Characteristics of loose connective tissue disorders.
\r\n\t
",isbn:"978-1-78984-671-3",printIsbn:"978-1-78984-670-6",pdfIsbn:"978-1-78985-657-6",doi:null,price:0,priceEur:0,priceUsd:0,slug:null,numberOfPages:0,isOpenForSubmission:!0,hash:"d5feb836870aef4d30893f10898e7791",bookSignature:"Dr. Gokul Sridharan",publishedDate:null,coverURL:"https://cdn.intechopen.com/books/images_new/10791.jpg",keywords:"HPV, Inflammation and Immunity, Cancer Stem Cells, Genomics and Epigenomics, Transcriptomics, Proteomics, Targeted Therapy, Immunotherapy, Surgery, Next-Gen Sequencing, Bioinformatics, Pharmacogenomics",numberOfDownloads:null,numberOfWosCitations:0,numberOfCrossrefCitations:null,numberOfDimensionsCitations:null,numberOfTotalCitations:null,isAvailableForWebshopOrdering:!0,dateEndFirstStepPublish:"February 10th 2021",dateEndSecondStepPublish:"March 10th 2021",dateEndThirdStepPublish:"May 9th 2021",dateEndFourthStepPublish:"July 28th 2021",dateEndFifthStepPublish:"September 26th 2021",remainingDaysToSecondStep:"9 days",secondStepPassed:!1,currentStepOfPublishingProcess:2,editedByType:null,kuFlag:!1,biosketch:"A pioneering researcher and academician with an interest in oral pre-cancer and oral cancer with special emphasis on salivary diagnostics.",coeditorOneBiosketch:null,coeditorTwoBiosketch:null,coeditorThreeBiosketch:null,coeditorFourBiosketch:null,coeditorFiveBiosketch:null,editors:[{id:"82453",title:"Dr.",name:"Gokul",middleName:null,surname:"Sridharan",slug:"gokul-sridharan",fullName:"Gokul Sridharan",profilePictureURL:"https://mts.intechopen.com/storage/users/82453/images/system/82453.jpeg",biography:"Dr. Gokul Sridharan is currently an associate professor in the Department of Oral Pathology and Microbiology at Y.M.T. Dental College and Hospital, Navi Mumbai. He obtained his Ph.D. for the work titled “Salivary and serum metabolomics in oral leukoplakia and oral squamous cell carcinoma.” His fields of interest include oral pre-cancer, oral cancer, salivary diagnostics, oral and maxillofacial diseases, and advanced diagnostic aids with an emphasis on bioinformatics and metabolomics. He has several scientific publications to his credit and actively contributes as a peer reviewer to numerous journals. He is an active member of the editorial boards of several journals of repute. 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All these disorders share many similarities with lipedema including painful lipomas, obesity, fibrosis, a risk of developing lymphedema and difficulty in losing the abnormal fat through diet and exercise. There are clinical characteristics specific for lipedema, including the onset of the disease, fat location and associated health issues (\nTable 1\n) [1, 2].
\nCharacteristic | \nLipedema | \nDD | \nMSL | \nFML | \nMSL | \n
---|---|---|---|---|---|
Abnormal fat location | \nLegs, arms, abdomen | \nGlobal | \nUpper; can be global | \nArms, thighs, trunk, abdomen | \nUpper; can be global | \n
Diet-resistant fat | \nYes | \nYes | \nYes | \nYes | \nYes | \n
Lipomas | \nYes | \nCommon | \nCommon in men | \nCommon | \nCommon in men | \n
Time fat change | \nPuberty; 3rd decade | \nChild-adult | \nAdult; child rare | \nChild-adult | \nAdult; child rare | \n
Painful fat | \nYes | \nYes | \nNot usually | \nLipoma | \nNot usually | \n
Sex predominance | \nFemale | \nFemale | \nMale | \nMale = female | \nMale | \n
Lymphatic dysfunction | \nYes | \nYes | \nYes | \nYes | \nYes | \n
Prevalence | \nPossibly common | \nPossibly common | \nRare | \nRare | \nRare | \n
Associated conditions | \nLymphedema | \nAutoimmune; diabetes | \nNeuropathy | \nMoles; neuropathy | \nNeuropathy | \n
Inheritance pattern | \nAutosomal dominant; incomplete penetrance | \nAutosomal dominant; sex-specific influence | \nAutosomal dominant or recessive | \nAutosomal dominant | \nAutosomal dominant or recessive | \n
Lipedema is often misdiagnosed as lifestyle-induced obesity that affects ~10% of women of European descent as well as other populations [3, 4]. Although both disorders are considered inflammatory diseases due to the presence of increased macrophages and hypertrophic adipocytes, there are significant differences between the two disorders. Among these is the location of the fat, primarily abdominal or spread widely over the body in obesity compared to the symmetric distribution in the lower extremities in lipedema, the texture of the skin (thin and soft in lipedema and thicker in obesity), easy bruising and pain upon the introduction of pressure in lipedema [5, 6].
\nThe focus of this review will be on the disease of lipedema, different stages and types, diagnosis and treatment, pathogenesis and current research in the field.
