Development and Evaluation of a Polyherbal Hair Gel for Promoting Hair Growth and Scalp Health

Hair is indeed an important part of overall appearance. Hair problems like hair fall, dandruff, lice, split ends, and grey hair are common concerns. Hair consists of a root, shaft, and tip. As people age melanin, the pigment responsible for hair colour, breaks down, leading to white or grey hair ^[1,2,3]. Absolutely, hair does indeed play a significant role in human appearance and self-expression. Proper hair care is essential to maintain its health and beauty. Hair is composed of keratinized cells and grows from follicles in the skin. Taking good care of your hair involves maintaining a healthy scalp, using suitable hair products, and adopting a balanced diet. The scalp is made up of soft tissue layers covering the head, containing hair follicles and sebaceous glands. The pH of the scalp is around 5.5, while the hair shaft's pH is approximately 3.671^[4]. The scalp's sebaceous glands and environmental changes make it prone to various fungal infections such as dandruff, and tinea capitis, and conditions like scalp psoriasis, folliculitis, head lice, and even hair loss (alopecia) ^[5] . Hair is a biologically intricate structure, each playing a distinct role in maintaining hair health. The root, anchored in the follicle and nourished by the dermal papilla, ensures continuous growth, whiles the shaft—made up of the cuticle, cortex, and medulla—determines the hair’s strength, texture, and flexibility. Hair follicles are supported by sebaceous glands and tiny muscles that facilitate movement, contributing to the dynamic nature of scalp hair. Hair loss, or alopecia, is a growing global concern, influenced by factors such as nutritional deficiencies, hormonal imbalances, stress, genetics, and medical treatments. Conventional therapies often show limited effectiveness, prompting interest in topical alternatives. Herbal hair gels, composed of plant-based extracts within a semisolid polymeric base, offer promising benefits. They not only deliver active compounds directly to the scalp but also support follicle health, reduce microbial infections, and help prevent conditions like dandruff, hair thinning, and premature graying—making them a natural and effective option for hair care^[6]. The current study formulated the hair gel which promotes moisturizing hairs for longer period of time in addition to that this gel effective against germs especially fungal infections. 

2. Raw materials biological specifications and its therapeutic significance

2.1. Flax seed gel:

Botanical Name: Linum usitatissimum

Common Name: Flax seed, Linseed, Jawas, Tisi, Alasi.

Native: Region extending from the eastern Mediterranean to india.

Biological Source: Linseed is the dried, ripe seed of Linum ustitatissimum Linn. Linseed oil is obtained by expression of linseeds, belonging to family Linaceae.

 Scientific classification:

Class: Magnoliopsida

Subclass: Rosidae

Order: Malpighiales

Kingdom: Plantae

Subkingdom: Tracheobionta

Division: Mangnoliophyta

Genus: Linum

Species: Linum usitatissium is commonly known as flax when grown for the fibre extracted from the stem and as linseed or oilseed flax when grown for the oil extracted from the seed.

Binomial Name: Linum usitatissimum ^[6] .

Flaxseed is indeed recognized as an important functional food ingredient due to its rich composition of α-linolenic acid (ALA), an omega-3 fatty acid, fiber, and lignans. ALA is a type of omega-3 fatty acid found in plants and is known for its various health benefits, including reducing hyperpigmentation and inhibiting melanin production, as well as exhibiting anti-inflammatory properties. Additionally, flaxseed oil and its lignans have shown potential health benefits in reducing the risk of cardiac disease, atherosclerosis, diabetes, cancer, arthritis, osteoporosis, autoimmune disorders, and neurological disorders^[7]. Flax plants, scientifically known as Linum usitatissimum, are cultivated and typically reach a height of 1.2 meters (3 feet 11 inches). They have slender stems, glaucous green lanceolate leaves measuring 20-40mm in length and 3mm in width. The flowers are pale blue, around 15-25mm in diameter, with five petals. The fruit of the flax plant is a round, dry capsule, usually 5-9mm in diameter, containing several glossy brown seeds that resemble apple seeds, measuring 4-7mm in length. Flax is a flowering crop that produces small, flat seeds with colours ranging from golden yellow to reddish brown. These seeds can be consumed in various forms, including whole seeds, ground seed (powder or meal), or flaxseed oil. In recent years, flax has gained attention for its reported health benefits. According to the American Botanical Council, there was a notable 177% increase in sales of flax products in 1999, reflecting its growing popularity ^[8].

