Role of Platelet-Rich Plasma Gel in Promoting Wound Healing Based on Medical Images of Wounds.

A wound is the pathological change of soft tissue under normal skin caused by various factors, such as collision, contusion, hot crush, avulsion, corrosive chemicals, operations, excessive wound tension after operations, local pressure that cannot be relieved for a long time, liquid immersion, local infection, and rejection reactions caused by allogeneic substances. The skin itself or its underlying soft tissue loses its integrity and continuity, thus losing its normal physiological function. Medical image analysis is a medical term that refers to the interdisciplinary fields of integrated medical imaging, artificial intelligence, digital image processing and analysis, mathematical modeling, and numerical algorithms. According to the time of wound formation, they can be divided into acute and chronic wounds. The common acute wounds include lacerations caused by trauma, surgical incisions, burns, and donor sites formed after skin graft operations. This article mainly studies the role of platelet-rich plasma gel nanocomposites in promoting wound healing. It is proven that ptt-rich plasma gel can significantly promote tissue repair and regeneration and accelerate wound healing in patients with severe burns. The atomic number of the nanocomposite has a better treatment effect on the nanoparticle approach. In this paper, chitosan nanocomposite membrane, nanocomposite algorithm, and the calculation method of enthalpy of formation of high alloy nanomaterials were used to study the role of ptt-rich plasma gel combined chitosan nanocomposite membrane loaded bone marrow stromal cells in promoting wound healing, and its effects were applied to the repair of special site burns, special burns, and different age burns. Good wound repair benefits from the correct treatment of the wound, which directly affects the stability and development of the internal environment. The difference in healing time between the two groups was statistically significant, and the recovery time of the PRP group was 0.001 less than that of the control group. The results showed that the wound healing time of the PRP group was significantly shorter than that of the control group (P < 0.05); after treatment, the content of VEGF in the wound tissue of the two groups increased, especially in the PRP group; the effective rate of the PRP group was 75.0%, which was higher than 68.8% of the control group. It can play an important role in the regulation of expression and the pathophysiological process of wound healing.

1. Introduction

Using image segmentation technology, these regions of interest can be extracted from medical images. Among these areas, some are response lesion areas, and some are normal physiologically structured tissues. For these extracted ROIs, their feature attributes can be extracted, and mining research can be carried out according to the extracted features. Platelet-rich plasma is a high-concentration platelet-rich plasma obtained by centrifuging the whole blood of animals or humans. After adding thrombin, it can become a gel, so it is also called platelet-rich gel or platelet-rich leukocyte gel. Ptt-rich plasma is obtained by whole blood centrifugation and is rich in high-concentration ptts. Its content is 4–8 times that of normal whole blood. PRP contains a variety of growth factors, such as ptt-derived growth factor and transforming growth factor β. These growth factors can promote cell proliferation, induce chemotherapy, and stimulate angiogenesis. These growth factors can also help reduce the number of patients. Ptt-rich plasma can promote collagen synthesis, matrix synthesis and sedimentation, and tissue formation. Domestic scholars, Deng, Chenliang, and others found that the proliferation of primary human skin fibroblasts gradually weakened and the content of collagen and hyaluronic acid in extracellular fluid decreased after ultraviolet irradiation; however, PRP could shorten the doubling time and increase the contents of collagen and hyaluronic acid in extracellular fluid.

PRP can increase the synthesis of collagen and hyaluronic acid in human photoaging skin fibroblasts and can treat skin aging. Foreign scholars, such as Jeong, used ultraviolet radiation to induce skin photoaging in mice to produce wrinkles and then used PRP subcutaneous injection for antiphotoaging treatment. The results showed that the skin was smooth after treatment with PRP, and the histology showed that fibroblasts and collagen increased significantly, indicating that PRP has the effects of treating and reversing photoaging. At the same time, the causes of common chronic wounds are often due to the comprehensive effect of various unfavorable tissue repair factors such as malnutrition, poor local blood supply, or various underlying diseases such as malnutrition, diabetes, deep venous blood stasis, and so on, which inhibit the wound healing process, so that the wound cannot be closed after more than 4 weeks of clinical treatment.