\nLipedema also referred to as lipedema, is a painful loose connective tissue disorder first described in 1940 by Allen and Hines [7]. Lipedema is characterized by symmetric enlargement of the buttocks, hips and legs due to deposition of loose connective tissue that includes fascia, adipocytes, immune cells and other structures; arms are also affected in 80% of patients [3, 4]. Feet are typically spared, but ankle cuffs are often noted in advanced stages of lipedema where the risk of lymphedema is also high [8, 9]. Patients with lipedema experience mobility issues, psychosocial distress, anxiety, eating disorders, sleep apnea and depression [1, 10].
\nLipedema is considered a hormone-related disorder affecting almost exclusively women during puberty, childbirth or menopause. Case reports of men with lipedema have been described in literature. Men with lipedema have elevated estrogen level and low to absent testosterone levels resulting in cirrhosis, gynecomastia and hypogonadism [11, 12, 13]. While the exact etiopathogenesis of this disease is unknown [10, 14], many studies have demonstrated that inflammatory cells, hypertrophic adipocytes, abnormal blood vessels and lymphatic dysfunction are associated with tissue damage and development of a fibrotic disease [14, 15, 16, 17].
\nLipedema consists of three stages characterized by the texture of skin and tissue formation. Stage 1 involves smooth skin over pearl-sized nodules in a hypertrophic fat layer; Stage 2 has skin indentations over a hypertrophic fat structure of pearl-to-apple-size masses; and Stage 3 includes pearl-sized nodules and much larger fat masses causing lobules of skin and fat to form mainly on the hips, thighs, and around the knees. Lymphedema, causing fluid accumulation in the limbs, may develop during any stage of lipedema and is referred to as lipo-lymphedema [1, 3, 10, 18, 19].
\nHealthcare providers often misdiagnose women with lipedema as they do not take into account the disproportionate size of the legs compared to trunk especially in Stage 1 and 2 along with the inability to lose fat from areas affected by lipedema. It is possible to confuse women with Stage 3 lipedema as having lifestyle-induced obesity due to fat involving more areas of the body.
\nIn addition to stages of lipedema, lipedema is also characterized by types determined by the area of the body that is affected. There are five types of lipedema; types I, II, and III are the most common. In Type I, fat is deposited in the areas of the buttocks and hips resembling saddle bags. In Type II, fat extends to the knees from the buttocks area with the formation of folds of fat around the inside of the knee. In Type III, fat spreads all over the lower body from the hips to the ankles. In Type IV, upper arms are affected causing difficulty in lifting the arm and stress on the shoulder. In Type V, fat is restricted to the lower legs. It is worth noting that patients with lipedema can clinically present with a mixture of types [3, 10].
\nPain, tenderness, bruising easily, symmetrical swelling of the legs, heaviness of affected limbs, burning sensations in the skin and fat, soft skin, negative stemmer’s sign and hypermobile joints are among the common symptoms observed in lipedema patients [2, 3, 6, 13]. Hypermobility in women with has been reported to contribute to joint damage and increase the risk of cardiovascular disease as seen in Ehlers Danlos Syndrome-Hypermobility Type (EDS-HT) with Beighton score higher than 5 [2, 3, 20, 21]. Thus, hypermobility causes structural changes in lipedema tissue resulting in increased fibrosis, dysfunction of blood vessels and accumulation of interstitial fluid.
\nWomen with lipedema also experience emotional symptoms due to unexplained weight gain including embarrassment, anxiety and depression that impact their overall quality of life [22, 23]. Symptoms may progress in advanced stages of lipedema that might be associated with increased cardiovascular and renal diseases. A study conducted by Herbst el al. in 2015 provides a detailed list of symptoms experienced by lipedema patients [3].
\nDiagnosis of lipedema involves a comprehensive physical exam based on the criteria listed by Wold and colleagues in 1951, [4] medical and surgical history, list of medications that might affect weight or fluid retention and family history. A physical examination includes assessment of the enlarged lower extremities carefully noting the texture of the affected areas such as velvety soft skin that can be found in hypermobility, nodular fat, pain when applying pressure, tenderness upon palpation and accumulation of fluid such as pitting or non-pitting edema which may indicate lymphedema [18, 24]. Bruising caused by increased capillary fragility [6], spider veins and telangiectasia showing on the surface of the skin due to venous insufficiency are also observed in lipedema patients [4, 10].
\nAlthough, there is no cure for lipedema, treatments like liposuction (tumescent and water jet) [25], complete decongestive therapy that includes manual lymphatic drainage [26, 27], compression garments, a healthy diet, physical activity, medications and supplements (statins, selenium, diosmin, amphetamines and butcher’s broom) have been shown to reduce pain, improve lymphatic function, decrease leakage from blood vessels, lessen inflammation and fibrosis and maintain a healthy gut [24, 28, 29, 30, 31, 32, 33, 34].
\nLiposuction is by far the most effective treatment to decrease the fibrotic lipedema fat and thereby maintain mobility which is essential for the welfare of women living with lipedema [35, 36, 37]. Water jet-assisted liposuction has been proven to be as effective as tumescent liposuction. Damage to the lymph vessels has not been show as evidenced in a histological study conducted by Stutz et al. on lipoaspirates collected from lipedema patients [32]. Nevertheless, special care should be taken with lipo-lymphedema patients, where accumulated lymph and or fibrotic tissue should be removed first. Furthermore, follow-up and compression therapy are advised for successful and effective treatment.
\nDeep tissue massage has also been demonstrated to improve the quality of subcutaneous adipose tissue by decreasing pain, fibrosis and fat tissue in women with lipedema [29, 38].