Fig. 1. Flax seed

2.2. Aloe vera Gel

Botanical Name: Aloe barbadensis miller

Common name: Aloe, Barbados Aloe, Medicinal aloe, Burn plant.

Native: Aloe vera originated in the Arabian peninsula.

Biological source: Dried Juice collected by incision from the bases of the leaves of various species of aloe.

Family: Liliaceae

Scientific classification:

Class: Liliopsida

Subclass: Liliidae

Order: Liliales

Kingdom: Plantae

Subkingdom: Tracheobionta

Division: Mangnoliophyta

Superdivision: Spermatophyta

Genus: Aloe Linn.

Species: Aloe vera is a succulent plant species of the genus aloe. It is widely distributed, and is considered an invasive species in many world regions.

Binomial Name: Aloe vera

Aloe vera gel is commonly used for scalp health and may help with certain hair-related issues. It can provide a soothing effect and potentially promote a healthy scalp environment. However, claims about aloe-emodin specifically stimulating hair follicles should be taken with caution, as scientific evidence on its effectiveness for hair growth is limited ^[9].  Aloe vera does indeed have properties that can help protect the hair and scalp from UV damage, which can result in hair problems like loss of shine and color, as well as roughness. It can act as a natural barrier against UV rays. Additionally, aloe vera contains vitamins A, C, and E, which can contribute to overall scalp and hair health. While it can be beneficial for maintaining hair health and potentially improving growth, it's essential to keep in mind that individual results may vary, and aloe vera alone may not be a guaranteed solution for hair loss.^[10]. Aloe vera is known to contain approximately 75 potentially active components, which include vitamins, enzymes, minerals etc ^[11].

Fig. 2. Aloe vera

2.3. Fenugreek plant:

Botanical name: Trigonella foenumgraecum

Biological source: Seeds and leaves of Trigonella foenumgraecum

Family: Fabacea

Scientific classification:

Kingdom:  Plantae

Division: Magnoliophyta

Class: Magnoliopsida

Order: Fables

Family: Fabaceae

Sub-family: Trifoliae

Genus: Trigonella

Sub-genus: Foenumgraecum

Species: Trigonella foenumgraecum ^[12] .

Fenugreek (Trigonellafoenum-graecum L.) is indeed a leguminous herb that has been used traditionally in various cultures for its potential health benefits. It contains a variety of compounds that could contribute to its effects on hair health, including B-vitamins, antioxidants, and trace elements^[13]. The primary constituents of fenugreek seeds include carbohydrates, proteins, flavonoids, alkaloids, saponins, free amino acids, glycosides, mucilage, and minerals. Additionally, fenugreek seeds contain other beneficial compounds and elements.^[14]. Fenugreek seeds contain a diverse array of bioactive compounds, including saponins like diosgenin, yamogenin, and gitogenin derivatives, trigonelline alkaloids, flavonoids, galactomannan, vitamins, and dietary fiber. These seeds are known for their pleasant fragrance and slightly sour taste. With a rich history as both a culinary and medicinal plant in ancient times, fenugreek seeds have gained substantial attention due to their therapeutic potential. Notably, they have been explored for their hypoglycemic, antiulcerogenic, hypocholesterolemic, and antihypertensive properties, which have captured significant interest recently. While fenugreek's positive effects on hair growth are recognized, the precise mechanism remains to be fully elucidated. Research suggests that fenugreek may engage with the synthesis of dihydrotestosterone (DHT) in a physiological manner, possibly by enhancing the blood supply to hair follicles and utilizing steroid saponins. DHT, a derivative of testosterone, is believed to contribute to hair loss in genetically predisposed individuals. The binding of DHT to hair follicles can lead to the gradual shrinkage of hair follicles and subsequent hair loss ^[15].

Fig. 3. Fenugreek

2.4. Jojoba Oil:

Botanical Name: Simmondsia chinensis

Common Name: Goatnut, deernut, wild hazel.

Native: Southwestern united states

Biological Source: Jojoba wax obtained from the plant S.chinensis, a shrub belonging to the Family: Simmondsiaceae.

