Foam-in-vein: A review of rheological properties and characterization methods for optimization of sclerosing foams

Varicose veins are chronic venous defects that affect >20% of the population in developed countries. Among potential treatments, sclerotherapy is one of the most commonly used. It involves endovenous injection of a surfactant solution (or foam) in varicose veins, inducing damage to the endothelial layer and subsequent vessel sclerosis. Treatments have proven to be effective in the short-term, however recurrence is reported at rates of up to 64% 5-year post-treatment. Thus, once diagnosed with varicosities there is a high probability of a permanently reduced quality of life. Recently, foam sclerotherapy has become increasingly popular over its liquid counter-part, since foams can treat larger and longer varicosities more effectively, they can be imaged using ultrasound, and require lower amounts of sclerosing agent. In order to minimize recurrence rates however, an investigation of current treatment methods should lead to more effective and long-lasting effects. The literature is populated with studies aimed at characterizing the fundamental physics of aqueous foams; nevertheless, there is a significant need for appropriate product development plat-forms. Despite successfully capturing the microstructural evolution of aqueous foams, the complexity of current models renders them inadequate for pharmaceutical development. This review article will focus on the physics of foams and the attempts at optimizing them for sclerotherapy. This takes the form of a discussion of the most recent numerical and experimental models, as well as an overview of clinically relevant parameters. This holistic approach could contribute to better foam characterization methods that patients may eventually derive long term benefit from.

caused by gravity. Given the lack of active mechanical work provided by the vein's valves, venous return relies almost entirely on external mechanical stimuli such as muscle contraction, although physiological venous valves in the lower limb veins prohibit the backflow of blood ( Figure 1). If and when blood leaks through these valves, over time the vessel may dilate resulting in incompetent valves (Gloviczki et al., 2011;Oklu et al., 2012). Consequently, these vessels are prone to insufficiencies in adults that can arise due to factors such as age, pregnancy, lack of exercise, and obesity. Once developed, these insufficiencies manifest into varicose veins-regions of twisted and dilated vessels ineffective at venous blood return back to the heart (Eckmann, 2009).
A common minimally invasive treatment is sclerotherapy, involving the injection of a surfactant into the vessel, causing lysis of venous endothelium and resulting in sclerosis of the varicose vein (Gloviczki et al., 2011). Although an effective treatment, sclerotherapy does not eliminate varicosities completely. In fact varicosities may reoccur in up to 64% of cases after 5 years (Zhang & Melander, 2014). More invasive methods such as venous stripping reduce the chances of recurrence (Jones, Braithwaite, Selwyn, Cooke, & Earnshaw, 1996;Van Rij, Jones, Hill, & Jiang, 2004). Thus, it is evident that non-invasive treatment options such as sclerotherapy need to be optimized. Some recent efforts have been made to optimize sclerosing foams in vitro (Bai et al., 2018;Critello, Fiorillo, & Matula, 2017;Wong, Chen, Connor, Behnia, & Parsi, 2015); however, they lack clinically relevant parameters that can correlate physical characteristics of foams with clinical outcomes of sclerotherapy. Other studies have instead defined new parameters that could directly reflect the performance of sclerosing foams Carugo et al., 2013).
Sclerosants are injected as foams in order to maximize contact with the vessel wall. In order to optimize sclerotherapy, it is not only important to understand the underlying physical phenomena occurring in aqueous foams, but to identify clinically applicable metrics that correlate with therapeutic outcomes. This demands an in-depth knowledge of current physical models describing foam behavior. To this end, the following details a review of current literature discussing all aspects of foam behavior, ranging from microscopic phenomena to its flow behavior, and recent advancements in foam sclerotherapy and its physical characteristics.

| VARICOSE VEINS
Veins are the main carriers of deoxygenated blood in the body and also serve as functional blood reservoirs. They contain one-way bicuspid valves pointing toward deep veins and the heart, which prevent backflow of blood. Muscle contraction in the lower limbs can aid the flow of blood toward the heart. A number of circumstances are known to cause varicosities. For instance, mechanical stress as a consequence of pregnancy or prolonged periods of standing and ageing have been associated with varicose veins (Tortora & Derrickson, 2014). The growing uterus during pregnancy increases external pressure on lower limb veins that causes a decrease in venous blood return; this in turn results in pooling of blood (i.e., venous reflux) and increased venous pressure (i.e., venous hypertension). Standing still also raises venous hydrostatic pressure, due to hydrostatic effects and the absence of muscle contraction (Tortora & Derrickson, 2014;Whiteley, 2011;Zhang & Melander, 2014). Beebe-Dimmer et al. explores the effect of various epidemiological factors such as occupation, age, gender and diet on prevalence rates of chronic venous diseases (Beebe-Dimmer, Pfeifer, Engle, & Schottenfeld, 2005).
Under normal conditions, peripheral venous pressure is between 4 and 6 mmHg in lying adults while standing still can increase venous pressure to around 90 mmHg compared to 20 mmHg in walking adults (Guyton & Hall, 2006). Over time, this increase in blood pressure causes mechanical stress to the vein wall and the valves, which could render valves incompetent and dilate the vessel lumen (vasodilation). Incompetent valves fail to prevent backflow of blood and-as a result-venous pressure increases further, causing greater mechanical stress and increasing reflux. Thus, a two-way causality between blood pressure and vasodilation occurs-that is, as one increases, so does the other. As a result, a loop is formed between the two phenomena as they exacerbate the effect of one another. Ultimately, this feedback loop between the venous pressure increase and dilation of the vein is thought to be the underlying cause of varicosities that eventually results in abnormal blood flow, deformed valves, and stretched vessel walls (Whiteley, 2011)  Additionally, the increase in venous diameter due to venous reflux reduces wall shear stress, which in turn stimulates endothelial cells activating an inflammatory cascade. Despite these breakthroughs, it is likely that multiple interacting mechanisms are responsible for the development of varicose veins (Castro-Ferreira et al., 2018). Another study describes the histological differences of physiological and varicose veins in more detail (Oklu et al., 2012).
Varicose veins can occur anywhere in almost any part of the body, but the most susceptible vessels are superficial veins of the lower limbs, specially the great and small saphenous veins. This is due to their relatively larger diameter that allows them to contain greater volumes of blood, which may lead to a greater hydrostatic pressure (Zhang & Melander, 2014). A study showed that great saphenous veins that contain varicosities (n = 152) have a mean inner diameter of 6.39 ± 2.21 mm while normal great saphenous veins (n = 48) have a mean inner diameter of 4.41 ± 0.96 mm (Musil, Herman, & Mazuch, 2008). A number of studies have conducted rigorous investigations on the causality of varicose veins with respect to the hemodynamic insufficiencies of upstream veins (Recek, 2006(Recek, , 2013(Recek, , 2017 (Lin, Zhang, Sun, Ren, & Liu, 2015). For a more detailed account, Whitely discusses current theories of venous reflux (Whiteley, 2011).
Varicose veins affect more than 20% of the population in developed countries (Zhang & Melander, 2014). Although non-fatal, varicosities can affect a patient's quality of life significantly through symptoms such as leg swelling and fatigue, aching, muscle cramps, itchiness, and others (Zhang & Melander, 2014). The economic impact of venous ulcers corresponds to the 2% of the total healthcare budget of all Western countries (Cilurzo et al., 2019).Treatments are aimed at removal or destruction of the abnormal vein segments. They can be invasive (e.g., venous stripping), more painful (e.g., endovenous thermal ablation) or non-invasive (e.g., ultrasound-guided sclerotherapy).
While reported adverse effects of sclerotherapy are fewer compared to other treatments, it can achieve similar outcomes with less pain and faster recovery (Carugo et al., 2013;Nastasa et al., 2015;Zhang & Melander, 2014).