\nAdditionally, a healthy non-inflammatory diet is highly recommended, even though it will not reduce the lipedema tissue, but it might slow the progression of the disease by reducing inflammation and pain, lessen the swelling and ultimately improve quality of life. No one plan works for everyone but a ketogenic diet with low processed carbohydrate and mild physical exercises like walking, swimming, Pilates, yoga and other home excise programs are suggested by lipedema specialists. These activates will help the function of lymphatic pump and maintain a normal metabolism.
\nFinally, it is very important to detect and treat lipedema at early stages thus preventing the complications that might occur due to the progression of disease. These complications comprise eating disorders, sleep apnea, diabetes mellitus, arthritis, hypertension, cellulitis, cardiac and renal disease.
\nThere are distinctive criteria for lipedema which are absent in lymphedema including a negative Stemmer’s sign, minimal pitting edema, thin skin, easy bruising, tenderness and pain [14, 39, 40]. Although lymphatic microaneurysms might develop in the later stages of lipedema leading to secondary lymphedema, imaging techniques like high-resolution cutaneous ultrasonography and magnetic resonance imaging showed no defects in the lymphatic system in early stages [24, 41, 42, 43]. Other methods have also been successfully used to differentiate lipedema from lymphedema which includes tissue dielectric constant and dual-energy X-ray absorptiometry techniques [44, 45, 46, 47, 48].
\nDysfunction of lymphatic vessels results in accumulation of interstitial fluid (edema) in adipose tissues triggering inflammation by the recruitment of macrophages resulting in fibrosis and difficulty with weight loss. As a consequence, adipose tissue loses its elasticity suggesting that lipedema might be a connective tissue disorder [15, 49]. Studies have also indicated that edema might induce growth of lipedema fat as well as hypoxia resulting in adipocyte cell death [50].
\nFurther, morphologic changes in lymphatic vessels and accumulation of interstitial fluid are present in some women with lipedema, with no change in transport of lymphatic fluid, which suggests these individuals might have a higher risk of progressing to lipo-lymphedema especially in advanced stages of lipedema [15, 51]. Accurate diagnosis of lipedema in association with lymphedema is essential for treating and following up of lipedema patients.
\nHormones, genetic factors, leaky blood vessels, dysfunctional lymphatics system, inflammation, hypertrophic adipocytes and interstitial thickening are among the factors that contribute to the pathogenesis of lipedema [10, 12, 15].
\nHormones play an essential role in the etiology of the lipedema, but how they affect the metabolism and function of adipocytes function is still unknown. Studies have shown that hormones, like estrogen and progesterone, have a direct effect on lipogenesis, insulin levels and adipose tissue distribution in the body. Dysregulation of hormonal levels lead to fat dysregulation, impairment of the lipogenesis-lipolysis mechanism, hypertension, insulin resistance and hyperinsulinemia [13, 52, 53]. Hormones might also have an impact on the nervous system which might explain the pain experienced by lipedema patients. Szél et al. hypothesized that alteration in estrogen (or estrogen receptors) maybe involved in the pathogenesis of lipedema by suggesting a link between accumulation of adipose tissue, imbalanced estrogen levels and inflammation of the peripheral and sympathetic nerves of the disease [13].
\nLipedema fat tissue is characterized by hypertrophic adipocytes, inflammatory immune cells, dilation of subdermal blood and lymphatic vessels. We and others have shown a high number of infiltrating macrophages in lipedema adipose tissue detected by the CD68 marker and observed as around blood vessels or as crown-like structures surrounding necrotic adipocytes. In addition to macrophages, mast cells and T-lymphocytes were detected in hyper-vascular areas mainly around blood vessels in lipedema fat tissue which might contribute to capillary permeability and accumulation of interstitial fluid [15, 16, 54].
\nAn article published in 2004 by Taylor et al. showed that accumulation of mast cells in lipedema tissue contributed to increased interstitial fluid, deterioration of adipocytes and potentially elastic fiber fragmentation due to the release of elastase [55], confirming that lipedema is a connective tissue disorder. Adding to that, direct cell-cell interaction between hypertrophic adipocyte and macrophages as well as secreted paracrine factors such as vascular endothelial growth factor (VEGF), a marker of angiogenesis, previously reported in the blood of women with lipedema [56] might be associated with increase in the number of blood vessels, dilation of capillaries, hypoxia, inflammation and tissue fibrosis found in lipedema patients [15, 18, 57].
\nAdipose tissue-derived stem cells are widely studied for their immunomodulatory, anti-inflammatory, anti-fibrotic, anti-apoptotic and pro-angiogenic effects [58, 59, 60], but how ASCs contribute to the development of lipedema has not been investigated yet. Due to their high therapeutic potential, ASCs are now considered an indispensable tool in regenerative medicine [61, 62, 63, 64]. Studies have shown the successful treatment with ASCs for many disease including graft-versus-host disease [65], wound healing [66], cardiovascular [67], inflammatory bowel disease [68], diabetes mellitus [69] and several injuries including kidney and spinal cord [70], bone and craniofacial reconstruction [71, 72], liver cirrhosis [73], multiple sclerosis [74]. In addition to their self-renewal ability, ASCs have the ability to differentiate into multiple lineages, including adipocytes, osteoblasts, chondrocytes, and endothelial cells [75, 76]. Thus, ASCs might play a role in lipedema adiposity by inducing the expansion and differentiation of progenitor adipose-derived stem/progenitor cells (pre-adipocytes) into mature adipocytes (hyperplasia). Suga el at. have shown an increase in proliferation of adipose-derived stem/progenitor cell proliferation using Ki67 and CD34 markers suggesting an increase in adipogenesis, hypoxia, and adipocyte necrosis, at least in one case [16].
