Control of cancer growth using single input autonomous fuzzy Nanoparticles

In this paper a single input fuzzy controller is applied on autonomous drug-encapsulated nanoparticles (ADENPs) to restrict the cancer growth. The proposed ADENPs, swarmly release the drug in local cancerous tissue and effectively decreases the destruction of normal tissue. The amount of released drug is defined considering to feed backed values of tumor growth rate and the used drug. Some significant characteristics of Nano particles compared to Nano-robots is their ability to recognize the cancerous tissue from the normal one and their simple structure. Nano particles became an attractive topic in Nano science and many efforts have been done to manufacture these particles. Simulation results show that the proposed controlling method not only decreases the cancerous tissue effectively but also reduces the side effects of drug impressively. Keyword: Nano medicine, Autonomous nanoparticles, Cancer, Single input fuzzy control, Proportional control.


Introduction
One of the most common causes of mortality in humans is cancer.Uncontrolled growths of body cells and abnormal modified cells have an important role in the initiation and development of cancer.Cancer cells can separate from the main tissues to which they belong and enter the blood and lymph tissue and go to the other tissues and there they are reproduced and continue to the defective growth cycle.In recent years, considerable progress has been made in the field of nanotechnology which enables us to produce pharmaceuticals and encapsulated nanoparticles for selective drug delivery to an organ-specific or tissue.Local drug delivery by AFNP (Autonomous Fuzzy Nanoparticles) reduces side effects on healthy tissues; as a result, physician has enough authority to select the type and dosages of drugs.Nano medicine is a noninvasive method for the prevention and cancer treatment compared with other existing method switch nowadays is being considered.Hamzeh et al. [1] demonstrated that their designed targeted DENPs, 80 nm in length and 30 nm in width, could successfully enter the interior of the atherosclerotic plaques to deliver http://www.ispacs.com/journals/jfsva/2015/jfsva-00229/International Scientific Publications and Consulting Services the drugs and imaging agents in laboratory mice.Freitas et al. [2][3] proposed a theoretical basis using chemical and thermal gradients to navigate Nano robots towards the coronary occlusion.Generally, the previous works are classified into two categories: DENPs and Nano robots.The capabilities of a Nano robot is much higher than a DENP, while manufacturing of Nano robots is difficult by current nanotechnology.Suraj and Reddy [4] proposed an algorithm for navigation of the Nano robots towards the blood clot in the constricted arteries.Hossain et al. [5][6] mathematically modeled the transport of coupled drug molecules and DENPs in coronary artery walls.Martel [7] employed magnetic nanoparticles and a specific MRI platform to design a swarm of synthetic micro scale Nano robots that are capable of traveling in the blood circulatory network.Nakano et al. [8] formulated the dynamics of local drug delivery by a nanoparticleeluting stent and compared its efficiency with the conventional stents.Nakano et al. [9] theoretically considered the dynamic motion of the magnetic nanoparticles in blood vessels and demonstrated that it could be controlled by external magnetic fields.Researches by authors and colleagues suggested two models in controlling Low-Density Lipoprotein Concentration in the Arterial Wall [10] and controlling cancer growth [11] by Proportional Drug-Encapsulated Nanoparticles and controlling cancer growth [12] by Fuzzy Drug-Encapsulated Nanoparticles.Usually when the drug binds to Nano small particles, turnaround time and the frequency of its movement in the body is improved.Hydrophilic property increases the total solubility of the detection therapeutic agents.In addition, high-performance nanoparticles targeted the special receptors which are located on the surface of cancer cells and this facilitates receiving particles loaded with medicine through andosity.The use of nanotechnology Includes drugs' surrounded particles which are sent to the cell nucleus.These nanoparticles are attached only to the cancer cells to destroy them by accurate transfer of drugs, without harming normal cells.One third of the usual dose is used in encapsulating the drugs which has good health outcomes and reduction in adverse events.for a drug to be effective in terms of treatment it is necessary to be protected until it reaches to the effect site and it's biological and chemical characteristics which should be preserved.Carriers can pass the drug exactly to the target cells and do no harm the adjacent cells.Nanotechnology has provided many opportunities to develop and improve the quality of drug delivery, such that drug carrier systems, have improved the solubility and stability, dosing control and half-life of presence of the drug in blood circulation.On the other hand, they should be small and flexible enough in order to simply arrive to the particular cell and second, to have the ability to release drug into the target cells or tissues.Drug release time is also important because if the drug is released too fast there is no possibility of complete absorption or it may have side effects.In this paper, encapsulated drug is designed by autonomous nanoparticle to control the dose in the body in which the proportional controller and is used.Also a fuzzy controller (public Estimator) is designed according to variations of biomedical systems and dependence of treatment's efficiency to physician's medical information.As autonomous nanoparticles release the drug locally, the Side effects on healthy tissues, has been significantly reduced and consequently the limitation of on selecting the type and dose of drugs is reduces.One of the differences between autonomous nanoparticle and existing methods in Nano-medicine is the process of carrying drug.Autonomous nanoparticle gives feedback from cancer cells at any time directly and based on this feedback, decides how much drug should be released.In fact autonomous nanoparticles are capable of deciding and consequently a true feedback control is achieved at the Nano scale.But modern nanoparticles cannot get feedback from the cancer cells at every moment, thus they have not the decision making unit.Since the cancerous tissue is full of uncertainties, so self-regulation is needed.Therefore, autonomous nanoparticles can deal with the uncertainties; it means that it has the autonomy.The difference between nanoparticles and Nano-robots is also considerable.Autonomous nanoparticle is much simpler than Nano-robots therefore autonomous nanoparticle that may lead to increase of their production in the future.However, due to the structural complexity of Nano-robots it is very difficult to be produced and requires great advances in the nanotechnology.Also this nanoparticle is capable of detecting healthy tissue from the unhealthy and its drug use is more efficient than modern nanoparticle carrying drug.It should be noted that the use of autonomous nanoparticle is as swarm, it means that a mass of autonomous nanoparticles are used in order to closed-loop http://www.ispacs.com/journals/jfsva/2015/jfsva-00229/International Scientific Publications and Consulting Services control be achieved.The proposed model is a new one for the ADENP environment and the cells of cancerous tissue.This model is based on the popular models of cancer [13].In the next section, the mathematical model is described and after that proposed controlling method is defined in section 3. The simulation results will be presented, in section 4.

