Evaluating post-mortem changes in skin hydration for post-mortem
interval estimation
Jeltje M.A. van Esch, LLM
10626786
MSc in Forensic Science, University of Amsterdam
August 15, 2016
Research project Master Forensic Science, 36 EC
Academic Medical Centre, Department of Biomedical Engineering and Physics
January 28
th– July 25
thSupervisor: dr. A.J. Riordan
Examiner:
Prof. dr. M.C.G. Aalders
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Evaluating post-mortem changes in skin hydration for post-mortem interval
estimation
J.M.A. van Esch, A.J. Riordan, M.C.G. Aalders
Department of Biomedical Engineering and Physics, Academic Medical Centre Amsterdam, The Netherlands Master of Forensic Science, University of Amsterdam
Selected Journal: Forensic Science International
Abstract
Changes in the water volume fraction in skin after death might provide information about the post-mortem interval and can be used when there is no longer the possibility of using the body temperature for post-mortem interval estimation. Transmission based near infrared spectroscopy was used to measure the absorption of near-infrared light in skin, at 1475nm and 1540nm. The absorption at these wavelengths is mainly due to the presence of water in skin and can be used to determine the water volume fraction of skin. This is determined on the basis of the Lambert-Beer Law, modified with a differential pathlength factor and a loss factor as a function of the reduced scattering coefficient and optical losses. Optimization and validation of the study was performed by skin fold measurements and phantom measurements. Skin biopsies of human cadaver skin as well as pig skin were used to measure and track the change in skin hydration after death. Biopsies from human cadaver skin were taken on the day the body arrived and 24 hours later, at three body sites; on the upward facing front side (chest) and back. The pig skin rested in a fume hood at room temperature over 6 and 12 days, and biopsies were taken throughout this duration. In total, four human cadavers were measured and two pig skin studies were performed. Minimal changes were observed in the human cadaver skin during the 24 hour measuring range. Dehydration was observed over time in the pig skin at 1-4 days, followed by hydration again as the skin decayed. The accuracy of the transmission based near infrared spectroscopy measurement has to be improved for future applications.
Contents 1. Introduction ... 2 2. Theoretical background ... 2 2.1 Skin characteristics ... 2 2.2 Post-mortem processes ... 3 2.3 Physics ... 3
2.3.1 Optical properties of skin ... 3
2.3.2 NIR spectroscopy ... 4
2.1.3 Lambert-Beer Law ... 4
3. Materials & Methods ... 5
3.1 NIR spectroscopy set-up ... 5
3.2 Phantom studies ... 5
3.3 Human cadaver studies ... 5
3.4 Pig skin studies ... 6
3.5 Data analysis ... 6
4. Results ... 7
4.1 Optimization of the NIR spectroscopy set-up and measuring method ... 7
4.2 Zemax simulations ... 7
4.3 Phantom studies ... 7
4.4 Human cadaver measurements ... 8
4.5 Pig skin measurements ... 9
5. Discussion ... 10
5.1 Zemax simulations ... 10
5.2 Phantom studies ... 10
5.3 Human cadaver measurements ... 10
5.4 Pig skin measurements ... 11
6. Conclusion ... 11
7. References ... 12
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1. IntroductionWhen a body is found and it is thought to be an unnatural death, the post-mortem interval (PMI) may contribute in getting clarity about the cause of death. The PMI can be of importance for the police to include or exclude possible suspects. Research into the estimation of the time of death, and thus the PMI, is therefore of great importance in forensic science.
Multiple methods exists to estimate the PMI. Factors such as livor mortis, rigor mortis and changes in the eyes occur during the early post-mortem interval, but are highly variable. According to Jackson & Jackson [1], the body temperature ‘represents the best measure available’ for the estimation of the time of death in the first 18 hours after death, using the nomogram of Henssge as the golden standard for these calculations [2].
Nonetheless, there is a lack of reliable methods for PMI estimation when there is no longer a possibility to use the body temperature for PMI estimation. This can either be due to the adjustment of the body to the environment temperature or because the environment is too complex (i.e. temperature changes etc.) A feature which gives the possibility of reliably estimating the PMI over a longer period, would thus be of great use.