\nAdding to that, inflammatory cytokines secreted by hypertrophic adipocytes and factors in the interstitial fluid could stimulate ASC differentiation into mature adipocytes. Alternatively, ASCs produce a plethora of pro- and anti-inflammatory cytokines that might contribute to angiogenesis and inflammation resulting in leaky and fragile blood vessels [77, 78]. Priglinger et al. have characterized lipedema ASCs isolated from liposuction samples and showed an increasing number of endothelial/pericytic cells using CD146 marker in lipedema patients compared to healthy individuals proposing that this increase might be a marker of repair of leaky blood and lymphatic vessels in lipedema tissues [54].
\nAlthough, ASCs might induce adipogenesis in lipedema an in-depth characterization of ASCs is required to confirm this theory. Otherwise, if ASCs prove to have anti-inflammatory, anti-fibrotic or pro-angiogenic effects, then they might be used to lessen tissue damage caused by leaky vessels; hence autologous treatment might be a promising tool for lipedema patients.
\nLipedema is a painful fat disease that should be differentiated from obesity and lymphedema. It is the responsibility of the healthcare provider to determine the accurate diagnosis of the disease for successful treatment and management. Liposuction, hands-on therapy, exercise, and a healthy eating plan are recommended for lipedema patients. Although the etiology of lipedema is complicated, hypertrophic adipocytes, inflammatory cytokines, and macrophages, hypoxia, leaky vessels and accumulation of interstitial fluid contribute to the pathogenesis of the disease and may also help guide treatment.
\nThis work was funded by a grant from the Lipedema Foundation.
\nThe authors declare no conflict of interest.
Heat flux is an important parameter to characterize heat transfer performance in many industrial applications, such as thermal protection of space shuttles [1], thermal management of electronic devices [2], metal heat treatment [3], maintenance of boilers [4] and nuclear reactors [5], spray cooling [6], geophysics [7], etc. Heat flux is often estimated by surface or internal temperature, which is also termed as inverse heat conduction problem (IHCP).
\nIHCPs are mathematically ill-posed, and a small error in temperature may significantly affect the accuracy of heat flux estimation [8, 9]. Several analytical and numerical methods have been proposed for the solution of IHCPs, such as sequential function specification (SFS) method, Tikhonov regularization (TR) method, transfer function (TF) method, Duhamel’s theory, etc. The SFS method is commonly used to solve IHCPs by minimizing the effect of random errors using temperature data at future time steps based on the least square method [10]. The TR method estimates all of the heat flux simultaneously for all time steps and is usually presented as whole time domain form, which often causes heavy computational load [11, 12]. The TF method analogizes the heat conduction problems to dynamic systems, in which heat flux is treated as the input of the system and the temperature profile as the response [13]. This method is simple in concept and one of the most accurate ways of estimating surface heat flux. However, it is relatively difficult to determine the analytic solution of the transfer function for the complex geometry problem. Duhamel’s theorem is based on the principle of superposition and assumes that the substrate thermal response at t equals the total sum of what the substrate experienced in small steps prior to t [14]. This method is simple and widely used in the surface heat flux estimation with known surface temperature. However, its assumption that the internal temperature equals to the surface one for indirect temperature measurement often causes significant calculation errors. Thus, Duhamel’s theory needs to be improved.
\nRecently, a filter solution based on TR has attracted the interest of many researchers [9, 15, 16, 17, 18, 19], which minimizes the sum of the squares of the errors between estimated and measured temperatures and stabilized by Tikhonov regularization. This solution is expressed in a digital filter form, allowing for a real-time heat flux estimation, and has been used for heat flux estimation of directional flame thermometer [20]. This method demonstrates superiority when solving IHCPs with a complex geometry. However, it can only be used to solve 1D single-layer IHCPs. The multidimensional, multilayer IHCP has yet to be solved.
\nAlthough IHCPs have been extensively investigated with regard to various other applications, little work has been conducted related to surface heat flux estimation during cryogen spray cooling (CSC) in laser dermatology. Spray cooling is widely applied in metallurgy, electronics, power plant, and laser dermatology for vascular skin lesions [21, 22, 23, 24, 25, 26, 27], because of the superiorities of high power density, ultrafast cooling rate, uniformity of heat removal, and low fluid inventory. In the laser treatment of vascular skin lesions (e.g., port wine stain, PWS), CSC can be implemented to prevent unwanted thermal damage of the epidermis induced by high laser absorption of melanin. Different with traditional steady spray cooling, CSC is a highly transient process with several tens of milliseconds to avoid cold injury. The transient surface heat flux is crucial for cooling performance evaluation, which needs accurate heat flux estimation method and rapid temperature measurement with fast response and small lag, as well as damping of algorithm [28].
