\n\n
\\n\\n
Released this past November, the list is based on data collected from the Web of Science and highlights some of the world’s most influential scientific minds by naming the researchers whose publications over the previous decade have included a high number of Highly Cited Papers placing them among the top 1% most-cited.
\\n\\nWe wish to congratulate all of the researchers named and especially our authors on this amazing accomplishment! We are happy and proud to share in their success!
Note: Edited in March 2021
\\n"}]',published:!0,mainMedia:null},components:[{type:"htmlEditorComponent",content:'IntechOpen is proud to announce that 191 of our authors have made the Clarivate™ Highly Cited Researchers List for 2020, ranking them among the top 1% most-cited.
\n\nThroughout the years, the list has named a total of 261 IntechOpen authors as Highly Cited. Of those researchers, 69 have been featured on the list multiple times.
\n\n\n\nReleased this past November, the list is based on data collected from the Web of Science and highlights some of the world’s most influential scientific minds by naming the researchers whose publications over the previous decade have included a high number of Highly Cited Papers placing them among the top 1% most-cited.
\n\nWe wish to congratulate all of the researchers named and especially our authors on this amazing accomplishment! We are happy and proud to share in their success!
Note: Edited in March 2021
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The contents of the book will be written by multiple authors and edited by experts in the field.",isbn:"978-1-78985-492-3",printIsbn:"978-1-78985-491-6",pdfIsbn:null,doi:null,price:0,priceEur:0,priceUsd:0,slug:null,numberOfPages:0,isOpenForSubmission:!1,hash:"839705a75a74ec1ee60f481628d59046",bookSignature:"",publishedDate:null,coverURL:"https://cdn.intechopen.com/books/images_new/8795.jpg",keywords:null,numberOfDownloads:null,numberOfWosCitations:0,numberOfCrossrefCitations:null,numberOfDimensionsCitations:null,numberOfTotalCitations:null,isAvailableForWebshopOrdering:!0,dateEndFirstStepPublish:"July 11th 2018",dateEndSecondStepPublish:"August 1st 2018",dateEndThirdStepPublish:"September 30th 2018",dateEndFourthStepPublish:"December 19th 2018",dateEndFifthStepPublish:"February 17th 2019",remainingDaysToSecondStep:"3 years",secondStepPassed:!0,currentStepOfPublishingProcess:1,editedByType:null,kuFlag:!1,biosketch:null,coeditorOneBiosketch:null,coeditorTwoBiosketch:null,coeditorThreeBiosketch:null,coeditorFourBiosketch:null,coeditorFiveBiosketch:null,editors:null,coeditorOne:null,coeditorTwo:null,coeditorThree:null,coeditorFour:null,coeditorFive:null,topics:[{id:"5",title:"Agricultural and Biological Sciences",slug:"agricultural-and-biological-sciences"}],chapters:null,productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"},personalPublishingAssistant:null},relatedBooks:[{type:"book",id:"6418",title:"Hyperspectral Imaging in Agriculture, Food and Environment",subtitle:null,isOpenForSubmission:!1,hash:"9005c36534a5dc065577a011aea13d4d",slug:"hyperspectral-imaging-in-agriculture-food-and-environment",bookSignature:"Alejandro Isabel Luna Maldonado, Humberto Rodríguez Fuentes and Juan Antonio Vidales Contreras",coverURL:"https://cdn.intechopen.com/books/images_new/6418.jpg",editedByType:"Edited by",editors:[{id:"105774",title:"Prof.",name:"Alejandro Isabel",surname:"Luna Maldonado",slug:"alejandro-isabel-luna-maldonado",fullName:"Alejandro Isabel Luna Maldonado"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"1591",title:"Infrared Spectroscopy",subtitle:"Materials Science, Engineering and Technology",isOpenForSubmission:!1,hash:"99b4b7b71a8caeb693ed762b40b017f4",slug:"infrared-spectroscopy-materials-science-engineering-and-technology",bookSignature:"Theophile Theophanides",coverURL:"https://cdn.intechopen.com/books/images_new/1591.jpg",editedByType:"Edited by",editors:[{id:"37194",title:"Dr.",name:"Theophanides",surname:"Theophile",slug:"theophanides-theophile",fullName:"Theophanides Theophile"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"3161",title:"Frontiers in Guided Wave Optics and Optoelectronics",subtitle:null,isOpenForSubmission:!1,hash:"deb44e9c99f82bbce1083abea743146c",slug:"frontiers-in-guided-wave-optics-and-optoelectronics",bookSignature:"Bishnu Pal",coverURL:"https://cdn.intechopen.com/books/images_new/3161.jpg",editedByType:"Edited by",editors:[{id:"4782",title:"Prof.",name:"Bishnu",surname:"Pal",slug:"bishnu-pal",fullName:"Bishnu