The most common types of wounds include pressure ulcers, venous stasis, ulcers of the lower limbs, and foot ulcers associated with diabetes. Causes of chronic trauma include venous insufficiency, peripheral vascular disease, systemic disease, trauma, scarring, and infection. There are various factors affecting wound healing, including systemic factors and local factors. With the continuous development of logistics, economics, and electricity, the number of traffic injuries, work-related injuries, and electrical injuries has increased year after year. The debridement is not complete or unreasonable after trauma, and the local blood flow is damaged. It also causes the local immune function of the wound to become worse, the healing to be difficult, and the healing time to be prolonged. The incidence rate of these wounds increases year by year. Safar believes that the structures produced in the perfusion bioreactor system were uniformly cellular. Human cartilage grafts have been successfully generated. BM MSCs are cultured on porous scaffolds with a relatively low proportion of nonexpanded ACS. The proposed coculture strategy is directly suitable for primary surgery on cartilage repair, but there is a lack of specific data [1]. Guo thinks that regenerative medicine products such as ptt-rich plasma gel may accelerate the healing process. Therefore, according to the effectiveness of autologous PRP gel in the treatment of refractory leg ulcers, it is compared with the existing conventional treatment methods. The study plan lasted for 8 weeks, or until 100% RE-epithelization of the wound was observed. The wound shrinkage, granulation tissue formation, wound microbial changes, and safety of 69 patients were evaluated; 25.71% of the ulcers in the autologous PRP group and 17.64% of the ulcers in the control group were completely epithelialized, but the necessary experimental data were lacking [2]. Domantas thinks that the preparation of rabbit ptt-rich plasma is verified. The effects of two anticoagulants, A and citrate glucose solution, as well as the gender on the PRP cell count and growth factor concentration in pure ptt-rich gel supernatant are determined. Variables were associated with the assessment, but the content of a numerical analysis was lacking [3].

The innovation of this paper is to study the effects of ptt-rich plasma gel combined with a chitosan nanocomposite membrane loaded with bone marrow stromal cells on wound healing using a chitosan nanocomposite membrane, a nanocomposite algorithm, and the calculation method of the enthalpy of formation of high alloy nanomaterials. With the advent of science and technology, the number of patients with hemiplegia and diabetes after cerebral infarction has increased, and the incidence rate of wound healing and its role have been increasing. Through the application of these innovative algorithms and the calculation of cytoplasmic healing wounds, it is beneficial for the effective treatment of patients with chronic diseases and to provide services for patients.

2. Wound Medical Image Analysis and Platelet-Rich Plasma Gel Analysis

2.1. Medical Image and Medical Information Data Mining

In recent decades, with the rapid development and popularization of medical imaging equipment, medical image data has exploded. The question of how to efficiently and accurately analyze medical images has become a major challenge. On the other hand, driven by electronic information technology, the use of computer technology to assist medical image analysis can not only improve the efficiency of radiologists' analysis and diagnosis but also improve their accuracy [4]. Therefore, computer-aided detection and diagnosis are becoming a cross-research field that has received increasing attention [5-7]. With the rapid development of medical digital equipment and the introduction of a large number of medical equipment in hospitals, hospitals store a large amount of medical image information about patients, which provides a rich data source for data mining of medical images. The data mining model of medical information is shown in Figure 1.

Figure 1

Application of medical data mining.

2.2. Nanocomposite Algorithm in Wound Treatment

2.2.1. Performance Test of Composite Membrane

Tensile resistance and elongation at break are important indexes to evaluate the mechanical properties of the composite membrane. The traction properties of the composite membrane were tested by a universal testing machine. The composite membrane was cut into rectangular strips (10 cm × 1 cm) and placed in a dryer (containing a saturated magnesium nitrate solution) with 50% relative humidity for at least 48 h [8]. The traction speed is 10 mm/min, and the distance between chucks is 4 cm; the average value is obtained from multiple measurements, and the calculation formula is as follows:

The tensile strength tester is suitable for peeling, shearing, and breaking testing of adhesives, adhesive tapes, self-adhesives, composite films, artificial leather, woven bags, films, paper, and other related products. Where A is the tensile strength, h is the tensile force on the membrane, M is the cross-sectional area of the membrane, t is the elongation at break, and u is the length at break [9]. Cut the composite film into small pieces and put it in a disposable plastic cup, then dry the sample in a constant temperature oven at 70°C for 6 h with a constant weight, weigh it as m, and then put it in a closed dryer for at least 72 h with a weight as n. The mist absorption rate can be calculated with the formula as follows:

2.2.2. Calculation Method of Formation Enthalpy of Binary Nanoalloy

When the material enters the nanoscale, the activity of atoms increases, which makes the change of thermodynamic state stable into a metastable state, which greatly reduces the relative stability of nanomaterials [10-12]. For incompatible materials, the stable state of an element is to maintain its basic form. With the decrease in material size, the activity of atoms will be enhanced, and thus it will be transformed into a metastable state. For alloys with negative enthalpy of formation, the enthalpy of the formation of nanoalloys is higher than that of the corresponding mass, it is expressed as follows:

On the nanoscale, the proportion of surface atoms increases, the activity of atoms increases, and the particles are in an unstable state. According to the thermodynamic theory of microsystems, the surface enthalpy of the formation of nanoparticles can be expressed as the significant increase in the surface energy of nanoparticles at the nanoscale. The enthalpy of the formation of nanoparticles is as follows: s is the surface of nanoalloy particles, and R is the surface energy per unit area of0k [13-15]. It is mentioned that the surface energy of nanocrystals is approximately equal to the surface energy between blocks. It can be considered that it does not depend on the change of the size of nanoparticles, where h is the size of nanoparticles and a is a specific shape factor. Therefore, based on the above description, we can express the enthalpy formation on the surface of nanoalloy particles as follows:

2.2.3. Nanoparticle

In the formula, the Avogadro constant, n is the atomic number of a single nanoalloy particle, and for spherical nanoparticles with diameters h and M, this is expressed as follows:Where R is the radius of spherical nanoparticles and R is the atomic radius of metal elements [16]. The enthalpy of formation of a spherical nanoalloy can be expressed as follows:

When calculating the enthalpy of formation of a binary nanoalloy, the binary nanoalloy is composed of G and L. According to the subrule model for calculating the enthalpy of formation of bulk alloys, it is modified as follows:

In the formula, G and l represent the percentage of metal g and metal L in the number of atoms, respectively.

2.3. Calculation Method of Formation Enthalpy of High Element Nanoalloy

Based on the enthalpy of formation of binary alloy, we assume that the influence of enthalpy surface formation can be ignored when nano-A, B, and, C transform the alloy into blocks. Therefore, when studying the enthalpy of formation of ternary block alloys according to a series of international subrule models, the calculated results are in good agreement with the experimental values, which shows the effectiveness of the semiempirical model C is approximately the overlap of the enthalpies of formation among A-B, B-C, and a-c [17, 18]. Only the pairwise interaction between binary alloys is considered, and the multicomponent interaction is ignored, which can be expressed as follows:

If we consider two kinds of polar molecules, A and B, we can know from the theoretical knowledge of solid-state physics that the surface energy of A and B is proportional to the square of their polarity. When a and B contact to form a van der Waals substance, the energy of the system will become zero, and the formula is as follows:

When there is a medium in differential form, the equations of the medium characteristics should also be considered. Here, we only consider the linear medium and the same sex, and the constitutive relation is as follows:

When it is brought into Maxwell equations, we can get the following results:

3. Platelet-Rich Plasma Promotes Wound Healing

3.1. Wound Healing

Growth factors released after PRP activation can bind to the transmembrane receptors of target cells and induce the expression of multiple genes in target cells, such as collagen synthesis, cell division, and proliferation, and fiber networks can charge cells. It provides fillings for cell proliferation and promotes blood coagulation and contraction injury. Ptts and leukocytes are deposited on the same horizontal plane during preparation because of the similar sedimentation velocities during centrifugation. Therefore, PRP also contains a certain concentration of white blood cells, which may increase the ability of the local wounds to resist infection. In recent years, the research on PRP in wound repair has gradually deepened.