\nIn transient CSC, two typical temperature measurements of fine thermocouple (FTC) and thin-film thermocouple (TFTC) are widely used to measure internal and surface temperature. Aguilar et al. [29] used the SFS method to estimate surface heat flux by internal temperature measured by a type-T FTC placed underneath a thin-layer aluminum foil, positioned on the top of epoxy resin surface to provide rapid heat transfer and mechanical support. Zhou et al. [28, 30, 31] measured time-dependent surface temperature by a type-T TFTC with thickness of 2 μm directly deposited onto the epoxy resin surface; this measurement accurately captured the temperature variation owing to its ultrafast thermal response (∼1.2 μs). Then, the surface heat flux was estimated by Duhamel’s theorem. However, TFTC cannot be used to measure the metal material temperature due to the electrical conductivity. Moreover, TFTC corrodes and oxidizes easily in high-temperature environments. Therefore, FTC measurement is widely used in many industries owing to its reliability and stability. Different with TFTC measurement with single-layer geometry, FTC measurement consists of three layers, namely, aluminum, thermal paste, and epoxy resin. Moreover, the radial and temporal surface temperature variations during CSC result in significant nonuniformity of the surface heat flux [14, 32]. Therefore, lateral heat transfer must be considered. For generality, 2D multilayer IHCPs need to be developed.
\nIn this chapter, the SFS, TF, and Duhamel’s theorem methods for TFTC and FTC measurements were compared based on one hypothetical heat flux. Duhamel’s theorem was improved to increase the accuracy of surface heat flux when using the indirect three-layer FTC measurement. Afterwards, the 2D filter solution was proposed to calculate the surface heat flux for 2D multilayer mediums. Six hypothetical triangular pulse heat fluxes were used to examine the accuracy and sensitivity of the algorithm. Finally, the 2D filter solution was employed to calculate the surface heat flux to investigate the cooling performance. Using estimated heat flux as evaluation index, the possibility of substituting the commercial cryogen R134a with high GWP (1430) by environment friendly cryogen with low GWP (<1) was discussed.
\nThe SFS method is widely used to solve IHCPs by minimizing the error between the measured temperature Yk\n and estimated temperature Tk\n for the current time and r future time steps based on the least square method [10]
\nSeveral functional forms of q(t) from tk\n to t\n\nk + r−1 have been proposed. The simplest one is that q(t) is a constant
\nThen, the temperature distribution is represented as a function of surface heat flux qk\n, and the temperature field is expanded in a Taylor series about a known value of surface heat flux \n
where Zi,k\n is the sensitivity coefficient defined by
\nThe solution for the estimated surface heat flux at time tk\n can be obtained by minimizing Eq. (1) with respect to qk\n:
\nThe values of r are selected based on the residual principle [33], which are Eqs. (3) and (4) for the direct and indirect temperature measurement methods, respectively. The detailed information about the SFS method can be found in previous publications [10, 34].
\nThe transfer functions establish the relationship between the input and output in a dynamic system, which can also be used to solve the linear heat conduction problems, where the heat flux is treated as the input of the system and the temperature is treated as the response [13].
\nThe estimated surface heat flux using Laplace transform can be described as
\nwhere θc\n(t) is the temperature allowance (θc\n(t) = Tc\n(t) − T\n0), the subscript c denotes the measurement position, the superscript* is the convolution integral operator, and T\n0 is the initial temperature. L\n−1[1/H(s)] is the Laplace inverse transform of the transfer function, which can be written as the function of time t, as follows:
\nSubstituting Eq. (7) into Eq. (6), q(t) becomes
\nAfter dispersing Eq. (8), it takes the following form:
\nAn assist question can be established to solve the temperature allowance θ assuming the boundary condition q(t) = 1. Substituting the numerical solution into Eq. (8), the surface heat flux q(t) can be obtained.
\nDuhamel’s theorem directly treated the measured internal temperature as the surface temperature of the substrate when using indirect FTC temperature measurement. A one-dimensional, direct heat conduction problem for the two surface temperature measurements can be solved to calculate the temperature distribution in the substrate [14, 35]:
\nwhere φ(x,t) is the temperature distribution response unit step function of the substrate and f(0) and T(τ) are the initial and time-varying surface temperature. The unit step function for a semi-infinite planar solid is [35].
\nSolving Eq. (10), the temperature gradient at the surface can be obtained:
\nThe simplification that the internal temperature equals the surface ones ignoring the heat dissipating capacity of the materials above the thermocouple, thereby often causing significant heat flux errors. Therefore, Duhamel’s theorem needs to be improved to deal with this problem, rather than directly estimate surface heat flux from the measured temperature data. Firstly, the real surface temperature is needed to be calculated from the internal measured temperature at x = c location, which can be expressed by a piecewise constant function of time as
\nwhere f is the surface temperature at the time of i·Δt. The temperature at x = c location can be solved by Duhamel’s theorem as [35].
\n\nEq. (14) can be written in expanded matrix form as
\nwhere Δφ(iΔt) represents φ(x, i·Δt)−φ (x, (i−1)·Δt). The surface temperature can be obtained by multiplying the inverse temperature transformation matrix on both sides of the equation from the measured internal temperature data. Afterwards, the surface heat flux can be estimated using Eq. (12).