| FOAM SCLEROTHERAPY
Sclerotherapy involves the injection of a surfactant solution-using a needle or a catheter-that damages the inner vessel wall. This process involves the activation of calcium signaling and nitric oxide pathways in response to the sclerosant's injection, causing endothelial cell lysis, vascular fibrosis, and subsequent endovascular occlusion ( Figure 3) Carugo et al., 2013;Eckmann, 2009). Upon injection, the efficacy of liquid sclerosants decreases due to dilution and rapid deactivation by blood components, making liquid sclerotherapy ineffective when conducted on larger veins such as saphenous veins (Cameron, Chen, Connor, Behnia, & Parsi, 2013;Carugo et al., 2015). Studies have revealed that some  L. et al., Copyright [2005], with permission from Elsevier) F I G U R E 3 Foam sclerotherapy causes endothelial cell damage resulting in endovenous occlusion of the injected sclerosant is consumed by lysing of blood cells (erythrocytes, leukocytes and platelets in blood) (Connor, Cooley-Andrade, Goh, Ma, & Parsi, 2015), while blood proteins (e.g., serum albumin) can cause sclerosant deactivation (Watkins, 2011). An earlier study has experimentally demonstrated the binding of serum albumin to sclerosing agents such as sodium tetradecyl sulfate (STS) and polidocanol, leading to inhibition (Parsi et al., 2008). To overcome dilution and deactivation, the sclerosant is mixed with a gas and is administered in large veins as a foam Cameron et al., 2013;Carugo et al., 2015). The main benefit of administering sclerosing foams lies in their capacity to mimic a piston that displaces intravenous blood, leading to a greater contact surface area with venous endothelium, reduced mixing with blood and subsequent deactivation, and reduced staining of the leg due to trapped blood in the collapsed vessel (Carugo et al., 2015). A recent study attempted to create polidocanol-liposome nanoconstructs to further stabilize the resulting foam while minimizing interaction of the surfactant with plasma proteins (Cilurzo et al., 2019).
Foam sclerotherapy is also used to treat diseases such as oesophageal variceal, haemangioma, vascular malformation, hemorrhoids and cystic diseases (Zheng, Wei, & Zhang, 2018). Lately a new approach called ultrasound-guided foam sclerotherapy (UGFS) has gained popularity among clinicians. The benefits of UGFS include accurate placement of the needle within the venous lumen, demonstration of the path travelled by the foam plug, and the potential to observe spasm within treated vessels (Gibson & Gunderson, 2018).
More recently, a novel technique known as sclerotherapy augmented phlebectomy (SAP) has been developed, which combines venous stripping of large varicose segments with sclerotherapy of smaller segments (Kolluri, Hays, & Gohel, 2018). Sclerotherapy is reported to be 32% cheaper than surgery (Belcaro et al., 2000). A study conducted in 2015 shows that sclerotherapy costs approximately £315 per session to the NHS (Marsden et al., 2015). According to the Vein Centre (United Kingdom), a private sclerotherapy treatment plan including consultation, foam sclerotherapy injection and compression stockings may cost up to a total of £800. If necessary, follow-up sessions would cost approximately £300 per session (Vein Centre, 2019). The following is an account on the production, formulation and clinical outcomes of sclerosing foam therapy.

| Methods of production
Various production methods may be utilized to produce sclerosing foams.  includes a thorough review on such methods. This section summarizes these methods and various studies conducted to evaluate their performance.