Scientific classification:

Class: Magnoliopsida

Subclass: Rosidae

Order: Caryophyllales

Kingdom: Plantae

Subkingdom: Tracheobionta

Division: Mangnoliophyta

Superdivision: Spermatophyta

Genus: Simmondsia Nutt

Species: The jojoba plant, simmondsiachinensis[Link] Schneider is a monotypic species of the family simmondsiaceae in the order caryophyllales^[16].

Jojoba oil stands out as a unique unsaturated liquid wax that can be readily extracted in significant amounts from plant sources. With a composition comprising approximately 52% of the total weight of the jojoba seeds, it shares a remarkable structural similarity with the oil derived from sperm whales. This resemblance has fuelled a growing fascination with jojoba oil as a potential substitute for spermaceti wax, which is obtained from sperm whale oil. This interest in jojoba oil as a replacement for spermaceti wax has been particularly notable since the 1970s. Simmondsiachinensis (Link) Schneider, commonly known as jojoba, is a plant native to North and Central American deserts. While its natural habitat lies in these regions, jojoba is now cultivated globally, with notable cultivation areas in Chile, Egypt, and Argentina. Among its historical uses, Native American communities in the Sonora desert, specifically in California, employed jojoba for various purposes. The plant's fruits were consumed after cooking, and its oil was utilized for therapeutic applications. These applications included addressing a range of ailments such as cancer therapy, liver and kidney disorders, obesity, parturition (childbirth), sore throat, superficial wound healing. In modern times, jojoba oil finds widespread use in the pharmaceutical and cosmetic industries. It is a common ingredient in cosmetics due to its reported ability to enhance the health of hair and skin. Specifically, jojoba oil is used to nourish hair, and it is believed to have properties that promote these tissues' general well-being ^[16]. The liquid derived from mature jojoba seeds constitutes approximately 44-47% of the seed's content and is recognized for its smooth and non-greasy texture. Its chemical resemblance to human skin's natural oil, sebum, has led to its popularity as a moisturizer and hair conditioner. Regular application of jojoba oil can effectively address issues like hair tangles, split ends, and dryness. Just as it serves the jojoba plant, the oil aids human skin by preserving moisture in daytime warmth, warding off dehydration, and granting protection in harsh night-time desert conditions^[17]. Jojoba oil is recognized for its potential hair-stimulating properties, making it a valuable ingredient in herbal hair loss solutions. Its popularity in this regard is well-established ^[18].

Fig. 4. Jojoba

2.5. Keratin:

Keratin is indeed a fibrous structural protein classified as a scleroprotein. It is highly abundant in various animal structures such as hair, nails, feathers, horns, and claws. Alongside collagen, it holds significant importance as a biopolymer in the animal kingdom. Its distinctive feature is its elevated cysteine content compared to other fibrous proteins like elastin, collagen, and myofibrillar protein^[19]. .Hair keratins contain a higher proportion of the amino acid cysteine in their head and tail segments compared to other types of keratins. In the human hair keratin family, there are 17 members. Among them, 11 are classified as acidic (type I) keratins, with isoelectric points falling in the acidic range of 4.8–5.1 and molecular weights ranging from 45 to 56 kDa. The remaining 6 keratins are categorized as basic (type II) keratins, with isoelectric points in the neutral to basic range of 6.4–7.4 and molecular weights ranging from 53 to 65 kDa^[20].    

Fig. 5. Keratin

2.6. Rosemary oil:

Botanical name: Salvia rosmarinus

Biological source: Oil of rosemary is distilled from the flowering tops of leafy twigs of rosmarinus officinalis

Family: Lamiaceae

Scientific classification:

Kingdom: Plantae

Sub kingdom: Tracheobionta

Super division: Spermatophyta

Division: Magnoliophyta

Class: Magnoliopsida

Sub class: Asteridae

Order: Lamiales

Family: Lamiaceae

Genus: Rosmarinus L.