3.2. Case Data Selection and Grouping

Sixty-four patients with chronic wounds were collected from the burn department of the People's Hospital. The causes of the wounds were different. There were 4 cases of bone exposure, 5 cases of tendon exposure, 2 cases of bone or tendon tissue exposure, and 18 cases of muscle tissue exposure. There were 35 cases of subcutaneous soft tissue exposure. 45 cases of granulation tissue aging, edema, and purulent mass adhesion; 19 cases of wound exudation were clear; the volume of the wound was (0.7–5.1) cubic centimeters; the curative effect of autologous ptt-rich plasma in the treatment of chronic wounds. After admission, 64 patients were randomly divided into the control group and the PRP treatment group, with 32 cases in each group being 21 years old; in the PRP group, there were 17 males and 15 females with an average age of (41.36 3 ± 21) years old. The average treatment time of chronic wounds in the PRP group before admission was (43.24 7 ± 75) days. The wound volume was (3.225 ± 07) cm3, and the average treatment time of chronic wounds in the control group was (50 ± 14) days; the wound volume (3.5 0 ± 67) cm3. The age and sex ratios of the two groups are shown in Table 1.

Table 1

Comparison of baseline data between the two groups.

Baseline data	Control group	PRP	P
Gender	20 ± 0.59	18	0.566
Male	15 ± 0.55	17	0.251
Female	44 ± 0.87	43.25	0.332
Age	45 ± 0.21	44.35	0.117
Course of disease	50 ± 0.14	41	0.653
Wound area	3.5 ± 0.67	3.3	0.228

Inclusion criteria: the patient's age needs to reach the legal age, the wound has not yet fully healed, the whole skin layer of the wound has been destroyed, bone, tendon, and muscle tissue have not been exposed, and the informed consent for surgery needs to be signed. Exclusion criteria: patients who could not operate; patients with adverse indications, immune system diseases, blood system diseases, and connective tissue diseases affecting wound healing; malnutrition in radiotherapy patients is serious and difficult to correct; if the wound is too large to fully fill the PRP, as shown in Table 2.

Table 2

Main instruments and reagents.

Serial number	Equipment	Reagent
1	Ultra-low temperature refrigerator	Quantitative analysis of enzyme
2	Electronic scale	Calcium chloride injection
3	Low speed centrifuge	Thrombin
4	Microplate reader	Sodium hyaluronate injection
5	Epidural puncture needle	Amino acid

3.3. Platelet-Rich Plasma Repair

PRP comes from autologous blood. Compared with other substances, PRP has lower immunogenicity and better biocompatibility. It can be obtained freely, and its cost is lower than other drugs. The biggest advantage of PRP is that it is not a single growth factor, but a kind of growth factor combined with the best proportion, which can play a synergistic role among factors as an organic whole. Many researchers have studied the role of growth factors in PRP. For example, PDGF is a powerful mitogen that promotes neovascularization, collagen synthesis, and epithelial formation. TGF- β can promote the proliferation of undifferentiated mesenchymal cells, regulate collagen synthesis and secretion of collagenase, inhibit the proliferation of macrophages and lymphocytes, and inhibit inflammation. VEGF can promote microvascular proliferation, improve tissue blood circulation, and prevent tissue necrosis. PRP is effective in the repair and regeneration of photoaging skin. PRP can accelerate fibroblast proliferation and collagen production, as shown in Figure 2.

Figure 2

The repair process of ptt-rich plasma.

3.4. Chitosan Nanocomposite Membrane

Chitosan has excellent moisture absorption, moisture retention, antibacterial property, and the ability to promote wound healing. Chitosan has been studied and applied in many aspects, such as pollution control, paper making, and agriculture. More importantly, chitosan has been studied and applied in many fields of the human body, such as wound dressings, antibacterial agents, antiaging, cosmetics, and vaccine adjuvants. In the field of bone tissue engineering, there are also many research studies on chitosan. As a scaffold for bone tissue engineering, chitosan, or its main composite, has many advantages such as anti-inflammatory properties, high porosity, good hydrophilicity, and degradation. Unfortunately, chitosan has a general mechanical property and cannot be used alone to support it. Therefore, chitosan is used in combination with other materials with good mechanical properties, which is expected to solve the disadvantage of poor mechanical properties. The composite carbon nano-chitosan combines the advantages of carbon nanotubes and chitosan nanotubes. Some studies show that materials made of carbon nanotubes have no cytotoxic effect, and this compound can be used as a paving material for bone tissue engineering. The appropriate zinc content in the material was studied by cytology tests with different zinc ions as regulators.