| Conventional clinical methods
Physician compounded foams (PCFs) are generally produced using either the Double Syringe System (DSS) (Hamel-Desnos et al., 2003) or the Tessari method (Tessari, Cavezzi, & Frullini, 2001). Figure 4 shows the different connectors and syringe arrangements used for both methods. The general consensus is to use a smaller syringe for liquid surfactant and a larger syringe for gas (Tessari, 2002). Most commonly, a 5 ml syringe containing liquid surfactant and a 10 ml gasfilled syringe are used (Tessari et al., 2001). The surfactant solution is passed into and out of the 10 ml syringe 10 times, creating a foam (Carugo et al., 2015). It is suggested to use silicone-free syringes for foam production, as silicone reduces the half-life of foam by interfering with molecular links and the foam lamellae (half-life is defined as the time required for half of the liquid content of foam to drain) (Geroulakos, 2006). These techniques-although effective in producing a homogenous foam-lack the capability to make more than 10 ml of foam at a time, which may be a requirement for treatment of extensive lesions. Due to this bottleneck, a modified Tessari method (Figure 4c) has been proposed which is capable of delivering 20 ml of foam at a time (Xu, Wang, Chen, Wang, & Liu, 2016). Additionally, Bai et al. (2018Bai et al. ( , 2019 has created a laboratory-made automated machine to produce Tessari foam under constant pump speed and cycling rates in order to eliminate variability in foam properties ( Figure 4d). There are no other studies that address the variability of PCF's properties due to inconsistent production criteria.
An ideal sclerosing foam needs to be sufficiently cohesive, viscous, and with a low bubble size dispersity in order to exhibit stable characteristics (i.e., lower drainage time and slower rate of coarsening) (Star, Connor, & Parsi, 2018). It can be hypothesized that properties of PCFs could be user-dependent; in other words, the quality of the administered foam may highly depend upon the clinician's extent of experience and knowledge on ideal foam characteristics. With the aim of creating a foam with consistent characteristics, Provensis Ltd. (a BTG International group company-recently acquired by Boston Scientific) has developed a product known as Varithena® for the semi-automated preparation of a polidocanol injectable foam (previously referred to widely in the literature as polidocanol endovenous microfoam, or PEM, as we will use throughout this review for consistency with other publications) (Carugo et al., 2016).

| Polidocanol endovenous microfoam
Other than a study evaluating the effect of pumping speed on quality of the resulting Tessari foam (Bai et al., 2018), the scope of available research on alternative methods of sclerosing foam production is limited. PEM (commercially known as Varithena®) is the only semi-automated clinical production method developed for sclerotherapy purposes so far. The production method and formulation of PEM are rather different compared to PCFs. Most PCFs that are made using polidocanol surfactant use volumetric concentrations of 0.5-3% and room air at a 1:4 liquid to gas ratio (Carugo et al., 2016;de Oliveira, de Morais-Filho, Engelhorn, Kessler, & Neto, 2018;Rabe & Pannier, 2010;Yiannakopoulou, 2016) to create the desired foam, while PEM uses a 1% polidocanol solution (Carugo et al., 2015) at a 1:7 liquid to gas ratio to improve foam stability. Where PCFs benefit from stability of room air due to the low solubility of nitrogen, Varithena® produces PEM using a low nitrogen (<0.8%) gas combination of 35% CO 2 and 65% O 2 (Carugo et al., 2015;Star et al., 2018) in order to negate the issues of injection of nitrogen into the blood stream (Ceulen, Sommer, & Vernooy, 2008;Forlee, Grouden, Moore, & Shanik, 2006). A Varithena® canister assembly ( Figure 5) automatically mixes gas and surfactant solution at the appropriate ratios, ensuring a consistent foam texture (bubble size distribution) and composition (Carugo et al., 2016). The formulation and production technique of sclerosing foams therefore is variable and impacts foam performance and ultimately clinical outcomes. Such studies are discussed in depth in Section 3.3.1. In addition to PEM, other separate studies report on the benefits of CO 2 containing sclerosing foams where a mixture of 30% O 2 and 70% O 2 is referred to as "physiological gas." It is reported that physiological gas can reduce the prevalence rates of skin irritation (Moneta, 2012) as well as significantly reducing the likelihood of other side-effects such as chest tightness and dry cough (Morrison et al., 2008;Wong, 2015) due to the greater solubility of CO 2 compared to N 2 .

| Alternative methods of foam production
Although PCFs and PEM are currently utilized by clinicians, other foam production techniques exist which have never been used to F I G U R E 4 (a) The Tessari apparatus comprises of two syringes connected via a three-way stop-cock set at a 30 off-set. (b) The Double Syringe System (DSS) apparatus includes two syringes connected via a Combidyn connector (Figure adopted from [Carugo et al., 2016]), (c) The modified Tessari apparatus. One syringe is filled with liquid while the two parallel syringes are filled with gas. Three syringes are connected via two three-way stopcocks (Reprinted from Xu et al., Copyright [2016], distributed under the terms of the Creative Commons Attribution 4.0 International License (http:// creativecommons.org/licenses/by/4.0/)). (d) Laboratory-made automatic foam production device (Modified and Reprinted from Bai T. et al., Copyright [2019], with permission from Elsevier) F I G U R E 5 Varithena® canister contains all required components and is capable of readily producing PEM on demand. The gas canister is placed on top of the polidocanol cannister. By twisting the canisters together in a clockwise direction, gas is transferred to the polidocanol canister, creating PEM. The gas canister is then replaced with a Varithena® transfer unit which allows the withdrawal of foam into a syringe (Modified and Reprinted from Carugo D. et al., Copyright [2015], distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/)) produce sclerosing foams. It has been reported that foams can also be produced by mechanical agitation of a surfactant solution via acoustic cavitation, using either a tip sonicator (Critello et al., 2017) or under the effect of an ultrasound field in a non-flowing fluid system (Fiorillo, Fiorillo, Critello, & Pullano, 2015). A study demonstrated that low-frequency ultrasound can produce foams with smaller bubbles compared to PCF foams. Ninety-eight percent of the bubbles were found to be smaller than 55 μm (mean of 19 μm) for the sonicated foam and using a sonicator demonstrated the potential for sonication to produce foams with smaller bubbles that can be dissolved in blood more easily after administration, reducing the risk of gas embolization.
Depending on the agitation apparatus utilized, the production method may result in a different foam microstructure. For instance, mixing a surfactant solution with a spinning mixer at 5,000-10,000 rpm in a baffled container ( Figure 6a) produces a closely packed bubble mixture of diameter ranging 10-100 μm, called a colloidal gas aphron (CGA) or a microfoam (Tseng, Pilon, & Warrier, 2006). CGAs have applications in the bioprocessing sector, namely fermentation in bioreactors, protein separation, and separation of metals or organic dyes from water (Larmignat, Vanderpool, Lai, & Pilon, 2008;Tseng et al., 2006). CGAs are different to other foam types in terms of bubble morphology. Where normal foam bubbles consist of a gas core coated by a monolayer of surfactant molecules, CGA bubbles were speculated to consist of a multilayer of surfactant and liquid (Figure 6b,c). This hypothesis was based on absence of the coalescence phenomena, and the fact that CGA bubbles produced in a dyed solution retain their color when transferred to a clear solution. This is now a proven hypothesis thanks to studies based on X-ray diffraction (Larmignat et al., 2008). CGAs are known to exhibit a low viscosity (similar to that of water) and can travel longer distances compared to conventional foams under identical experimental conditions. Furthermore, they do not exhibit extensive instabilities such as liquid drainage (Tseng et al., 2006). Nonetheless their application in sclerotherapy has not been explored yet.