\nTwo different methods were employed to measure the surface temperature during CSC. Figure 1 shows a schematic of the thin-film thermocouple (TFTC) and the fine thermocouple (FTC) measurements. The type-T TFTC with a thickness of 2 μm was directly deposited onto the epoxy resin surface using the magnetron technique. It has perfect contact with the underlying substrate and a fast response time (∼1 μs). The FTC measurement with a response time of 3.33 ms [36] consists of a fine type-T thermocouple (∼10 μm bead diameter) underneath a thin layer of aluminum foil (∼10 μm), which is positioned on the surface of the epoxy resin substrate (∼5 mm), as shown in Figure 1(b). The thermal paste with thickness of 100 μm is placed between the aluminum foil and the epoxy resin, ensuring good thermal contact and providing mechanical support.
\nSchematic of the TFTC and FTC measurements with single temperature sensor [28]: (a) TFTC measurement and (b) FTC measurement.
A hypothetical triangular pulse heat flux is commonly used to examine the accuracy and sensitivity to random noises of the algorithms [10, 13]. This given heat flux is first set as the surface boundary condition, and then the temperature adding random noise (ε = 1°C) at the measured point corresponding to the two different measurement methods is obtained by solving the direct heat conduction problem. New surface heat flux can be predicted based on the calculated temperature through different algorithms.
\n\nFigure 2 shows the new estimated heat fluxes using different algorithms with random noise using TFTC and FTC measurements. The heat fluxes calculated by Duhamel’s theorem, SFS, and the transfer function method all agreed well with the hypothetical ones using the TFTC measurement. When using FTC measurement (Figure 2(b)), the estimated heat flux obtained from Duhamel’s theorem and SFS methods changed nonlinearly over time. Furthermore, they can hardly match the exact heat flux well. Thus, they were unsuitable for estimating the surface heat flux in the indirect surface temperature measurement with FTC. In comparison, both the transfer function and improved Duhamel’s theorem can provide linear and accurate results that match the given heat flux exactly.
\nResults of the comparison between estimated heat fluxes (scatters) and hypothetical ones (solid lines) [28]. (a) single-layer IHCP with single TFTC and (b) three-layer IHCP with single FTC.
\nFigure 3 shows the variation in surface temperature as a function of time, measured by the direct measurement method with the TFTC and the indirect measurement method with FTC. The temperature first decreased rapidly when the R404A droplets impinge on the substrate surface, following a relatively slow change as the thin liquid film forms on the surface. It began to resume to the ambient temperature after the liquid film completely evaporated. It is notable that the surface temperature measured by the TFTC measurement decreased faster than that by the indirect FTC measurement method, which showed a definite delay.
\nVariations of surface temperature measured by TFTC and FTC measurements [28].
\nFigure 4(a) depicts the time-varied surface heat flux predicted by Duhamel’s theorem, SFS method, and transfer function method with TFTC measurement. It can be seen that all the three algorithms predicted very similar results. They first increased rapidly to their maximum values, then dropped quickly to a certain value (∼350 kW/m2), and finally gradually decreased to zero. Note that the estimated result by the SFS method increased faster and had a slightly greater maximum heat flux than that obtained by the other two algorithms.
\nVariations of surface heat flux predicted by different algorithms [28]. (a) TFTC measurement and (b) FTC measurement.
\nFigure 4(b) represents the heat flux predicted by different algorithms under the FTC measurement. As mentioned above, Duhamel’s theorem was inappropriate for predicting surface heat flux directly from internal measured temperature. Thus, the q\nmax and the magnitude of its increase rate by Duhamel’s theorem were both far lower than the case with other algorithms. It seems that the heat flux was significantly delayed and reduced. Other surface heat fluxes predicted by the transfer function and newly improved Duhamel’s theory had almost the same varying history, with a larger q\nmax than that predicted by the SFS method.
\nAlthough the TF and improved Duhamel’s theorem can accurately estimate the surface heat flux with multilayer mediums, it still failed to solve 2D IHCPs. Moreover, large nonuniformity radial and temporal surface temperature variations during CSC often occurred [14, 32]. Therefore, lateral heat transfer must be considered. The 2D algorithm for 2D multilayer medium is urgent to be developed. In this chapter, the 2D filter solution was proposed and validated based on the three-layer FTC temperature measurement.
\nThe 2D general model with K heat fluxes, J temperature sensors, and I layers is shown in Figure 5. The multiple surface heat fluxes are assumed to be uniform in a specific upper lateral surface area (e.g., 0 ≤ x ≤ x\n1). The temperature sensors are placed at the lateral midpoint of each uniform surface heat flux range in the ith layer, and the interval between two thermocouples is ∆x. All sensors are placed at an identical depth (y = H\nT) from the upper surface. The adiabatic boundary condition is considered on the three other sides (x = 0, x = W, and y = H). The initial temperature of the substrates is T\n0.
\nGeometry model of a 2D multilayer IHCP [36].
The discrete solution of temperature for direct heat conduction problems with K heat fluxes and J sensors can be presented in a matrix form as follows [37].