4. Experimental Analysis of Platelet-Rich Plasma Promoting Wound Healing

4.1. Comparison of Wound Healing Time between the Two Groups

Ptt-rich plasma can concentrate and separate the whole blood from the rest of the blood. PRP contains 4–5 times higher ptt concentration than the whole blood. Activated ptts can stimulate cell proliferation and differentiation in PRP through the blood, which plays an active role in promoting soft tissue repair. Spss20.0 is used to analyze the collected data, and the average value of the measured data is obtained, which is in accordance with the normal distribution or near normal distribution. Two independent t-test samples are used for group comparison of the complete random items. For the comparison between coupling design groups, the counting data is represented by composition relation and speed. The Pearson square test and Fisher's probability method are used for the comparison between groups; the healing time difference between the two groups was statistically significant, and the recovery time of the PRP group was significantly lower than that of the control group, as shown in Table 3.

Table 3

Comparison of healing time between the two groups.

Group	Control group	PRP group
Healing time	18.34 ± 0.029	12.36 ± 0.561
T	5.543 ± 0.034	3.243 ± 0.198
P	0.002	0.001

There was no significant difference in the content of VEGF in granulation tissue between the two groups before treatment (t = -0.947, P=0.348), indicating that there was no difference in the content of VEGF in granulation tissue between the two groups before treatment, and there was a significant difference in the content of VEGF in granulation tissue between the two groups before and after treatment, as shown in Figure 3.

Figure 3

Comparison of VEGF content in granulation tissue of the two groups before and after treatment.

A large number of studies in ptt-rich plasma have shown that PRP can promote cell proliferation and tissue repair. The results show that PRP can promote the expansion and regeneration of skin soft tissue, and the proliferation of skin epidermal cells is active. Therefore, in this study, the PRP extract interacted with human immortalized keratinocytes in vitro to observe whether the effective components of PRP have a proliferation effect on HaCaT cells.

4.2. Chitosan Nanocomposite Membrane

Chitosan is a kind of natural alkaline polysaccharide with wide sources and a low price. It has the advantages of excellent moisture absorption, moisture retention, antibacterial properties, and the ability to promote wound healing. Among the chitosan compounds with different zinc ion concentrations, the compound with 0.2% zinc ion content was in the low zinc group, and the compound with 1% zinc ion content was in the medium zinc group.

Chitosan has broad-spectrum antibacterial activity and good biodegradability, which has broad prospects in the field of bone tissue engineering. Aryaei prepared the composite of chitosan and multi-walled carbon nanotubes using the solution blending method and the freeze-drying method. Its mechanical properties and ability to promoting osteoblast proliferation and differentiation are better than a pure chitosan scaffold. The degradation rate of chitosan scaffolds can be reduced by adding multiwalled carbon nanotubes to the scaffolds. Carboxyl single-walled carbon nanotubes (CNTs) were prepared through experiments with a cycle of 14 d. These researchers found that this biomaterial can repair alveolar bone defects in diabetic rats and has a potential therapeutic effect on diabetes.

4.3. Application of Platelet-Rich Plasma Gel in Wound Healing

The wound healing process roughly experienced four phases: hemostasis, inflammation, proliferation, and remodeling, which gradually appeared and overlapped. A variety of cells, cytokines, and inflammatory mediators play different roles in various stages of wound healing. Wounds are often due to the prolonged course of disease and difficulty in healing, which seriously affects the quality of life of patients, causes patients to bear pain, and at the same time makes patients bear a large mental and economic burden. Chronic wounds not only have the characteristics of slow recovery and easy recurrence but also aggravate the original disease. Therefore, it has become one of the current research hotspots to promote the repair of chronic wounds, prevent infection, reduce the medical expenses of patients, and improve the quality of life. Platelet-rich plasma (PRP) refers to blood products obtained after the concentration and separation of autologous whole blood. PRP contains 4 to 5 times higher platelet concentration than whole blood. After activation, the platelets are degranulated by the alpha particles in it. Release a large amount of high-concentration growth factors. Its action process is shown in Figure 4.

Figure 4

Treatment of platelet healing mechanism.

Ptt-rich plasma (PRP) is a ptt concentrate extracted from whole blood. It contains a large number of growth factors, such as blood transfer growth factor, epidermal growth factor, ptt growth factor, insulin growth factor, vascular endothelial growth factor, and so on. They can promote the division and proliferation of different types of living tissue cells, promote the formation of fibrous tissue and granular tissue, promote matrix synthesis and precipitation, improve the speed and ability of collagen synthesis, stimulate epithelial cell regeneration, and induce thromboembolic hyperplasia and neovascularization. Hyaluronic acid and collagen are important components of the skin. They play an important role in maintaining the elasticity and moisture of the skin and in maintaining the appearance and elasticity of the skin. In the human body, hyaluronic acid is abundantly present in the skin, joints, and eyes to prevent dryness and maintain tissue elasticity. The skin tissues are shown in Table 4.