| Mechanism of action
In general, surfactants are compounds that contain a hydrophobic hydrocarbon chain and a hydrophilic head. They are classified into (with a net negative charge), and zwitterionic (containing two oppositely charged head groups). POL is non-ionic whereas STS is anionic.
The non-ionic nature of POL together with its long hydrocarbon chain make it a milder surfactant compared to STS which is known to be at least three times more potent than POL (Parsi, 2015). The clinical utility of surfactants relies on their ability to reduce the surface tension of a solution. For instance in foams, surfactant molecules adsorb at the gas-water interfaces, preventing coalescence of gas bubbles allowing for a more stable foam (Parsi, 2015). Injection of liquid or foamed sclerosant into vessels causes damage to vascular endothelium, transforming the pathological vessels into a fibrous cord and resulting in vessel sclerosis (Zheng et al., 2018).

| Foam therapeutic effects
Sclerotherapy transforms the varicose segment into a fibrous cord that in the case of small vessels fades over time, while in larger vessels-such as the great saphenous vein-the diameter is significantly reduced (Zheng et al., 2018). Whether valves regenerate following this treatment, at present remains unclear and no studies to date address this question. Furthermore, venous reflux is eliminated (de Oliveira et al., 2018). There is a gap in the literature on the extent of sclerosant diffusion into the vessel wall, and the fate of the treated vessel. Although sclerotherapy is relatively efficient in the short term, 70% of patients have been reported to exhibit varicosities up to 10 years post-treatment (Campbell et al., 2003). Evidently, sclerotherapy could potentially be optimized to result in more desirable outcomes. While invasive methods such as surgery and venous stripping can reduce recurrence rates by approximately 20% (Jones et al., 1996), the scope of research on optimization of non-invasive methods, such as sclerotherapy, is limited. According to a number of studies, varicose vein recurrence is due to neovascularization; that is, the formation of new blood vessels in response to ischemia via migration of endothelial cells to regions experiencing ischemia, resulting in a functional vascular network (Jones et al., 1996;Van Rij et al., 2004). Furthermore, histological analysis of varicose vein cells suggest that varicose endothelium exhibit abnormal morphologies (Somers & Knaapen, 2006). Thus, it can be hypothesized that any remaining abnormal endothelial cells post-sclerotherapy may migrate and proliferate to reform more varicose veins.
A number of reasons may be responsible for this treatment inefficiency; dilution of the injected foam or deactivation of sclerosant molecules during treatment could reduce lytic activity leaving some endothelial cells undamaged. In addition, it has been reported that buoyancy exerted by blood on the foam could reduce foam-vessel contact surface or cause inhomogeneous bubble size distribution (Cameron et al., 2013). In conclusion, it is crucial to maximize endothelial cell lysis during treatment. These challenges are addressed in Section 5.3 in more depth.

| Side effects
Sclerotherapy has been associated with a number of adverse events. Table  1 summarizes the side-effects of sclerotherapy (Yiannakopoulou, 2016;Zheng et al., 2018). The most common side effect has been reported to be pigmentation around treated blood vessels. A number of more serious effects can arise, namely deep vein thrombosis, neurological issues, and skin necrosis. Sclerotherapy has proven to result in lower incidence of embolic-related events compared to invasive procedures such as surgery (Zheng et al., 2018). Use of air has been reported to cause adverse neurological symptoms and increase the likelihood of gas embolism due to the low solubility of nitrogen in blood (Ceulen et al., 2008;Forlee et al., 2006). Additionally, visual disturbances have been reported to be more frequent after foam sclerotherapy (Yiannakopoulou, 2016

| Chemical formulation
The focus of this section will be on POL-based foam due its aforementioned advantages.

