# Mathematical Modelling of the Effects of Plasma Treatment on the Diffusivity of Biofilm
## 1 Introduction  
The biofilm is one of the most prevalent types of growth in nature and is critical in the development of various clinical infections [1]. Biofilms develop when microorganisms come together and adhere to surfaces. These surfaces may be drinking water pipes, indwelling medical devices, or a human tissue [2]. The microorganisms within the biofilm are protected by a matrix formed by the bacteria known as extracellular polymeric substances (EPSs), which consists of polysaccharides, proteins, and extracellular DNA (eDNA). EPS maintains the structural integrity of the biofilm, allowing the bacteria to adapt to the surrounding environment [3]. Moreover, the EPS bind cells to the surface and to one another, which blocks the diffusion of antimicrobials to the microcolonies that are forming and protecting the biofilm from the host's defense mechanism [2]. The EPS preventing the diffusion of antimicrobials and from the host's defense mechanism are responsible for various infections in the clinical setting. Whenever a biofilm develops on implanted medical devices such as catheters and orthopedic implants, it becomes hard to eradicate them by chemotherapeutic and other sterilization processes [4]. Thus, biofilm associated infections such as catheter-related blood stream infections and prosthetic joint infections become problematic and difficult to control [4]. Removal of the medical device or internal prosthesis will be the primary surgical treatment for such chronic infections associated with the biofilm. Even with surgical treatment, there are several disadvantages such as increased patient morbidity and mortality, higher health care costs because of repeated surgeries,extended hospitalization, rehabilitation, and antibiotic therapy [5]. Therefore, new alternatives such as non-thermal plasma for clinical infections treatment are critical to study. There has recently been a few studies using nonthermal plasma source for endoscopic plasma delivery [6; 7]. One of the study published by [PERSON] et al. demonstrated the development of a unique pulsed plasma gun for several applications such as remote high voltage fast commutation, plasma medicine applications, and small diameter catheters decontamination [8]. Such a plasma gun produced very fast-moving plasma bullets of nanosecond duration or bullet bursts from a pulsed dielectric barrier discharge (DBD) reactor. These kind of plasma can be propagated inside branched complex organs and plasma across needles or catheters that open up new opportunities for plasma technology in clinical applications and medical device disinfection [6]. Use of non-thermal plasma in combination with chlorhexidine (CHX) could conceivably be a suitable antimicrobial tool for removing these biofilms in clinical settings. The biocide CHX is one of the most widely used antiseptic for decontaminating skin, oral, and medical devices. Plasma is mainly a cocktail of positively and negatively charged ions, electrons, neutral atoms, molecules, and electric field [9; 10; 11; 12], and is used extensively for bacterial sterilization and decontamination [13; 14], cancer treatment [15; 16], wound healing and disinfection [17; 18], and in vitro blood coagulation [19]. One of the reviews published by [PERSON] et al. discusses an overview of atmospheric pressure plasma sources (APPS) for microbial decontamination [20]. Various plasma sources such as corona discharges, dielectric barrier discharge (DBD), atmospheric pressure plasma jet, and microwave driven discharges are used for microorganism decontamination, as discussed in the cited review article. In a study done by [PERSON] et al., complete inactivation of bacteria in liquid within 5 min was achieved by DC corona plasma exposure in ambient air [21]. Another DBD plasma source used by [PERSON] et al. resulted in complete inactivation of \(10^{7}\) and \(10^{8}\) CFU (colony forming unit) within 10 and 15 s of plasma treatment [19]. [PERSON] et al.