Pal"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"3092",title:"Anopheles mosquitoes",subtitle:"New insights into malaria vectors",isOpenForSubmission:!1,hash:"c9e622485316d5e296288bf24d2b0d64",slug:"anopheles-mosquitoes-new-insights-into-malaria-vectors",bookSignature:"Sylvie Manguin",coverURL:"https://cdn.intechopen.com/books/images_new/3092.jpg",editedByType:"Edited by",editors:[{id:"50017",title:"Prof.",name:"Sylvie",surname:"Manguin",slug:"sylvie-manguin",fullName:"Sylvie Manguin"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"371",title:"Abiotic Stress in Plants",subtitle:"Mechanisms and Adaptations",isOpenForSubmission:!1,hash:"588466f487e307619849d72389178a74",slug:"abiotic-stress-in-plants-mechanisms-and-adaptations",bookSignature:"Arun Shanker and B. 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Then the research was extended to ordinary Sparre-Andersen renewal risk models where the inter-claim times have other distributions than the exponential distribution. Dickson and Hipp [1, 2] considered the Erlang-2 distribution, Li and Garrido [3] the Erlang-n distribution, Gerber and Shiu [4] the generalized Erlang-n distribution (a sum of n independent exponential distributions with different scale parameters) and Li and Garrido [5] looked into the Coxian class distributions. One difficulty with these models is that we have to assume that a claim occurs at time 0, which is not the case in usual setting.
\nAlbrecher and Teugels [6] considered modeling dependence with the use of an arbitrary copula. In a similar dependence model to Albrecher and Teugels as well, Asimit and Badescu [7] considered a constant force of interest and heavy tailed claim amounts.
\nBarges et al. [8] followed the idea of Albrecher and Teugels [6] and supposed that the dependence is introduced by a copula, the Farlie-Gumbel-Morgenstern (GGM) copula, between a claim inter-arrival time and its subsequent claim amount.
\nAdékambi and Dziwa [9] and Adékambi [10] provide a direct point of extension but assuming that the claim counting process to follow an unknown general distribution in a framework of dependence with random force of interest to calculate the first two moments of the present value of aggregate random cash flows or random dividends.
\nThe discounted aggregate sum has also been applied in many other fields. For example, it can be used in health cost modeling, see Govorun and Latouche [11], Adékambi [12], or in reliability, in civil engineering, see Van Noortwijk and Frangopol [13].
\nThe delayed or modified renewal risk model solves this problem by assuming that the time until the first claim has a different distribution than the rest of the inter-claim times. Not much research has been done for this model at this stage. Among the first works was Willmot [14] where a mixture of a “generalized equilibrium” distribution and an exponential distribution is considered for the distribution of the time until the first claim. Special cases of the model include the stationary renewal risk model and the delayed renewal risk model with the time until the first claim exponentially distributed. Our focus is to extend the work of Bargès et al. [8], Adékambi and Dziwa [9] and Adékambi [10] by allowing the counting process to follow a delay renewal risk process and thus derive a recursive formula of the moments of this subsequent Discounted Compound Delay Poisson Risk Value (DCDPRV).
\nFor example, young performer companies typically have a high growth rate at the beginning, but as they mature their growth rate may decrease with the increasing scarcity of investment opportunities. That makes dividends dependent on the economic climate at the dividend occurrence time. Obviously the distribution of inter-dividends time in times of economic expansion and in times of economic crisis cannot be identically distributed. So it would be appropriate to use a delayed renewal model to model the distribution of the inter-dividend time. A delayed renewal process is just like an ordinary renewal process, except that the first arrival time is allowed to have a different distribution than the other inter-dividends times.
\nThe chapter is organized as follows: In the second section, we present the model of the continuous time discounted compound delay-Poisson risk process that we use and give some notation. In Section 3, we present a general formula for all the moments of the DCDPRV process. A numerical example of the first two moments will then follow in Section 4.