Species: officinalis

Binomial nomenclature: Rosmarinus officinalis L ^[21]. Rosmarinus officinalis, L., native to the Mediterranean region, is an aromatic plant belonging to the Lamiaceae family. The province of Murcia in Southeast Spain plays a significant role in processing and importing rosemary. This herb is recognized as a distinctive spice in the United States and Europe, where it is commercially utilized for its antioxidant properties^[22]. Rosemary oil is a widely recognized herb for promoting hair growth. It serves as an essential oil that can be combined with carrier oils like olive, coconut, or jojoba oil. Apart from preventing gray hair, it offers multiple advantages, including soothing the scalp, addressing dandruff, and supporting overall hair health ^[23]. It appears that this substance contains varying levels of 1,8-cineole, camphor, α-pinene, verbenone, and borneol, with the concentrations depending on location and seasonal changes. This substance has shown the ability to reduce microbial contamination in water-based emulsions. It has been historically utilized due to its diverse biological properties, including stimulating blood circulation in hair follicles, as well as possessing antibacterial, antioxidant, cytotoxic, antimutagenic, and antiphlogistic actions^[24].

Fig. 6. Rosemary Oil

3. Materials and Methods

All ingredients used in the formulation were of cosmetic pharmaceutical grade, procured from certified suppliers. Botanical components were standardized according to relevant monographs from the Ayurvedic Pharmacopoeia of India and applicable international compendia. Aloe vera gel (Aloe Barbadensis Leaf Juice) was used in a cold-processed, standardized 99% formulation. Flaxseed gel (Linum Usitatissimum Seed Extract) was prepared via cold mucilage extraction, ensuring approximately 15% solid content. Fenugreek extract (Trigonella Foenum-Graecum Seed Extract), standardized to 4% diosgenin, was obtained in hydroalcoholic, spray-dried form.  Cosmetic-grade hydrolyzed keratin (Hydrolyzed Keratin) of low molecular weight was incorporated for its reparative properties. Rosemary essential oil (Rosmarinus officinalis Leaf Oil), verified via GC/MS for purity, was used as an active herbal stimulant. Cold-pressed golden jojoba oil (Simmondsia Chinensis Seed Oil) was included as a natural emollient.Carbopol 940 (Carbomer) was utilized as the gelling agent, requiring neutralization with cosmetic-grade triethanolamine. Additional functional ingredients included vegetable-grade glycerin (≥99.5%, Glycerin), D-form panthenol (≥98%, Panthenol), and potassium sorbate (≥98%) as a preservative, used at 0.2% w/w concentration. Distilled water served as the vehicle for all aqueous preparations. Formulation and mixing processes were carried out using a magnetic stirrer with a hot plate, precision balance (±0.01 g), calibrated pH meter, and borosilicate glassware including beakers, measuring cylinders, and pipettes. For potential scale-up, a high-shear homogenizer was considered. The final gel products were stored in pre-sterilized, air-tight containers under controlled conditions.  The herbal hair gel was formulated using natural and functional ingredients known for their hair growth and scalp conditioning properties. Ten different formulations (F1–F5) were prepared by varying the concentration of aloe vera gel, while all other components were kept constant. To formulate and optimize a high-performance herbal hair gel using standardized botanical extracts and cosmetic-grade excipients, following Good Manufacturing Practices (GMP) and scientific formulation principles suitable for industrial-scale cosmetic production^[25] Table 1. All raw materials used were of cosmetic or pharmaceutical grade. Botanical ingredients were standardized as per applicable pharmacopeial references.

Table 2. Composition of hair gel and its therapeutic benefits:

Table 3. Optimized Composition of Herbal Hair Gel Formulations (F1–F5)

The herbal hair gel formulations (F1–F5) were developed using a multi-phase method that adheres to cosmetic formulation standards recommended by regulatory bodies and compendial references (CTFA, EU CosIng, and USP). Each phase ensured optimized blending of hydrophilic, lipophilic, and bioactive ingredients under controlled conditions to produce a stable and effective gel.

4.1 Preparation of Aqueous Gel Base

Carbomer (Carbopol 940) was used as the primary gelling agent. Precisely 1.5 g of Carbomer was weighed and slowly dispersed in 80 mL of distilled water using a magnetic stirrer set at moderate speed. The dispersion was maintained under constant stirring for 20 minutes and then allowed to fully hydrate for 60 minutes at ambient temperature (25?±?2°C) under aseptic conditions with the container covered to prevent contamination. This step is crucial to ensure full polymer swelling and avoid lump formation.

