. and photoionization are included by implementing a Green’s The interaction of plasmas, and DBDs in particular, function propagator [23]. In this study, the model was applied with wounds is complicated by the wound not being a to the investigation of the propagation of plasma filaments in passive participant. The wound has electrical properties, a DBD, their intersection with wounds filled with liquid, the permittivity and conductivity, which influence the distribution generation of electric fields inside the wound-filling liquid and of electric fields. The wounds are also not simply flat near platelets in the liquid. The liquid, platelets and tissue are homogeneous structures—they have different shapes and sizes modelled as non-plasma materials with specified dielectric and which vary from patient to patient—which perturb or shape the conductive properties. In most regions of the computational vacuum electric fields. The properties (shape, conductivity, mesh, the tissue is treated with material-averaged electrical permittivity) of a single wound will evolve during its healing properties. In a sub-region of the tissue, individual cells process. The perturbed vacuum electric fields then influence are resolved with appropriate permittivities and conductivities the formation and propagation of the DBD filaments. This in to represent, for example, cytoplasm and cell membranes. turn determines the flux of reactive species onto the surface Poisson’s equation is solved throughout the computational of the wound and subsequent penetration of electric field domain, including the gas phase and the solid tissue. The into the wound. The activation of platelets to, for example, gas phase reaction mechanism for 1 atm of humid air and emit growth factors that may have important roles in wound other computational algorithms are the same as those described healing may depend on these electric fields. The platelets in [23]. The numerical grid uses an unstructured mesh with are themselves not passive components as their shape and triangular elements and refinement regions to resolve the permittivity determine the degree of electric enhancement details of the plasma filaments, cell interior and nuclei. The at their borders and penetration of the electric field to their mesh consists of approximately 11 200 nodes, of which about interior. 5000 are in the plasma region to resolve plasma filaments and In this paper, we discuss results from a numerical the majority of the remainder are expended in resolving the investigation of DBD treatment of liquid-covered wounds in cellular structure described below. humid air. The goal of this study is to provide insights to the To investigate the possible synergetic effects and the manner in which the DBD filaments electrically interact with generation of electric fields in the wound, we use the the wound, the BP covering the wound and platelets within geometries shown in figure 1. These geometries are intended the BP. These unique interactions dominantly occur during to represent a conventional DBD with a powered electrode the few nanoseconds when the filament intersects and spreads at the top covered by a dielectric material (ε/ε0 = 3). The on the wound during individual discharge pulses. In this dielectric material which represents tissue is placed on a investigation, we examined only single discharge pulses onto grounded electrode. The tissue in this case is represented as small wounds that have sizes commensurate with the plasma layers of epidermis, dermis and a subcutaneous layer that are filament of the DBD.