\nWe use the same model as the one in Bargès et al. [8], where the instantaneous interest rate \n
Define our risk model as follows:
The number of claims \n
the positive claim occurrence times are given by \n
the positive claim inter-arrival times are given by \n
\n\n
The \n
\n\n
\n\n
The discounted aggregate value at time \n
where \n
We introduce a specific structure of dependence based on the Farlie-Gumbel-Morgenstern (FGM) copula. The advantage of using the FGM copula and its generalizations lies in its mathematical manageability. The joint cumulative distribution function (c.d.f.) of \n
for \n
for \n
where \n
With these hypotheses, we present in Section 3 recursive formula of the higher moments of this present value risk process, for a constant instantaneous interest rate.
\nIt is often easier to calculate the moments of the random variable \n
The mathematical expectation of total claims plays an important role in the determination of the pure premium, in addition to giving a measure of the central tendency of its distribution. The moments centered at the average of order 2, 3 and 4 are the other moments usually considered because they usually give a good indication of the pace of distribution, and these give us respectively a measure of the dispersion of the distribution around its mean, a measure of the asymmetry and flattening of the distribution considered.
\nMoments, whether simple, joined or conditional, may eventually be used to construct approximations of the distribution of the DCDPRV.
\nThe Laplace transform of the
where
\n\n
Conditioning on the arrival of the first claim leads to
\nWe have
\nWe let,
\nsuch that the above equation becomes
\nLet us \n
where \n
We consider the case where the canonical random variable \n
That is, we have:
\nThe
Taking the Laplace transform of the above equation, we get:
\nBut,
\nThen the Laplace transform of \n
Substituting Eq. (14) into Eq. (13), we have:
\nSolving the above equation for the ordinary case, where \n
Rearranging the above equation, we will get
\nThe first moment of \n
\n
From Theorem 3.1, we have:
\nFrom Bargès et al. [8], we have
\nSubstituting Eq. (22) into Eq. (21), yields
\nwith
\nSubstituting Eqs. (24), (25), (26) and (27) into Eq. (23), yields:
\nRearranging the above equation, will give
\nIf \n
which is exactly the result of Bargès et al. [8].
\nThe inverse of the Laplace transform in Eq. (29) will give
\nIf \n
which is exactly the result of Léveillé et al. [15].
\nIf \n
which is exactly the result of Bargès et al. [8].
\nIf \n
which is exactly the result of Léveillé et al. [15].
\nThe second moment of \n
The result in Theorem 3.1 when \n
From Bargès et al. [8], we have.
\nand
\nSubstituting Eqs. (39) and (40) into Eq. (38), yields:
\nand rearranging Eq. (38), will give:
\nwhich can be simplified to
\nwith,
\nWhen
\nwhich is exactly the result of Bargès et al. [8].
\nThe Laplace transform in Eq. (49), is a combination of terms of the form:
\nwith \n
\n\n
Since the inverse Laplace transform of \n
Using Eq. (49) in Eq. (53), it results that
\nwhere \n
If \n
\n
Then,
\nTo finally have:
\nwhich is exactly the result of Léveillé et al.[15].
\nIf \n
\n\n
Then,
\nwhich is exactly the result of Bargès et al. [8].
\nIf \n
which is exactly the result of Léveillé et al. [15].
\nNoting for \n
We can rewrite \n
The term \n
where \n
and
\nFor the numerical illustration, suppose that \n
\n\n | \n\n\n | \n\n\n | \n\n\n | \n
---|---|---|---|
−1 | \n482.3375 | \n4450 | \n16,428 | \n
0 | \n438.1057 | \n4407.1 | \n16,385 | \n
1 | \n393.874 | \n4364.2 | \n16,342 | \n
\n\n
\n\n | \n\n\n | \n\n\n | \n\n\n | \n
---|---|---|---|
−1 | \n597.1633 | \n4578.7 | \n16,557 | \n
0 | \n554.5237 | \n4535.5 | \n16,513 | \n
1 | \n511.8841 | \n4492.3 | \n16,470 | \n
\n\n
\n\n | \n\n\n | \n\n\n | \n\n\n | \n
---|---|---|---|
−1 | \n33900.85 | \n29646.71 | \n7928.481 | \n
0 | \n23972.65 | \n20976.12 | \n5711.548 | \n
1 | \n359.8795 | \n1036.223 | \n1542.412 | \n
\n\n
\n\n | \n\n\n | \n\n\n | \n\n\n | \n
---|---|---|---|
−1 | \n34027.1 | \n29756.44 | \n7954.606 | \n
0 | \n24061.85 | \n21053.72 | \n5731.564 | \n
1 | \n366.1484 | \n1035.491 | \n1545.671 | \n
\n\n
\n\n
From the results in Section 4.1, we can compute the premium related to the risk of an insurance portfolio represented by \n
The loading for the risk differs according to the premium calculation principles.