Mathematical models
Here, a model based on a known cancer models for the ADENP with drug-related and cells cancer tissues is presented [10,13].In this model, the tumor growth has been affected in the condition of using the total cells number including population function of numerous immune cells diffiusion i.e the number of the active antigens of tumor cells CD8 + T, natural killer cells (NK) and all lymphocytes of circulating blood in addition to the concentration of IL-2 and chemotherapy drug in the blood flow [14].In the equations below: T(t) is the total tumor cell population; N(t) is the concentration (cells/l) of NK cells per litter of blood; L(t) is the concentration (cells/l) of CD8 + T-cells per litter of blood; C(t) indicates the concentration (cells/l) of lymphocytes per litter of blood including NK cells and CD8 + T-cells; M(t) shows the concentration (mg/l) of chemotherapy drug per litter of blood; I(t) is the concentration (IU/l) of IL-2 per litter of blood; VL(t) defines the number of tumor-activated CD8 + T cells injected per day per litter of blood volume (in cells/l per day); VM(t) is the amount of doxorubicin injected per day per litter of body volume (in mg/l per day); and VI(t) indicates the amount of IL-2 injected per day per litter of body volume (in IU/l per day); CDenp is drugencapsulated by Nanoparticles and UDenp, is the Controller.Figure 1, shows the cancer cells, immune cells, drugs and autonomous nanoparticles.The model equations are as follows [10][11][12][13]: In equation (2.1), a is the Growth rate of tumor, b is inverse of carrying capacity, c denotes the rate of NKinduced tumor death, Rate KT is rate of chemotherapy-induced tumor death and T is Medicine efficacy coefficient.
In the equation (2.3), m is the rate of activated CD8 + T-cell turnover.θ is the Concentration of IL-2 to halve CD8T-cell turnover, Rate of q: CD8 + T-cell death due to tumor interaction.r 1 is the rate of NK − lysed tumour cell debris activation of CD8 + T − cell r 2 is the rate of CD8 production from circulating lymphocytes, p I is the rate of IL-2 induced CD8 + T-cell activation, g I is the concentration of IL-2 for halfmaximal CD8T-cell activation, u is the CD8 + T-cell self-limitation feedback coefficient, K is the concentration of IL-2 to halve magnitude of CD8T-cell self-regulation, j is the rate of CD8T-lysed tumor cell debris activation of CD8T cells, K is the tumor size for half-maximal CD8T-lysed debris CD8T activation,K L is the rate of CD8T depletion from medicine toxicity, δ L is the medicine toxicity coefficient.