\nwhere T is the real temperature matrix, X is the sensitivity matrix, and q denotes multiple heat fluxes. The sensitivity matrix X is [19]
\nwhere
\nwhere N and n are total time steps and current time step. Excessive temperature ϕ can be presented as follows:
\nwhere t\nd is the time step. The sum of the squares of the errors between the estimated and measured temperatures plus one-order regularization, S, is
\nwhere Y is the measured temperature matrix. αt\n and αs\n are regularization parameters with respect to temporal and spatial terms. The superscript ‘denotes the transpose of a matrix. Ht and Hs are temporal and spatial regularization matrixes. Minimizing S, estimated heat flux matrix \n
Generally, the 2D multilayer IHCPs are solved layer by layer, starting from the ith layer with the known experimental measured temperature. The heat flux is estimated at the interface with the (i−1)th layer. Thereafter, the interface heat flux between the (i−1)th and (i−2)th layers can be calculated by using the known interface heat flux as the input. Finally, the surface heat flux is estimated [18]. The interface heat fluxes \n
Notably, X\ni\n is different from X in the solution of single-layer IHCP. X\ni\n is calculated by using (I − i + 1) layers below the ith layer. The estimated interface temperature \n
The interface heat fluxes (\n
where X\ni,d and X\ni,u have a similar form as the sensitivity matrix and X is for single-layer IHCP. However, excessive temperature ϕ in X is different. For X\ni,d, ϕ yields
\nFor X\ni,u, ϕ can be described as
\nBy substituting Eq. (23) into Eq. (25), the estimated interface heat flux is derived as
\nInterface heat flux \n
Given that most filter coefficients can be disregarded except for those of the (mp + mf + 1) time step, the solutions for IHCPs (Eqs. (22) and (28)) can be simplified into a general filter solution, thereby allowing the real-time heat flux monitoring and small computational load [8, 19, 38]:
\nwhere f\n\nk,m\n denotes the filter coefficient in the mth column from one row of F associated with the kth unknown heat flux. Notably, αt\n and αs\n significantly affect the accuracy of the estimated heat flux, which should be determined for a specific IHCP [9, 18, 19]. These parameters can be optimized by the optimal comparison criterion developed for solving 2D single-layer and multilayer IHCPs [36]. The sum of the squares of the errors, Rq, between the estimated and real heat fluxes was used to examine the accuracy of the calculation:
\nA more efficient means is to minimize the expected value of Rq [19, 38] as follows:
\nwhere E is the expected value, tr denotes the sum of the diagonal elements, and σY\n (0.01°C [38]) is the uniform measurement errors. E(Rq) contains two components: E\n\nq,bias\n:
\nand E\n\nq,rand\n in the filter form
\nTo examine the accuracy of the estimated heat fluxes, the mean relative error (MRE) between estimated and hypothetical heat fluxes was employed as follows:
\nThe 2D three-layer geometry (Figure 6) with six FTC sensors was used to validate the accuracy of surface heat flux estimated by 2D filter solution. For FTC measurement, the multiple surface heat fluxes were assumed to be uniform in a specific upper lateral surface area (e.g., 0 ≤ x ≤ x\n1) and different from each other. Temperature was measured from the spray center (x = 0 mm, TC1) to the periphery (x = 10 mm, TC6), and the lateral distance between two FTCs was ∆x = 2 mm. The geometry width with TFTC measurement was W = 11 mm, which is half that of the spray diameter because the computational domain is symmetric.
\nGeometry model of three-layer IHCP with six FTCs [36].
The optimal comparison criterion developed for 2D IHCPs was employed in this study to optimize the Tikhonov regularization parameters (αt\n and αs\n). As shown in Figure 7, logarithmic random component E\n\nq,rand\n increased as the regularization parameters αt\n and αs\n decreased. E\n\nq,bias\n and E(Rq) reached their minimum value at αt\n = αs\n = 10−9. Eventually, the optimum regularization parameters were determined to be αt\n = αs\n = 10−9.
\nGeometry model of three-layer IHCP with six FTCs [36].
As shown in Figure 8, the estimated heat fluxes agreed well with the hypothetical ones. However, small deviations were observed at the descent stage after the maximum heat flux for q\n1 to q\n6. The qMRE\n of q\n1–q\n6 for TFTC measurement was 2.63%, 2.66%, 2.76%, 2.78%, 3.00%, and 5.18%, respectively. Adding the random noise at the measured point, the maximum qMRE\n increased to 3.71%, which indicated that the accuracy and stability of the filter solution are satisfactory.
\nResults of the comparison between estimated heat fluxes (scatters) and hypothetical ones (solid lines) for three-layer IHCP with FTCs [36].
To investigate the importance considering lateral heat transfer, the estimated surface heat flux (Figure 9(a)) and simulated temperature (Figure 9(b)) using the estimated surface heat flux as boundary, calculated by 2D filter solution and 1D improved Duhamel’s theorem, were compared taking the example of 2D three-layer geometry with FTC measurement. For FTC measurement containing aluminum film with high heat conductivity coefficient (λ = 236 W∙m−1∙K−1), the maximum heat flux calculated by the 1D method is underestimated by 60% than that calculated by 2D filter solution, indicating that the lateral heat transfer cannot be disregarded, especially when the heat conductivity coefficient of the material is large. As shown in Figure 9(b), the simulated temperature using estimated surface heat flux as boundary calculated by 2D filter solution agreed well with measured temperature, indirectly indicating the accuracy of 2D filter solution. However, the large simulated temperature deviation was observed using 1D improved Duhamel’s theorem, owing to the inaccurate estimated surface heat flux disregarding lateral heat transfer.
\nComparative results at spray center calculated by 2D filter solution and 1D improved Duhamel’s theorem [36]. (a) surface heat flux and (b) temperature at sensor location.