| Effect of formulation on foam properties
Different production methods result in different bubble sizes in the manufactured foams. A recent study (Carugo et al., 2016)  CO 2 ). The results show that PEM exhibits the narrowest size distribution (130-500 μm) compared to PCFs. After ageing, the PEM bubble size distribution shifts toward larger bubbles but it remains consistent with no bubbles >875 μm in diameter. The results of this study demonstrate that the gas composition is not the sole factor responsible for enhanced properties of PEM, but that the production mechanism for Varithena® (see Figure 5) also plays a crucial role in producing a consistent foam microstructure (Carugo et al., 2016). Other studies discuss the effect of needle size (Bottaro, Paterson, Quercia, et al., 2019), liquid-to-gas ratio ( food preparation, firefighting and cosmetics (Gopal & Durian, 1999;Herzhaft, 1999;Höhler & Cohen-Addad, 2005;Tseng et al., 2006).
The ordered arrangement of surfactant molecules in the liquid films allows the foam structure to have a minimum interfacial energy density, though this can vary for foams of different liquid-gas ratios.
Thus, the foremost parameter to define is the liquid volume fraction (ϕ l )-the ratio of liquid volume to the total foam volume. At the close-packing fraction (ϕ l, c -liquid volume fraction of close-packing), gas bubbles are undeformed spheres and are almost touching one another. ϕ l, c was determined numerically to be 0.0931 and 0.2595 for two-dimensional and three-dimensional emulsions (Princen, 1985). However, ϕ l, c is not recognized as the threshold between wet and dry foams. As liquid volume fraction decreases below the close-packing fraction, gas bubbles deform and start to form polyhedral cells. At a low liquid volume fraction (ϕ l À! 0) foam is said to be "dry" (see Figure 9b). In a dry foam, bubbles at equilib- T A B L E 1 A list of the most common adverse events associated with sclerotherapy (liquid or foam) and their corresponding rate of incidence (Yiannakopoulou, 2016;Zheng et al., 2018) Adverse event Incidence rate

| Ageing
Ageing refers to irreversible time-dependent changes occurring in the structure of stationary foams and is governed by various mechanisms.

| Drainage
In a dry foam (ϕ l À! 0) all the liquid content of a foam is confined in the films, nodes and Plateau borders. Gravity causes the liquid to flow downwards resulting in thicker Plateau borders in lower regions. Consequently, the capillary pressure in the lower region increases according to the Laplace-Young law, inducing capillary flow upwards.
Thus, the drainage of liquid out of the foam is governed by gravity and capillary forces (Figure 9). These two forces work against one another; however, gravity dominates capillary forces and liquid will inevitably flow downwards. A commonly used method in the literature to study drainage (known as "forced-drainage study") involves forcing the surfactant solution into drained dry foam at a given flow rate (Saint-Jalmes, 2006). More in-depth discussions of numerical models describing ageing and drainage of foams are given in (Karakashev, 2017;Parikh, 2017;Saint-Jalmes, 2006). CGAs are reported to age in a different manner compared to conventional aqueous foams. According to Tseng, where dry polyhedral foams exhibit capillary flow, dry CGAs lack such flows because bubbles retain their spherical morphology even in dry forms due to the presence of liquid within their multilamellar structure (Tseng et al., 2006).

| Coarsening
Gas diffusion through the liquid-gas interface (also referred to as Ostwald ripening in literature) is another mechanism that contributes to the evolution of aqueous foam structure (Figure 10a). The driving force behind diffusion is the difference in Laplace pressure of neighboring bubbles. Laplace pressure (i.e., the pressure difference between the inside and the outside of a bubble) is inversely proportional to bubble radius; as a result, gas diffuses from smaller bubbles (high pressure) into bigger bubbles (low pressure). This process is also referred to as a T2 event. A major consequence of coarsening is an increase in mean bubble diameter over time (Höhler & Cohen-Addad, 2005;Saint-Jalmes, 2006). It is reported that coarsening rate increases with gas solubility and gas volume fraction (Cohen-Addad et al., 2013). Figure 10b illustrates the effect of different gases on the rate of bubble coarsening. Nitrogen-based sclerosing foams are much more stable compared to oxygen based or carbon dioxide-based foams. Nitrogen contributes to foam stability due to its low solubility in water, although it may be responsible for adverse side-effects (Ceulen et al., 2008;Forlee et al., 2006). This has led to the notion that low nitrogen-content foams such as PEM could decrease the likelihood of adverse events, though statistical studies on clinical outcomes of PEM are yet to be carried out.

| Rheology
Rheological modeling of foam is not as simple as that of Newtonian fluids due to attributes such as yield stress, rheomalaxis, and wall slip. This section will provide a brief overview of these attributes while discussing possible simplifications that could be employed to characterize sclerosing foams more precisely. Aqueous foams are complex multiphasic fluids which exhibit solid-like and fluid-like behaviors simultaneously (Gopal & Durian, 1999). Mechanical and rheological studies prove the existence of viscoelastic as well as viscoplastic behaviors in liquid foams (Dollet & Raufaste, 2014;Kraynik, 1988).

| Microstructural evolution of shearing foam
Under an extremely small shear stress, foam structure resists flow.
Instead, it deforms linearly with the applied stress in a reversible manner (viscoelasticity) (Gopal & Durian, 1999). As stress increases, flow occurs at the "yield stress" when bubble rearrangements take place resulting in plastic deformation (Figure 11a). The onset of deformation is defined by the so-called "T1 event" during which bubble rearrangements occur (Figure 11b). If the viscoelastic behavior of foams prior to yielding is to be neglected, foams can be thought of as viscoplastic materials with a yield stress (Kraynik, 1988).
An aqueous foam behaves as a pseudoplastic ( The coupling between the ageing phenomena and shearing can give rise to time-dependent rheological effects due to the continuously evolving structure of foams, adding another layer of complexity to foam rheology. Consequently, rheological properties of foams depend on the deformation history as well as the shear rate. Literature refers to this time-dependent rheological behavior as "thixotropy." It is worth noting that the presence of static and dynamic yield stress is associated with thixotropic materials, whereas simple yield stress materials are known to exhibit no stress overshoot (as seen in Figure 11a) resulting in a well-defined yield stress (Dinkgreve et al., 2016). Figure 12 summarizes the classification of time-dependent rheologies. Originally, thixotropy referred to materials which microstructure progressively breaks down due to applied shear and slowly rebuilds at rest ("timethinning"), although the term has been generally used to refer to all time-dependent rheologies (Barnes, 1997;Bekkour & Scrivener, 1998).
Clay-based surfactants, yogurt and flocculant solutions are among materials with time-dependent rheology (Barnes, 1997). On the other hand, the foam structure evolves irreversibly; thus the term "rheomalaxis" is often used to describe such irreversible changes of viscosity over time (Bekkour & Scrivener, 1998;Hackley & Ferraris, 2001).