4.2 Incorporation of Hydrophilic Actives

In a separate clean beaker, a hydrophilic phase was prepared by dissolving 2 g of glycerin (vegetable grade) and 0.5 g of panthenol (D-form) in 10 mL of distilled water. Subsequently, standardized Aloe vera gel (Aloe Barbadensis Leaf Juice, 10–18 g), flaxseed gel (Linum Usitatissimum Seed Extract, 15 g), and fenugreek extract (Trigonella Foenum-Graecum Seed Extract, 4 g) were added to the solution. This phase was gently stirred using a glass rod or low-speed stirrer until a homogenous mixture was obtained. The complete hydrophilic mixture was then added slowly into the hydrated Carbopol gel base under continuous stirring to ensure uniform dispersion without entrapping air.

4.3 Addition of Lipophilic Components

To introduce the lipophilic actives, 7 drops of cold-pressed jojoba oil (Simmondsia Chinensis Seed Oil) and 6 drops of rosemary essential oil (Rosmarinus Officinalis Leaf Oil) were added dropwise to the existing emulsion. Gentle mixing was performed at low shear to ensure a stable dispersion without phase separation. This step was executed under ambient temperature conditions to maintain the integrity of the volatile essential oil.

4.4 Incorporation of Bioactive Protein

Hydrolyzed keratin (1.5 g), a key bioactive, was pre-dissolved in 5 mL of lukewarm distilled water (≤40°C) to avoid denaturation. The protein solution was added slowly to the main batch under gentle stirring to maintain the molecular stability and enhance integration into the gel matrix.

4.5 Preservation and Final Adjustment

Potassium sorbate (0.2 g) was dissolved in 2 mL of warm distilled water and added to the formulation as a preservative. pH adjustment was then carried out using a freshly prepared 1% (w/v) triethanolamine solution, dropwise, until the pH reached the target range of 5.0–5.5. This step not only stabilizes the formulation but also activates the gelling mechanism of Carbopol 940. The total weight of the formulation was adjusted to 100 g with distilled water. The mixture was stirred slowly for an additional 10 minutes to achieve a uniform, lump-free gel. The final product was transferred into pre-sterilized, air-tight storage containers under aseptic conditions and stored at room temperature away from direct sunlight.

4.6. Packaging and Storage

Upon completion of the formulation process, the herbal hair gel was immediately transferred into pre-sterilized, air-tight containers made of high-density polyethylene (HDPE) to prevent microbial contamination and oxidative degradation. The containers were sealed and labeled appropriately. The packaged products were stored in a cool, dry environment, shielded from direct sunlight to preserve the integrity of thermolabile and photosensitive constituents such as rosemary essential oil and panthenol. For stability assessment, accelerated and real-time storage conditions were recommended in accordance with ICH guidelines. Preliminary shelf-life testing was advised at 3-month and 6-month intervals under controlled conditions of 25°C ± 2°C and 60% RH ± 5% to monitor physicochemical properties, microbial load, and overall formulation stability.

Fig. 7. Preparation of flax seed gel

The formulated herbal hair gel underwent a comprehensive series of evaluation tests to assess its physicochemical stability, functional properties, and dermatological safety, adhering to internationally recognized protocols for semisolid cosmetic products.

5.1 Physical Appearance

The physical characteristics of each formulation (F1–F5) were evaluated visually for clarity, homogeneity, color, and odor. Observations were made under natural light conditions to ensure reproducibility. The gels were examined for the presence of any particulate matter or signs of microbial growth. Such assessments are standard in cosmetic product evaluations to ensure consumer acceptability and product consistency^[33].

5.2 pH Measurement

The pH of each formulation was measured using a calibrated digital pH meter (±0.01 accuracy). A 1% w/v aqueous dispersion of the gel was prepared in distilled water, and readings were taken at room temperature (25?±?2°C). All formulations were expected to exhibit pH values within the cosmetically acceptable range of 4.5 to 5.5, ideal for scalp application and compatibility with the skin’s natural acid mantle ^[34].

5.4 Spreadability

The spreadability of the gel was assessed using the parallel plate method, a standard approach for semisolid formulations. Approximately 1 g of gel was placed between two glass petri dishes. A 125 g weight was placed on the upper plate for 1 minute, and the spread diameter was measured. Spreadability (S) was calculated using the formula:

S=M×LTS = \frac{M \times L}{T}S=TM×L?

Where S is spreadability (g·cm/s), M is the mass applied (g), L is the distance moved (cm), and T is the time taken (s). Higher spreadability values indicated better application performance. This method is widely accepted for evaluating the ease of application of topical formulations ^[35].

