## 2 Materials and Methods
### Theoretical Modeling
#### 2.2.5 Interpretation  
The **energy required per cycle** to homogenize the solution is **-0.39 mJ**. The **work lost due to viscosity is negligible**, meaning the **mixing is efficient**. The **power requirement** for continuous homogenization is **-3.95 mW**, which is **very low** and easily achievable with a small motorized vibration system. The calculations result in a required power of 3.95 mW per oscillation axis x = 2. 3.95 mW \(\times\) (X) = 3.95 mw \(\times\) 2 = 7.9 mW (Power required to achieve a homogeneous solution)  
The proposed circuit is an astable circuit, which ensures an alternative start of the microvibration-generating motors on the two axes XOY. The choice of axes was determined due to the hypotheses regarding the sedimentation of the administered drugs. These axial movements at the previously calculated forces ensure the homogeneity of the drugs. The proposed circuit is based on two transistors in an astable circuit. The role of the transistors is to control the eccentric motors intermittently so as not to interfere with the movements. The proposed circuit is based on two transistors in an astable circuit (Figure 3, astable circuit with eccentric motors). The role of the transistors is to control the eccentric motors intermittently so as not to interfere with the movements. Two NPN transistors with a positive base were chosen in order to be able to make this device at a minimum price. The NPN BLC 547 transistors support a thermal dissipation power of 625 mW, with a power of 100 mA. The supply voltage of 9 v with 100 mA can easily provide power to the eccentric motor of 48 mW. Thus: 9 v \(\times\) 100 mA = 900 mW  
calculating the safety index  
900 mW/500 mW = 1.8 safety index  
In the attached circuit, we have a safety index = 1.8. The assessment of quality and safety measures in medical practice has become increasingly relevant and essential in modern healthcare. In the intravenous administration of injectable treatments, the dynamic interplay between injection quality and patient safety presents challenges in independently quantifying either parameter. By developing a standardized metric that integrates both quality and safety--referred to as the Quality-Safety Index--a unified method for evaluating these factors can be theoretically established. This approach would allow for a more comprehensive analysis within the context of individual patient profiles, clinical evaluations, and personalized treatment protocols. Figure 3: Astable circuit with eccentric motors—vibration generators on two axes. The safety rate refers both to the rate of component overload during operation and to the potential risks associated with medical malpractice. The two vibration generators are located on different axes of symmetry at 90 degrees to each other. The role is to ensure the homogeneity of the drugs inserted into the patient. Certain wavelengths of light could influence the surface interactions of drugs such as insulin and propofol with plastic syringe materials. This effect would probably work through photoexcitation, modification of the surface charge, or breaking of molecular bonds responsible for adhesion. The proposed system is distinguished by two different wavelengths, 470 nm and 700 nm (500 mW), respectively. The first wavelength of 470 nm (400 mw) is the one that treats the walls of the syringe. This wavelength, generated by the laser diode, has the role of impressing the plastic material by behavioral changes on the chemical substances. Following laser treatment of the syringe walls, chemicals no longer adhere to the plastic surface for 12 h (the investigation period chosen was 12 h). The UV wavelength of 470 nm is applied to the empty syringe, without treatment as in the image below (Figure 4). Certain wavelengths of light can modulate the interaction between drugs like insulin and propofol and the plastic surfaces of syring. This effect is primarily driven by photoexcitation, which alters surface charge properties or disrupts molecular adhesion mechanisms.