| Thixotropy
The most common method of measuring thixotropy is the hysteresis loop test. It involves a linear increase (loading) followed by a subsequent decrease (unloading) of shear rate (or shear stress) at constant shear stress (or shear rate) from zero to a predefined maximum value (Barnes, 1997;Hackley & Ferraris, 2001). Thixotropic and anti-thixotropic loops differ in relative positions of loading and unloading curves. As illustrated in Figure 13a, the loading curve of a thixotropic material lies above the unloading curve whereas for an anti-thixotropic material the unloading curve lies above the loading curve (Chhabra, 2010;Hackley & Ferraris, 2001). More in-depth discussion of time-dependent rheological models is provided in (Chhabra, 2010;de Souza Mendes, 2009;Hackley & Ferraris, 2001;.

| Complications of rheomalaxis
Rheomalaxic flow in tubular structures will inevitably result in complications such as the wall slip phenomena. When a fluid undergoes laminar flow in a tube (i.e., Poiseuille flow), shear rate increases with the distance from the tube centerline. In other words, the foam near the wall experiences the greatest shear rate. This results in rapid structure breakdown, causing the formation of a liquid film between the bulk foam and the tube that is responsible for the wall slip phenomenon (Barnes, 1997). It has been reported that foams under Poiseuille flow can exhibit a plug-flow behavior as a consequence of the wall slip phenomenon during which the bulk material does not experience deformation (Bertola, Bertrand, Tabuteau, Bonn, & Coussot, 2003;Herzhaft, 1999). A number of numerical and experimental methods exist that tackle the wall slip problem that will be discussed later in Section 5.1.6.

| PHYSICAL CHARACTERIZATION OF SCLEROSING FOAMS
The most fundamental studies of foam and emulsion rheology are the works of Khan et al. (Khan et al., 1988;Khan & Armstrong, 1986, 1987 and Princen et al. (Princen, 1983, 1985Princen & Kiss, 1986, 1989. Khan et al. (Khan et al., 1988;Khan & Armstrong, 1986, 1987) developed a theory of stress tensor for deformation of monodisperse (i.e., constant bubble size) 2D dry foams, assuming a hexagonal foam cell geometry. This was then extended to polydisperse (i.e., variable bubble size) foams and further studies on yield stress. Results showed that yield stress increases with gas volume fraction (Khan et al., 1988) and is independent of cell size distribution about a constant mean (Khan & Armstrong, 1987).
Princen's approach was to develop an elastic stress-strain relationship as a function of gas volume fraction and bubble contact angle for 2D foams (Princen, 1983(Princen, , 1985 that was extended to 3D foams (Princen & Kiss, 1986, 1989. This resulted in a numerical expression for yield stress as a function of interfacial tension (i.e., surfactant solution), gas volume fraction and an empirical contribution of each bubble to bulk stress (Princen, 1983). The resulting model was  (Princen, 1985).

| Current theoretical and experimental methods
The aforementioned studies are the cornerstones of foam physics, yet the scope of their application in the evaluation of sclerotherapy is limited. We therefore describe in detail methods for measuring the rheological properties of foams that may be critical to their performance as sclerosing agents and we point the reader to the work of Chhabra (2010) which provides additional thorough review of the general rheology of non-Newtonian fluids.

| Conventional rheometry
In conventional rheometers, the fluid of interest undergoes Couette flow between two parallel plates (see Figure 15a for a representation of the velocity profile in Couette flow). Rheometers are of two types: controlled shear rate or controlled shear stress, depending on user choice of the appropriate independent variable. The most frequently used equation for modeling yield stress materials is the Herschel-Bulkley (HB) model (Cheddadi et al., 2012;Cohen-Addad et al., 2013): where τ is shear stress (Pa), _ γ is shear rate (s −1 ), τ y is yield stress (Pa), K is fluid consistency index, and n is fluid flow index. An exponent of 1 would reduce the HB model to the linear Bingham model for yield stress fluids (Dollet & Raufaste, 2014), whereas n > 1 and n < 1 correspond to pseudoplastic (shear-thinning) and dilatant (shear-thickening) behaviours (Björn, de La Monja, Karlsson, Ejlertsson, & Svensson, 2012). Note that in the absence of yield stress (τ y = 0), Equation (1) would reduce to the power-law equation (τ = K _ γ n ) (Chhabra, 2010).
A simple mathematical manipulation of Equation (1) would yield: Fitting stress data obtained from a controlled shear rheometer on a plot of ln(τ − τ y ) versus ln _ γ ð Þ would be sufficient to calculate the consistency and flow indices of a given foam. Given that yield stress is the y-intercept of a τ − _ γ graph, it may be determined by extrapolation of shear stress as shear rate approaches zero on a ln(τ − τ y ) − ln _ γ ð Þ plot (Marze, Langevin, & Saint-Jalmes, 2008). Studies report that most aqueous foams exhibit pseudoplasticity given that they report a flow

| Oscillation rheometry
An alternative to conventional rheometry is the application of oscillatory shear. As opposed to a linear increase in shear rate, this F I G U R E 1 5 (a) Couette flow of a fluid between two parallel plates exhibits a linear velocity profile. The fluid is sheared as one of the plates moves while theother remains stationary. This concept is utilized in conventional rheometers. (b) Poiseuille flow of a fluid inside a tube exhibits a parabolic velocity profile with maximum velocity at the tube centerline and minimum velocity at tube walls. Poiseuille flow is the closest simplification of vascular flow and is the most biomimetically applicable flow model technique involves subjecting the foam to a sinusoidal shear given by γ = γ 0 sin(ωt) where ω and γ 0 are angular frequency and strain amplitude (Bair et al., 2014;Dollet & Raufaste, 2014). The oscillatory stress response is therefore given by: where G 0 and G 00 are storage and loss moduli that quantify elastic deformation and viscous dissipation respectively. Stress-strain curves obtained using this method show a clear transition from a viscoelastic response below yield stress to a non-linear power-law response, thus making this method desirable for yield stress determination (Dinkgreve et al., 2016). This method could be applied to measure the yield stress of sclerosing foams using rheometers which has never been done before. As it will be discussed later, rheometry of aqueous foam is error-prone due to the wall slip phenomena which can be eliminated by pasting sandpaper on the rheometer walls.