𝛼
is the ratio of rate of circulating lymphocyte production to turnover rate,  is the rate of lymphocyte turnover,   is the rate of lymphocyte depletion form medicine toxicity,   is the medicine toxicity coefficient.
In the equation (2.5),  is the rate of excretion and elimination of doxorubicin.
In the equation (2.6),   is the rate of excretion and elimination of IL-2,  is the rate of IL − 2 production from CD8T cells,  is the rate of IL-2 production from CD4/naive CD8T cells,  is the concentration of IL − 2 for half − maximal CD8T − cell IL − 2 production.
The the equation (2.7), d is the immune system strength coefficient Ɩ is the immune strength scaling coefficient,  is the value of ( L T ) l necessary for half maximal CD8 + T cell toxicity.
In literatures it was shown that immunotherapy in combination with chemotherapy in patients with strong immune system is very useful.In contrast, in patients with impaired immune systems, immunotherapy may have relatively little effect on destroying cancerous tissue [15].The proposed model shows that with a swarm of autonomous nanoparticle carrying drugs, tumor cells can be destroyed with minimum side effects.
Parameter values in the model simulations have been considered according to [13].
Existing Research in the field of chemotherapy, are seeking to produce drug carriers with different routes of drug entry, finding new therapeutic targets such as blood vessels feeding the tumor and developing specific and purposeful dosage form.The effectiveness of a therapy is the ability of killing cancer cells directly with the minimal side effects.Accordingly, it is possible to design nanoparticles which are able to pass the obstacles with no harmful influence on healthy tissues [16].Parameter values in the simulation model have been considered based on the previous works [13].http://www.ispacs.com/journals/jfsva/2015/jfsva-00229/International Scientific Publications and Consulting Services 3 The proposed controlling methods

Motivtion
Global drug delivery and local drug delivery by nanoparticles are two purposeful cases for cancer therapy.
From the control engineering point of view, the global drug delivery is an open control loop and drug delivery by autonomous nanoparticle is targeted by a closed loop control.In overall drug delivery, the drug is released directly into the bloodstream.And only a small dose of drug can be taken to avoid drug toxicity.This method cannot identify unhealthy cells (abnormal) from healthy (normal).Thus the drug is released blindly (open loop control).Which leads to unwanted side effects in normal tissues.Although therapy by overall drug delivery is economically much cheaper.Accordingly, we proposed the proportional autonomous nanoparticles and Fuzzy autonomous nanoparticles.These autonomous nanoparticles release drugs locally and as a swarm so side effects on healthy tissues, is reduced.Autonomous nanoparticles have a sensor which recognizes cancer cells continuously at any moment, and accordingly decides about the amount of drug release at the site of cancerous tissues.In the following, we will explain these structure of the autonomous nanoparticles.

Structure of proposed autonomous Nanoparticles
Proposed autonomous nanoparticles utilizes three simple units, consisting of sensor unit, control unit and operator unit which in case of any disturbance enables us to feel the human body and independence of required medicines consistently.Figure 2 depicts the structure of autonomous nanoparticles.Nanoparticle sensor unit diagnoses the number of cancer cells in every moment, and then by the control unit, decides how much drugs must be released via operator unit which includes medicines control valve.So through this way drug consumption is more efficient.Nanoparticle control unit consist of linear controller or nonlinear controller.
In this paper, we consider the nanoparticles as a system, and our vision is mathematical.So Specific nanoparticles can be designed by specific medicines and chemical and physical structure.An autonomous nanoparticle does not include any propulsion unit, while it acts like a molecule in terms of emission or natural convection to the transport pharmaceuticals.

Applying proportional controller
Autonomous nanoparticle operates with proportional controller as a simple structure closed-loop control, which reduces the computational complexity.proposed controller is as follows: KT U drug  In equation (3.8), T is the number of cancer cells and is the release rate of drugs and K is the Adjustable parameters in the controller and which according to the desired performance, is designed like rate of drug delivery.Freitas works [2], [18] in the field of Nano-robotics is a base and hypothesis structure in medicine.Today, in nanotechnology, nanoparticle is easy to carry and its hardware architecture is of interest to be used reasonably.In recent years, much work has been done in the field of sensors and stimulants Nano scales.Different data from empirical studies shows the nanometer manufacturing of control valves which will be used for drug delivery [17], [19].Particle size in many of these effects is less than 100 nm, which is promising enough to build an autonomous nanoparticle in near future.

Apply fuzzy controller
Knowledge-based systems such as, Fuzzy logic have been successfully implemented in multifarious applications where the human expertise and dealing with uncertainty play a vital role in decision making process [8].Fuzzy logic avoids arbitrary rigid boundaries by taking into account the continuous character of imprecise informations.A fuzzy system is characterized by the inference system that contains the rule base for the system, input membership functions that are used for the fuzzification of the input variables and defuzzification of the output variables.Fuzzification is a process where crisp input values are transformed into membership values of the fuzzy sets.After the process of fuzzification, the inference engine calculates the fuzzy output using fuzzy rules which are linguistic in the form of if then rules.De-fuzzification is a mathematical process used to convert the fuzzy output to a crisp value.System the rules and the membership functions should be tuned according to the application.In the proposed fuzzy system, Mamdani minimum inference method [9] is used and defuzzification is carried out using centroid defuzzifer.Mamdani's inference system can be mathematically written as, )  is the output membership function and  is the combined membership in the rule antecedent.