5.5 Washability

Washability was assessed by manually applying a small quantity of gel onto the forearm skin, followed by rinsing under running tap water after 10 minutes. Ease of removal, absence of residue, and tactile after-feel were qualitatively noted. A gel that could be easily removed with water without leaving a greasy or sticky residue was considered to have excellent washability. This parameter is essential for consumer satisfaction and compliance ^[36] .

5.6 Skin Irritation Test

A preliminary skin irritation test was conducted in accordance with the OECD Test Guideline No. 439, which describes an in vitro procedure using reconstructed human epidermis (RhE) to identify irritant chemicals . A patch test was performed by applying a small amount of gel on the volar forearm of healthy human volunteers (n=10) and occluded for 24 hours. The application sites were examined for signs of erythema, edema, or any dermatological reactions. Absence of visible irritation or sensitization indicated good dermatocompatibility and potential for safe topical use ^[37] .

5.3 Phase Separation Test

Formulations were stored at ambient conditions and observed periodically for signs of phase separation or syneresis over a period of 30 days. The presence of distinct aqueous and oil layers or gel liquefaction was used as an indicator of instability. No phase separation was considered indicative of physical stability ^[38].

6. RESULTS AND DISCUSSION

6.1 Physical Appearance

The visual assessment of the herbal hair gel formulations (F1–F5) revealed distinct differences in physical attributes. Formulations F1 and F2 exhibited a creamy appearance and white color, whereas F3, F4, and F5 were characterized by a gel-like consistency and a light green color, indicating successful incorporation of the herbal actives. All formulations maintained homogeneity without visible particulates or microbial growth during the observation period. A pleasant odor was noted across all samples, contributing to user acceptability.

6.2 pH Evaluation

The pH values of the formulations ranged from 3.93 to 4.60. F3 exhibited the lowest pH (3.93), while F5 recorded the highest value (4.60). Formulations F2, F4, and F5 were within the cosmetically acceptable range of 4.5–5.5, ensuring compatibility with the scalp’s natural pH and reducing the risk of irritation. The acidic nature of the gels is favorable for maintaining scalp micro biota balance and minimizing dermatological reactions. These results corroborate existing studies proposing pH optimization as a critical factor in hair and scalp care formulations ^[34] .

6.3 Phase Separation Test:

None of the formulations exhibited any signs of phase separation or syneresis over the 30-day observation period at ambient conditions, indicating robust physical stability of the gel matrix. The absence of distinct oil or aqueous layers confirms the emulsification integrity and uniform distribution of ingredients. This aligns with findings emphasizing that emulsion-based semisolid products should maintain their homogeneity for enhanced shelf stability and performance ^[39].  

6.4 Spreadability

Spreadability, a key determinant of user compliance and application ease, was evaluated via the parallel plate method. The spread diameter increased progressively from F1 (4.0 cm) to F5 (6.0 cm), suggesting enhanced rheological properties with the incorporation of active herbal components. Higher spreadability in F5 could be attributed to its optimal viscosity and moisture retention, facilitating smooth topical application. These findings are consistent with studies highlighting that increased spreadability correlates with improved tactile aesthetics and user satisfaction ^[40] .

6.5 Washability

All gel formulations demonstrated excellent washability characteristics. The gels were easily rinsed off with tap water without leaving behind any sticky or greasy residues, indicating desirable rinse-off behavior. This feature enhances consumer preference and product usability. Similar results have been reported, affirming that water-soluble gels containing natural polymers exhibit superior wash-off properties ^[41] .

 6.6 Skin Irritation Test

The dermatological safety of the formulations was confirmed through a 24-hour occlusive patch test on human volunteers. No erythema, edema, or irritation was observed at 12 and 24 hours across all formulations, suggesting good dermatocompatibility. This outcome aligns with the OECD Test Guideline No. 439, which describes an in vitro procedure using reconstructed human epidermis (RhE) to identify irritant chemicals . These results reinforce the formulation's suitability for regular scalp application without adverse dermatological effects ^[42] .

a) Physical appearance:

Fig. 8. PH Test

Fig. 9. Spreadability Test

d) Spreadability:

e) Skin irritation test :

f) Washability:

The prepared herbal hair gel was applied then washed in water. After washing there is no trace of gel.

Fig. 10. Picture representation of formulation (F1-F5)