| Classification of rheological models
With a few exceptions (see below), almost all studies of foam rheology use rheometers as the primary experimental apparatus. These studies divide into three major categories, the third of which is of particular interest to sclerosing foam development.
The second group aims to study the microstructural events in a foam through the development of numerical theories of rheology that involve stress contribution per foam cell, viscous dissipation, inertial and capillary forces, and so forth (Denkov et al., 2005(Denkov et al., , 2008(Denkov et al., , 2009Khan et al., 1988;Khan & Armstrong, 1986, 1987Princen, 1983Princen, , 1985Princen & Kiss, 1986, 1989. These studies also use rheometers to validate their models. Almost all of the reviewed articles here use rotational rheometers that are equipment of different geometries such as the cone-plate, Couette and concentric cylinders (Song, Salehiyan, Li, Lee, & Hyun, 2017).
Although the results of rheometric studies are of great value from a physical characterization perspective, they are irrelevant to clinical procedures. In other words, rotational rheometers lack the capability of mimicking the bio-physical environment of sclerotherapy. This coupled with the challenge of thixotropic characterization, raises concerns regarding the validity of such equipment to study sclerosing foams. In other words, flow of foam in veins leads to a different deformation history than in rheometers. A more biomimetic setting is therefore required to characterize foams in more clinically relevant settings, leading us to the final category.

| Poiseuille rheometry
The third category of studies employs "Poiseuille rheometry" (also referred to as pipe viscometry) (Bekkour & Scrivener, 1998;Enzendorfer et al., 2002;Gardiner, Dlugogorski, & Jameson, 1998;Larmignat et al., 2008;Tseng et al., 2006). This has received attention specifically from the petroleum industry due to its potential to mimic industrial conditions (Herzhaft, 1999). The same potential makes Poiseuille rheometry an attractive route of experimental study for foam sclerotherapy. In contrast to conventional rheometers that utilize Couette flow, Poiseuille rheometry utilizes Poiseuille flow which is more relevant to vascular flow (Figure 15b), and also allows quantification of wall slip. Current protocols on pipe rheometry of CGAs (Larmignat et al., 2008;Tseng et al., 2006) and foams used in firefighting (Gardiner et al., 1998) Although Equation (4) can provide estimates of foam viscosity, it does not account for the non-Newtonian behavior of foam or the wall slip phenomena. The volumetric flow rate and pressure drop may however be used to calculate apparent wall shear rate (_ γ observed ) and wall shear stress (τ w ) (Gardiner et al., 1998): Plotting τ w against _ γ observed would yield a rheogram, the gradient of which would be equal to the foam's apparent viscosity at any particular shear rate. However, Poiseuille flow assumes a no-slip boundary condition at the walls; as discussed in Section 4.2.4, wall slip is present during Poiseuille flow and needs to be quantified.

| Wall slip correction
An inevitable complication of foam flow in a pipe is the wall slip phenomenon. Given the shear-thinning nature of blood (Nanda et al., 2017), wall slip is not only a likely phenomenon in physiological vessels, but also it has been attributed to vascular malformations such as microaneurysms (Drapaca, 2018). A consequence of wall slip is inconsistent shear rate calculations for a constant pressure drop over different pipe diameters (Herzhaft, 1999). Khan et al. (1988) (Enzendorfer et al., 2002;Larmignat et al., 2008).
where β(τ w ) is the slip coefficient, which itself is a function of τ w . Equation (7) is then subtracted from the apparent shear rate in order to compute the true shear rate. True shear rate is calculated from Equation (8): Note that while cross sectional area A = πd 2 4 and linear velocity = Q A , Equation (5) by can be manipulated to yield: Keeping Equation (9) in mind while multiplying Equation (8) by 8/ d, and substituting Equation (7) into Equation (8) yields: Equation (10) implies that a plot of _ γ observed against 1/d 2 must yield a straight line. The slip coefficient is then computed by dividing the slope (8τ w β(τ w )) by 8τ w and is subsequently plotted against wall shear stress. Curve fitting models are then used to find the relationship between slip coefficient and wall shear stress (least square fit, if directly proportional) to find the equation of the line β(τ w ) = aτ w + b. Finally, the corrected true shear rate is calculated by rearranging Equation (10): The Oldroyd-Jastrzebski slip correction has proven efficient at collapsing τ w − _ γ true curves into a master curve independent of pipe diameter (Bekkour & Scrivener, 1998;Enzendorfer et al., 2002;Gardiner et al., 1998;Larmignat et al., 2008).

| Volume equalization
Finally, there is one last technique which can normalize the data corresponding to foams of different liquid to gas ratios; namely the "volume equalization" method. It was originally reported that the power-law equation can be normalized with respect to the specific expansion ratio (ε, defined as the ratio of liquid density to foam density) : Equation (12) (Enzendorfer et al., 2002;Larmignat et al., 2008). Volume equalization can be applied to foams produced using different methods in order to obtain method-specific flow and consistency indices.
Wall slip is a phenomenon that certainly occurs during the injection of sclerosing foams in varicose veins. Given the lack of rheological data on sclerosing foams in the literature, it is important to conduct wall slip correction during the rheological characterization of sclerosing foams in order to obtain the most accurate results. Volume equalization can then be applied to wall slip corrected data in order to compare viscosity values corresponding to foams of different liquid-to-gas ratios.