Single input -Autonomous Fuzzy Nanoparticle (AFNP)
Single input -AFNP contains cancer cells as the input and includes the following Fuzzy rules:

Simulation Results
In this section, the proposed model for the control of cancer is simulated using MATLAB.Drug concentrations of proposed ADENP and the molecular weight of pharmaceuticals for cancer patients have been considered as follow [10].Maximum number of drug molecules to the encapsulated ADENP is 1500 and the mass of each nanoparticle is considered to be 60000 times larger than m [10].

Proportional controller Simulation Results
Figure 5, shows the effects of nanoparticles on tumor cells and.Since during the first day, number of cancer cells increases, proportional autonomous nanoparticles release drugs at higher rate [20].This will cause that much more autonomous nanoparticles reach the end, but the concentration of autonomous nanoparticles signals reduces after several days of declines.A few days later, the arrival rate of new proposed autonomous nanoparticles and the amount of damage concentration of autonomous nanoparticles signal will be stable.So the period of end of nanoparticle drug becomes slower.Finally after about 10 days, release rate of molecules and drug removal rate (due to reaction) reaches to a balance point and also drug concentration signal reaches to a constant value.Figure 5(a) shows the number of tumor cells within 10 days, as you can see, in this proposed method, after 8 days the number of cancer cells reaches zero.Figure 5(b), shows the reduction in number of natural cell killer (NK) at the period of treatment which its reduction is rapid in the first few days and at the end of the treatment period it gets to equilibrium.Figure 5(c), shows a chemical drug consumption, which due to the number of cancer cells in the early days, more drugs are used to destroy cancer cells, thus by reduction of cancer cells in the final days of treatment, drug consumption reduces.Figure 5(d) and 5(f) and 5(g), show the concentration of immune cells according to the number of cancer cells and drug use during the 10 days.As you can see, in the final days of treatment, the numbers of immune cells increase.Figure 5(e), shows the concentration of lymphocytes emissions per liter of blood.

Simulation results of single input AFNP
Figure 6 shows the effects of the proposed single input AFNP on tumor and immune cells within 10 days.Since on the first day, there is higher number of cancer cells, single-input AFNP release drugs with higher rate [14].After a few days, there is an equilibrium between the input rate of the AFNP and their damage and the concentration of the AFNP's signal will be sustained.In this method, the number of tumor cells converges to zero after 5 days.According to the results objecting applying proportional controller and fuzzy nanoparticles it can be observed.Well as single-input Fuzzy autonomous nanoparticles has better performance than Proportional autonomous nanoparticles also.In this section, some results of proportional autonomous nanoparticles and single-input are compared with each other.The results are shown in Figure 7. http://www.ispacs.com/journals/jfsva/2015/jfsva-00229/International Scientific Publications and Consulting Services In this paper a new approach for controlling tumor growth is proposed using single input fuzzy and proportional Nano particles.Fuzzy controller is a nonlinear robust one which has ability of controlling system considering to linguistic knowledge and whiteout any need for knowing the exact model of dynamical system.The proposed nanoparticles have the ability of cancerous tissue recognition and decreasing the side effects.Also we optimize the drug amount and time duration of treatment considering to simulation results.Related to simulation results it is clear that the fuzzy controller performs more effective results, in terms of time duration of treatment and consumption, compare to proportional controller.

2 )
Where e / f is the ratio of NK cell synthesis with turnover rate, f indicates the rate of NK cell turnover, p shows the Rate of NK cell death due to tumor interaction.PN indicates the rate of IL-2 induced NK cell proliferation, gN shows the Concentration of IL-2 for half-maximal NK cell proliferation.KN indicates the rate of NK depletion from medicine toxicity, δN shows the Medicine toxicity coefficient.http://www.ispacs.com/journals/jfsva/2015/jfsva-00229/International Scientific Publications and Consulting Services

Figure 4
Figure4shows the relationship between input and output membership.

Figure 4 :
Figure 4: The relationship between input and output membership functions.

Figure 5 (Figure 5 :
Figure 5: the impact of proposed autonomous nanoparticles on tumor cells and Safety in 10 days.(a) Number of tumor within 10 days.(b) Number of decreased natural killer (NK) shows the duration of treatment.(c) Shows the chemical drugs.(d), (f), (g) the concentration of immune cells and cancer cells in drug use during the 10-days show.(e) The concentration of emissions per liter of blood lymphocytes show.(h)drug released by ADENP.

Figure 6 :
Figure 6: the impact of single-input Fuzzy autonomous nanoparticles (AFNP) on tumor cells and Safety in 10 days.(a) Number of tumor within 10 days for a single-input AFNP show.(b) Number of decreased natural killer (NK) shows the duration of treatment.(c) Shows the chemical drugs.(d), (f) the concentration of immune cells and cancer cells in drug use during the 10-days show.(e) The concentration of emissions per liter of blood lymphocytes show.(g) Drug released by AFNP.