Table 4

Histological changes of expanded skin.

Serial number	Skin tissue
1	Epidermis
2	Dermis
3	Skin appendage
4	Subcutaneous fat layer
5	Muscle
6	Capsule layer

Most of the refractory wounds suffer from a variety of basic consumptive diseases due to the decline of the overall function of the body, which makes the body's self-healing ability poor and often delayed. The general treatment methods are systemic nutritional support, long-term dressing changes, debridement, skin grafting, and skin flap repair, but the effect is often poor. The process of wound repair includes granulation tissue formation, tissue regeneration, and epithelial regeneration. In PRP, α- Activated granules can produce a lot of endogenous growth factors to supplement the deficiency of cytokines in chronic wound healing; in addition, PRP contains a large amount of fibrin collagen, which can be used as a scaffold for cell attachment. The leukocytes in PRP also have an antibacterial effect. The first clinical application of PRP was reported by Whitman et al., who applied PRP to oral and maxillofacial wounds, resulting in ptt activation and growth factor release in PRP, which had a good effect on wound healing. From the VAS pain score before and after treatment in the observation group and the PRP group, it can be seen that the pain level of the PRP group is about 5, and the pain level of the observation group is between 6 and 9. It can be seen that the pain level of the PRP group is lower than that of the observation group. The comparison of VAS pain scores between the two groups is shown in Figure 5.

Figure 5

Comparison of VAS pain scores between the two groups before and after treatment.

The treatment effect is shown in Figure 6.

Figure 6

Comparison of clinical efficacy between the two groups after one week of treatment.

The repair and remodeling of wound tissue occur in the extracellular matrix, so it is essential to reconstruct the structure of the extracellular matrix for wound repair. In normal skin tissue, the network of collagen fibers in the extracellular matrix exists as a crisscross basket structure, while in scar tissue, the network of collagen fibers often exists in disorder. Based on this, it is very meaningful to construct a scaffold with a cross structure that can simulate normal skin collagen fibers, as shown in Figure 7.

Figure 7

Wound healing (https://alturl.com/fsoz6).

The process of wound repair is a complex and comprehensive physiological process that involves various cells and cytokines. Generally speaking, a complete wound repair process consists of three parts, namely the inflammatory response stage, the proliferation stage, and the matrix remodeling stage. Compared with normal skin, refractory wounds such as diabetic wounds often experience more complex and abnormal healing processes. Because of the special pathological microenvironment of the difficult wound, the process of wound repair often experiences repeated inflammatory reactions, so the wound cannot be repaired in time. The inflammatory response occurred after the wound was damaged.

5. Conclusion

In this paper, we use the chitosan nanocomposite membrane, the nanocomposite algorithm, and the calculation method of formation enthalpy of high-element nanoalloys to study the effect of platelet-rich plasma gel combined with chitosan nanocomposite on promoting wound healing. At present, skin tissue expansion is widely used in plastic repair and reconstruction, breast reconstruction, and ear reconstruction. At present, studies suggest that extra skin expansion mainly comes from three aspects: biological proliferation, intercellular proliferation, and mechanical creep. Among them, biological proliferation is an effective tissue expansion, and mechanical creep is the main reason for expansion and contraction. At present, there are still two main disadvantages of skin and soft tissue expansion: first, the treatment cycle is long, and the longer time may lead to more complications; second, the effective expansion of skin tissue is often insufficient. Therefore, the focus of the expander research is how to increase the effectiveness of expansion and reduce the expansion water injection cycle. There are many ways to promote the expansion of skin and soft tissue, including bone marrow-derived stem cells, external growth factors, and some chemicals. These studies have their limitations and are difficult to widely use in a short time. Compared with other substances, PRP has no immunogenicity and better biocompatibility, it is easy to obtain with the best proportion of a class of growth factors, as an organic whole to play a synergistic effect between factors. PRP plays an important role in promoting cell proliferation and angiogenesis. [4].