| In silico models
Recent advances in computational modeling have spawned a generation of in silico models that attempt to study various aspects of structural evolution in foams. A number of studies employ Surface Evolver (open source); a numerical modeling software that allows determination of random dry foam topology associated with the minimum interfacial energy density (Cox, 2005;Evans, Kraynik, Reinelt, Mecke, & Schröder-Turk, 2013;Kraynik, Reinelt, & van Swol, 2003. Surface Evolver is capable of simulating cell-level events, but it does not allow rheological modeling in tubes or vessels. Another technique is molecular dynamics (MD), which aims to simulate events at a molecular level and has been used to calculate interface formation energies and surface concentration per surfactant molecule in liquid films (Jang & Goddard, 2006). Another study used MD to evaluate the effect of different foaming gases (N 2 , O 2 , and CO 2 ) on interfacial phenomena such as gas diffusion and coalescence in SDS foams. Transient simulation in MD showed that CO 2 molecules interact with both the hydrophobic and hydrophilic ends of surfactant molecules, which allows them to permeate through the liquid films more rapidly. As a result, channel openings in foam films were observed, which could accelerate CO 2 diffusion even further ( Figure 16). Simulation results were then verified experimentally where CO 2 foams showed the highest rate of coalescence (refer to Figure 10) (Sun, Qi, Sun, Zhao, & Li, 2016). MD simulations can also potentially shed more light on the mechanism of interaction between surfactants and cell membranes.
In contrast to MD, a numerical software such as ANSYS® could prove insightful for modeling rheology and multiphasic flow of foams in a continuous phase. To this end, Wong et al. has employed a computational fluid dynamics (CFD) model to simulate sclerosing foam injection into a varicose vein. Foam was simulated as a "pseudo-fluid" via the volume of fluid (VOF) model in ANSYS® Fluent (Wong, Chen, Connor, Behnia, & Parsi, 2014), while bulk rheological properties of foam were selected based on previous experimental findings . The in silico results were then compared with experimental findings to evaluate the accuracy of the model in capturing foam's behavior. It was demonstrated that CFD could capture foam behavior to a reasonable degree of accuracy when injected into a straight channel; however, CFD's accuracy of simulating injection into a branched system was limited (Wong et al., 2014).
Although software packages such as Surface Evolver or MD show potential in capturing microstructural phenomena with a reasonable degree of accuracy, CFD modeling of foam remains underdeveloped.
This could be due to lack of experimental data on fundamental rheological parameters and models of aqueous foams. Moreover, a CFD package often offers time-dependent viscosity models, which may be able to capture foam behavior more accurately, although experimental characterization is due prior to computational time-dependent models. Older in silico models of foams, such as the Potts and the "bubble" model, are briefly described in Höhler et al., which are not within the scope of this review (Höhler & Cohen-Addad, 2005).
There is also a growing demand to eliminate animal testing that can be replaced with in silico models; however, the capability of current models to simulate foam flow is yet to be fully studied.
Recently, organizations such as the Food and Drug Administration (FDA) have formulated new guidelines that accept CFD methods in the research and development pipeline of new medical treatments (Bluestein, 2017

| Optimizing sclerotherapy
Based on the reviewed literature thus far, the scope of foam characterization studies with respect to end-point applications (sclerotherapy or otherwise) is limited compared to fundamental physical studies. Only a handful of studies have focused on characterizing foam physics in application-relevant setups that are discussed here.
Apparent viscosity is a parameter that could be used as an independent variable in future studies against other clinically relevant variables such as dwell time or lytic activity within physiologically relevant shear rates. Furthermore, replicating surface properties of vessels in in vitro studies is crucial in order to accurately replicate the interaction between foam and vessel wall.
• There may be other clinically relevant properties of foams that need to be studied. Other than dwell time, the capability of a known volume of foam to displace blood could be a potentially useful parameter. This may be correlated with rheological properties of sclerosing foams such as viscosity. Moreover, PCFs (all foams other than Varithena®) are formulated in-house prior to administration, and user-variability is a factor that can also affect lytic activity.
• Surfactant drainage after injection could potentially affect treatment outcomes. It is unclear how fast liquid is drained from shearing foam during sclerotherapy. Further studies are needed in order to characterize the extent of foam dilution and mixing with blood after injection.
• • The possibility still exists that parameters such as flow index, yield stress, loss and storage moduli of sclerosing foams are relatable to clinical outcomes. These parameters are yet to be quantified accurately.
• PVMs could benefit from clinical imaging data in order to create more accurate varicose vein models. Future in silico studies may utilise specialist software in order to create accurate vascular geometries.
• While molecular dynamics simulations have proven to accurately explain microstructural events such as coarsening, they can also be utilized to study the surfactant-cell interaction. Such studies are yet to be undertaken.
• CFD simulations are yet to be improved upon in order to capture macrostructural flow of foams. However, they can be used to extract an approximate propagation path of the foam plug after injection. To this end, a more accurate viscous characterization of foam is required as well as biomimetic varicose vein geometries.

ACKNOWLEDGMENTS
Authors would like to thank the Engineering and Physical Sciences Research Council (EPSRC), for having contributed to fund Alireza Meghdadi's PhD studentship through an EPSRC DTP scheme (awarded by the Faculty of Engineering and the Environment, University of Southampton). We also thank Mr. Masih Motamedvaziri for creating the illustration of foam sclerotherapy (Figure 3).

CONFLICT OF INTEREST
Stephen