\nDenote by \n
where \n
Denote by \n
where \n
Denote by \n
where \n
The standard deviation principle defines the loaded premium as:
\nwhere \n
In this case, the safety loading \n
The principles of standard deviation and variance only require partial information on the distribution of the random variable, \n
Often, the actuary only has this information for different reasons (time constraints, information …).
\nIf the actuary has more information about the random variable, \n
But he does not know much about \n
We have derived exact expressions for all the moments of the DCDPRV process using renewal arguments, again disproving the popular belief that renewal techniques cannot be applied in the presence of economic factors. Our results, for the DCDPRV process, are consistent: (i) with the results of Léveillé et al. [15] for \n
Within this framework, further research is needed to get exact expressions (or approximations) of certain functional of the \n
Our models have applications in reinsurance, house insurance and car insurance. They can also be used in evaluation of health programs, finance, and other areas.
\nFor example, consider the case of a male currently aged 25 who is starting a defined contribution (DC) pension plan and is planning to retire in, say, 40 years at the age of 65. He anticipates that when he reaches that age he will convert his accumulated pension fund into a life annuity in order to hedge his own longevity risk and avoid outliving his own financial resources. The value of his retirement income will depend not only on the value of his pension fund, but also on the price of annuities at the time. Other things being equal, this means that his retirement income prospects will be affected by the distribution on future annuity value: the greater the dispersion of that distribution, the riskier his retirement income will be. For the assessment of the accumulated pension fund and its variability our models can be used. We can suppose that this man makes a deposit to a bank account, and that the time between successive deposits follows a renewal process and the force of interest is stochastic. Our model allows us to calculate the accumulated pension fund and its variability at the age of 65.
\nAnother possible application is in reliability, to model the net present value of aggregate equipment failures costs until its total breakdown. A piece of equipment is deemed to be beyond repair when the repair time exceeds a predetermined gap. Of course, another possible definition of total breakdown is when the cost of repair exceeds a predetermined gap. But, since the cost of repair is defined per unit time, the two definitions are somewhat equivalent.
\nProsthetics are artificial substitutes for body parts lost through congenital defects, injury (accident or combat-related) or disease. These devices can be worn on the outside of the body or surgically implanted and are made of a variety of materials that may serve a cosmetic and/or functional purpose. They have evolved from simple fiber-based appendages (ancient Egypt) to the sophisticated lower limb “blades” and bionic arms that enable amputees to transcend barriers to their activities. Prosthetics today are strong and light, made of aluminum, plastic or composite materials that are better molded to the patient limb. Furthermore, the advent of microprocessors, computer chips and robotic technology provide a range of motion that fits the lifestyle choices of the amputee.
Achieving a comfortable and functional connection between an amputee and their prosthetic limb is critical to the success of the prosthesis. Therefore, the socket system is the most significant component for overall success of the prosthesis [1, 2]. Plaster wraps or computer aided designs are the primary means to custom fit sockets to maximize socket performance and comfort without adversely affecting residual limb health (Figure 1). Currently, the lack of quantitative feedback to determine appropriate socket fit is a major drawback in this process. Prosthetists use anecdotal visual cues combined with subjective verbal feedback from patients to minimize suspension-dependent movement between the socket and residual limb. This subjective information is used to revise socket parameters such as volume, geometry, and type of suspension to provide a “best” fit for the amputee. In day-to-day living, the volume of mature residual limb (>18 months postamputation [3]) are subject to short-term [4] and long-term [5, 6] changes in volume that compromise socket fit and performance.
(A) Prosthetists use a scanning device to digitize limb shape. (B) Digital model is modified to create a positive mold for socket fabrication tailored to the residual limb. (C) Tissue injury as a result of using a pin-locking suspension system. (D) Injury healed once the amputee was fit and began wearing an elevated vacuum suspension socket (EVS).