The dynamic internal temperature measured by six FTCs with ∆t = 50 ms and L = 30 mm is depicted in Figure 10(a). The temperature histories were similar, but differences existed in the specific values. The minimum temperatures (T\nmin) at r = 0, 2, 4, 6, 8, and 10 mm were −43.42, −36.13, −29.55, −28.22, −27.32, and −22.45°C, respectively. Additionally, the measured temperature was lower at the spray center (r = 0 mm) than periphery. Figure 10(b) presents the estimated heat fluxes calculated by the filter solution for 2D three-layer IHCP with FTC measurement. The estimated heat flux profiles at different locations in this figure were also similar. However, a large difference was observed in heat fluxes at different lateral locations. The best cooling capacity was found at the spray center (r = 0–2 mm).
\nVariations of surface temperature and heat flux with FTC measurement [36]. (a) measured surface temperature and (b) estimated surface heat flux.
The extremely high global warming potential (GWP = 1430) of commercially used cryogen R134a with boiling point of −26.1°C will cause severe environmental hazards, and the substitution of R134a in clinical application is urgent. R1234yf with boiling point of −29.5°C may be a potential candidate for environment protection due to its low GWP (<1). In this chapter, the clinical potential of R1234yf substitution for R134a was investigated.
\nUsing the maximum surface heat flux correlation obtained by experimental spray characteristics (droplet temperature, velocity, and diameter) and surface heat transfer performance (surface heat flux calculated by 2D filter solution), Figure 11(a) shows the variations of effective surface heat flux with different R134a and R1234yf as a function of spray distance. The effective surface heat flux (qe\n) was obtained by multiplying the maximum surface heat flux, and cooling concentration within the radius of 2 mm is the interested area [39]. The effective surface heat flux by using R134a and R1234yf increased firstly due to the droplet temperature reduction as spray distance increased. Then, qe\n reaches their maximum value and finally decreases slowly. The maximum qe\n of R134a and R1234yf is 262.1 and 225.8 kW/m2 at the optimal spray distances of 25.6 and 25.1 mm (see Figure 11(a)), respectively. The substitution of R1234yf for R134a can produce remarkable reduction of global warming potential to <1. However, the cooling capacity should be enhanced for the clinical application in laser treatment, owing to the 13.8% reduction in effective heat flux (from 262.1 to 225.8 kW/m2). Therefore, the enhancement of cooling capacity is necessary for the implementation of R1234yf in clinical laser treatment of PWS.
\nVariations of effective surface heat flux as a function of spray distance [39]. (a) effective surface heat flux with R134a and R1234yf and (b) effective surface heat flux before and after cooling enhancement with R1234yf.
According to our experience, two simple ways are available to enhance the cooling capacity, i.e., changing the nozzle diameter and decreasing the back pressure by decreasing the boiling point of cryogens [40, 41]. As shown in Figure 11(b), the enhancement of effective surface heat flux at different spray distances was remarkable. After reducing the nozzle diameter and decreasing the back pressure, qe\n increases rapidly due to violent evaporation, and the peak value of the effective heat flux (268.3 kW/m2) is increased by 18.8%. This result is comparable with that of R134a under 1 atm, which proves the potential of R1234yf in the clinic CSC for the laser treatment of PWS.
\nSeveral algorithms including the SFS, TF, and Duhamel’s theorem methods were analyzed and compared in predicting time-varying surface heat flux during CSC. Duhamel’s theorem was improved to get the accurate results through the transformation of internal temperature into surface temperature, when the indirect surface temperature measurement (FTC) method is used. A hypothetical triangular pulse heat flux was employed to analyze the accuracy and sensitivity to noise of the algorithms under TFTC and FTC measurements. The estimated result of Duhamel’s theorem and SFS method widely deviated from the given heat flux under the three-layer FTC measurement method, whereas the transfer function and improved Duhamel’s theorem all provided the exact estimated heat flux.
\nThe 2D filter solution was proposed to solve a general 2D multilayer IHCP for the estimation of surface heat flux. An optimal comparison criterion was employed to optimize the key parameters, namely, αt\n and αs\n. Six hypothetical triangular heat fluxes and random temperature errors of 1°C were employed to analyze the accuracy and sensitivity of the filter solution for 2D three-layer IHCPs with FTC measurement. The qMRE\n values for FTC measurement with and without the random temperature errors were all within the acceptable range, which validates the good accuracy and stability of the filter solutions. The maximum heat flux calculated by the 1D method was underestimated by 60% than that calculated by 2D filter solution considering lateral heat transfer. The 2D filter solution was more accurate than the 1D method. Moreover, lateral heat transfer should not be ignored, especially when the heat conductivity coefficient of the material is large.
\nThe surface heat transfer characteristics of spray cooling with R134a and R1234yf were investigated based on 2D filter solution. The maximum effective heat fluxes q\n\ne,max were 262.1 and 225.8 kW/m2 for R134a and R1234yf at different spray distances of 25.6 and 25.1 mm. Through the cooling enhancement of reducing the nozzle diameter and decreasing the back pressure, q\n\ne,max of R1234yf was increased by 18.8% (D = 0.4 mm and Pb\n = 0.04 MPa). The enhanced q\n\ne,max is a bit higher than that of R134a in normal condition, which provides a theoretical basis for potential application of low GWP R1234yf in clinics.
\nThis work was supported by the National Natural Science Foundation of China (51727811) and Fundamental Research Funds for the Central Universities.
\nThe authors declare no conflict of interest.
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