More than 80% of amputations in the U.S. are the result of complications from vascular disease and diabetes [7, 8]. Less than 10% of lower-limb amputation results from trauma [9]. In the US, among those that live with a lower-limb amputation, a growing number of which are Service men and women [10, 11, 12], the limb volume changes adversely affect fit, performance, and residual limb health [6]—including skin breakdown and ulceration [13] (Figure 1) that can require surgical revision of the amputation. The requirement for surgical revision is known to be as high as 30% [14]. This review primarily focuses on skin health in the residual lower limb and the need for objective monitoring and evaluation of changes at the interface of the biological entity (limb skin) and the artificial entity (prosthetic limb) for sustained optimal limb health. Similar issues could apply to the residual upper limb.
There are two main types of prosthetics that replace a partial or complete loss of the lower limb and these include: (a) below the knee or transtibial (TT), where a prosthetic lower leg is attached to an intact residual upper limb, (b) above the knee or transfemoral (TF), where a prosthesis replaces the upper and lower leg and knee. Each of these types of prostheses is composed of key parts: the prosthetic limb, a socket (interface between the biological component (e.g., patients’ body) and the artificial limb), the attachments and the control system.
The piece that interfaces between the residual limb/body part and the artificial limb is called the socket and is typically molded around a plaster cast taken from the residual limb. A range of suspension systems are available for use on amputees and the choice of socket primarily depends on subjective information obtained by the prosthetist. The fit of a socket has to be precise or the artificial limb may cause discomfort or tissue damage resulting in the inability to wear the prosthesis for a time and leading to surgical interventions.
The most common systems in use are pin/shuttle lock, suction, and vacuum. The pin/lock system uses a padded liner with a pin on the end which is inserted into a shuttle lock built into the bottom of the connecting socket. A modification of this system is the lanyard, which connects the socket to the liner and limits shear and rotation. The suction system has a soft liner, a one-way valve and a sealing valve. Suction enables even adhesion to the interior surface of the socket and lowers the friction and shear. The vacuum system actively creates a seal around the socket and liner and enhances the adhesion of the limb to the socket, thereby regulating residual limb volume changes and promoting better circulation and reduced shear. The pin-lock is most popular but is associated with issues such as bell clapping (lateral displacement), pistoning (vertical displacement) (Figure 2) and distal tissue stretching (milking) which result in complications such as gait asymmetry, skin sores, and stump pain at the distal end. Suction and vacuum systems help minimize these complications and are currently popular (~95%) among Service Members and veterans with limb loss.
Classification of residual limb movement within the socket. The timing and waveform profile are distinct in each of these types of movements.
The importance of the socket/limb interface has been highlighted in several published reports. The primary concerns reported from prosthesis users include the fit of the artificial limb and comfort. A study by Klute et al., identified that the time-consuming prosthesis fitting process can contribute to excess pressure and friction on the residual limb, resulting in skin and deeper tissue damage and related pain and discomfort [15]. The outcome of this study emphasized the need for a fitting process that included objective measures to complement and improve user feedback.
Several studies employing radiological [15, 16, 17], acoustic [18], and optical [19] approaches have been used to analyze the movement of the residual limb within the socket of lower limb systems. These have numerous shortcomings primarily related to lack of clinical translatability and testing capability in a limited range of movements. The LimbLogic® vacuum system developed as a result of a Veterans Affairs (VA) grant funded collaborative work with Ohio Willow Wood was commercialized for clinically relevant quantification of prosthetic socket performance. Elevated vacuum suspension (EVS) [20, 21] (Figure 3) creates subatmospheric pressure between the prosthetic socket and liner worn over the residual limb. Studies performed with this system identified that variances among individuals may be a result of different gait styles, tissue types, residual limb geometries, prosthesis weight distribution, and socket fit. The results demonstrated that elevated vacuum pressure data provide information to quantify initial socket fit and monitor changes from an initial set point. The correlation between displacement and vacuum pressure fluctuation was dependent on socket fit. In general, higher vacuum pressure settings resulted in the lower amounts of displacement and vacuum pressure fluctuation within each socket fit condition. However, the rates of decreases created distinct trends in the data that correlated to particular fit conditions.
Elevated vacuum suspension schematic and probe measurement points. (A) Illustration of test socket with recess for in-socket silicone probe holder. (B) Residual-limb measurement sites. Green and yellow indicate measurement sites of high and low stress, respectively. LDF = laser Doppler flowmetry, TCOM = transcutaneous oxygen measurement (reprinted with permission from Rink et al. [
Therefore, the effectiveness of lower limb prosthesis is largely measured by its ability to minimize in-socket movement of the residual limb, conserving residuum health. Movement of the residual limb within the prosthetic socket contributes to increased risk of skin ulceration [22]. Technological advancements in residual limb scanning and socket manufacturing have empowered prosthetists to design and fit customized sockets that account for unique amputee residual limb shape and volume. However, unlike the rigid socket that is fixed in geometry and volume, the morphometry of the residual limb is dynamic. Mature residual limbs experience diurnal changes in volume of up to 2% [4] because of a number of factors including activity level, ambient environment, body composition, dietary habits, and hormones [6]. Furthermore, chronic remodeling of a mature residual limb can result in even greater (~10%) volume changes over the course of weeks [23] and months [5]. Thus, socket fit and residual limb movement in the socket are subject to time-dependent changes. Because socket movement increases risk of residuum dermal injury and ulceration [22], there is a clear need to evaluate the efficacy of using a socket monitoring system that can quantify residual limb movement inside the socket to aid in the socket fitting process. Such a system has the potential of minimizing risk to residual limb health [6] while maximizing functional performance.
Achieving a comfortable and functional connection between an amputee and their prosthetic limb is critical to the success of the prosthesis. Therefore, the socket system is the most significant component for the overall rehabilitative success of the prosthesis [24, 25]. Socket comfort is achieved by appropriately loading and off-loading the residual limb, where the optimal biomechanical performance of the prosthesis is achieved by transfer motions of the residual limb without loss or excess motion to the prosthesis. In an effort to maximize socket performance and comfort without adversely affecting residual limb health, a prosthetist custom fits a socket for every patient using plaster wraps or computer aided design. Currently, this process suffers from a lack of quantitative feedback to determine appropriate socket fit. Prosthetists aim to create a comfortable and intimate socket interface, but current approaches are limited as they rely on anecdotal visual cues along with subjective verbal feedback from the patient. Prosthetists then use this information to revise socket parameters such as volume, geometry, and type of suspension to provide a “best” fit for a patient.
In light of the subjective inputs that currently inform prosthesis form, fit, and therefore function, there is a clear need to provide objective measures to optimize prosthesis fitting and provide continual feedback to both end-user and prosthetist as the residual limb volume and shape are susceptible to change over time. Under the current paradigm of prosthetic socket fitting, inadequate and/or misinformation communicated to the prosthetist can lead to sub-optimal fit and comfort of the prosthetic system. This contributes to repeat clinical visits to rectify areas of discomfort, or in more extreme cases rejection of the prosthesis and preference toward other assistive devices such as wheelchairs. Two surveys administered to lower limb prosthesis users indicated a high prevalence of skin sores or irritation occurring within the socket, with fit likely being a contributing factor [24, 25]. If left unresolved, such limb health issues may necessitate disuse of the prosthesis.
Most amputees have an active and satisfying quality of life with a majority that wear a prosthesis at least 7 h a day to aid in mobility and everyday living. An improper fit or alignment, lack of adequate gait training and development of poor habits are common features of a vast majority of amputees who use a prosthesis resulting in at least one deviation or problem. The increased load or weight is often placed on the intact limb as a result of these deviations can cause discomfort or pain in the joints and lead to some form of degenerative joint disease or disability in extreme cases. Three of the most common secondary complications in lower-limb amputees due to compensatory and/or altered stresses are osteoarthritis, osteoporosis and back pain.
About 75% of patients with lower-limb prosthetics have skin problems [26, 27]. The lack of a normal pressure-distributing anatomy the residual limb is prone to issues such as elevated shear forces, stress risers, increased humidity, and prolonged moist contact within the prosthesis, which can contribute to ulceration. Ulcers or pressure sores, are the most common skin conditions in prosthetic users [24] and can vary in size and magnitude requiring prolonged recovery time out of the prosthesis, a new socket fitting and sometimes surgical interventions [26, 27].
Skin ulcers are typically the end result of vascular insufficiency and improper skin barrier function. Reperfusion of blood, as seen in reactive hyperemia, to nutrient- and oxygen-deprived tissue is another causative factor of tissue injury that contributes to ulcer formation [28]. In lower-limb amputation, this was identified as a complication of prosthesis use in the early 1960s [29]. Key among the factors to monitor in attempting to preserve and promote residual limb health would be maintenance of skin barrier function, perfusion and oxygenation.
There are few examples of evidence based research related to the effect of socket systems, particularly elevated vacuum suspension systems on limb health [30, 31, 32]. A recent study was the first to directly test the effect of EVS on residual-limb skin health and blood flow [20]. This study used a standardized non-invasive imaging (Figures 4–7) approach with a combination of out-of-socket imaging (e.g., hyperspectral imaging, transepidermal water loss (TEWL) and surface electrical capacitance (SEC)) and in-socket imaging (e.g., transcutaneous oximetry (TCOM), laser Doppler flowmetry (LDF)) [20, 33]. Outcomes of this study identified that elevated vacuum suspension socket systems promote better residual limb skin physiology by preserving the skin barrier function (TEWL measurements), rescuing against loss of tissue oxygenation during activity and attenuating reactive hyperemia. Customized test sockets for people with TT and TF amputations with embedded in-socket silicone probe holder (Figures 3 and 8) housed perfusion (LDF) and tissue oxygen (TCOM) measurement probes and enabled multiple temporal measurements from the same sites to be taken in study without the individual probes interfering with one another.
Laser speckle imaging (LSI) for skin perfusion. (A) Black box over transtibial amputee represents field of view (FOV) for perfusion mapping and quantification. (B) Representative perfusion maps acquired pre- and post-activity (over-ground walking) in sound and residual limb. (C) Perfusion was measured by laser Doppler flowmetry out-of-socket with liner on (O) and in-socket while resting with weight bearing on the residual limb (I) under SoC (black bar) and EVS (white bar) conditions. Data are mean perfusion units ± SE (shown as error bar). *p<0.05 O vs I within gp at time point (reprinted with permission from Rink CL et al. [
Hyperspectral imaging for skin oxygen saturation. (A) Black box represents field of view (FOV) for qualification of tissue oxygen saturation (StO2) in residual limb. (B) Representative oxygen saturation map. (C) Reactive hyperemia quantified as percent changed in tissue oxygen saturation pre- and postactivity was determined in standard of care (SoC) (black bar) and EVS (white bar) socket systems at baseline and after 16 weeks of use (final). Data are mean ± SE (shown in error bar), *p < 0.05 SoC vs. EVS (reprinted with permission from Rink et al. [
Transepidermal water loss (TEWL) for skin barrier function. (A) Schematic of TEWL probe over the skin as it measures differences between relative humidity of ambient air and directly above skin. (B) Photograph of a TEWL measurement. (C) TEWL was measured 15 min after socket doffing in people with transtibial and transfemoral amputation (n = 10) under standard of care (SoC) (black bar) and EVS (white bar) conditions. Data shown are from areas of high stress and low stress combined. Data shown are from areas of high stress and low stress combined. Data are mean ± SE (shown as error bars). *p < 0.05 SoC vs. EVS within time point. †p<0.05 baseline vs. final within prosthesis group (reprinted with permission from Rink et al. [
Surface electrical capacitance for skin hydration. (A) Close-up view of SEC probe. Photograph of SEC measurement collection from a subject. SEC measurements from (B) transtibial and (C) transfermoral subjects immediately after liner removal and after equilibration with air for 15 min (reprinted with permission from Rink et al. [
Silicone gel probe holder for in-liner measurement. (A) Temperature, transcutaneous oxygen measurement (TCOM) wand laser Doppler flowmetry (LDF) probes were embedded in a silicone gel insert to enable real-time measurement of limb temperature, oxygenation, and perfusion respectively. (B) Placement of probes on residual limb of transtibial participant. Oxygen permeable TegadermTM was used to adhere the TCOM probe to the limb. (C) The silicone gel insert enabled reproducible placement and spacing of probes and buffered against the liner from pressing probes tightly against skin (reprinted with permission from Rink et al. [
Residual limb skin health is a key determinant of quality of life for individuals with lower limb amputation. Skin health problems, caused by shear forces and stress to the residual limb, are known to affect the ability of individuals with lower limb loss to perform household tasks, use their prosthesis, engage in social functions, and participate in sports. Therefore, objective measures to during socket fitting combined with real-time monitoring of skin physiological parameters such as barrier function, hydration and perfusion are likely to provide a better fitting and functional artificial limb for long-term use.
The authors acknowledge grant funding from the United States Department of Defense (DoD) Congressionally Directed Medical Research Programs (CDMRP) grant award W81XWH-16-2-0059.
The authors declare no conflict of interest.