The stages of decomposition of the human body have been described in literature. One of these stages is the decomposition of skin [3,4], and several studies have been performed with this focus. Histological research has shown that skin starts to degrade within the first 48 hours after death [5–7] . Previous research into the function of skin has shown that the outermost layer (stratum corneum) plays an important role in the skin barrier function [8]. When the skin barrier is disrupted the amount of water loss increases. Applied to forensic science, it can be imagined that the skin will degrade over time and that the skin barrier falls apart, causing the skin to dehydrate and the water volume fraction of skin to decrease over time. Subsequently, due to the fluids descending in the body by gravity, an increase in water may be expected at the bottom of the body and thereby an increase in the ratio of the water volume fraction of skin at the top of the body compared to the bottom of the body. If it can be found that this is the case, the post-mortem change of skin hydration over time may add a novel feature to apply in PMI estimation.
To the best of our knowledge, no research has been performed into quantitatively determining the water volume fraction of skin over time, post-mortem. Therefore, the objectives of this study are to:
1. Measure the water volume fraction of skin (up to the dermis) using near infrared spectroscopy;
2. Gain more insight into the process of dehydration of skin after death, using near infrared spectroscopy;
3. Investigate whether the water volume fraction of skin changes over time, post-mortem;
4. Investigate whether the change in skin hydration post-mortem can be used to estimate the post-mortem interval.
To measure and follow the post-mortem change of skin hydration over time, transmission based near infrared (NIR) spectroscopy is used. This technique allows us to quantitatively estimate the water volume fraction of skin, making use of the optical properties of skin and a method which is based on the law of Lambert-Beer. Phantoms which mimic the optical properties and characteristics of skin as close as possible, are used for the validation and optimization of the measurement technique and method, as well as living human subjects and skin biopsies of human cadavers and pigs.
In the next section the theoretical background will be explained further, explaining the skin characteristics and post-mortem processes as well as the physics behind the method used.
2. Theoretical background
2.1 Skin characteristics
Skin consists of several layers (Fig. 1). The stratum corneum, forming the skin barrier, is the upper layer with dead flattened cells. The stratum corneum is part of the epidermis which is about 100-200μm thick. Below, the dermis is located, which is 1-4mm thick and lastly there is the subcutaneous fat layer, which is of 1-6 mm thickness [9].
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The volume fraction of water in these layers varies,from 15% in the upper layer up to 60-80% in the epidermis and dermis [8,11–16]. Additionally, the thickness of these layers, the epidermis, dermis as well as the subcutaneous fat layer, varies a lot among individuals and body locations [17–20].
To research the skin, human skin or skin models can be used. Intralipid is a commonly used skin phantom model simulating the optical properties of biological tissue [21–24], since it contains similar light absorption and scattering characteristics to tissue. Troy et al. (2013) mentions that 2 vol% intralipid mimics the skin most accurately, which is therefore the phantom used for this current study. Besides the use of phantoms, animal skin can be used as well. Pig skin is the most comparable to human skin. Similar to human skin, there are differences among locations, and the rostral back is said to mimic human skin closely [25–29].
2.2 Post-mortem processes
Several studies have been performed into the decomposition of human skin using histology [5,6].
Kovarik [6] studied the ‘gross and microscopic appearance’ of skin in the early post-mortem interval in a cool environment temperature (3-25°C). Skin biopsies of three individuals were taken at four different sites during one week. Subtle changes of dermal degeneration were observed in all individuals at the second day. Separation of the dermal/epidermal junction was observed later on, at day 4, 6 and 7.
Bardale [5] studied 30 human cadavers in a warmer environment temperature (23-27°C). Skin samples were taken in the first 24 hours after death. Already after 6-9 hours a focal degeneration of the dermis was observed. At 12-18 hours of the post-mortem interval a separation of the epidermis/dermis could be determined and approximately 18 hours after death the dermis started to disintegrate.
Doukas [7] performed research into skin viability [30] after death, i.e., the presence of living cells. They used fluorescein diactate (FDA), which is converted into fluorescein by living cells, and ethidium bromide (EB), which can only enter a dead cell. He states that the skin viability decreases dramatically between 18 and 48h post-mortem.
Based on the histology and fluorescence, it can be concluded that the skin starts to degrade over time post-mortem. This implies that a post-mortem change in the water volume fraction of skin may be observed as well.
2.3 Physics
2.3.1 Optical properties of skin
The manner in which light interacts and travels through tissue, depends on multiple factors. The absorption and scattering of light are the main factors to be considered [9,31–35].
Absorption causes light to lose intensity when travelling through skin due to photon interactions with the molecules that make up the skin, such as water [32]. All the constituents present in skin have a characteristic absorption spectrum that defines how much intensity light of a specific wavelength will lose when traveling a specific distance through the substance [33]. In skin, multiple constituents exist, such as blood, fat, collagen and water. Since this study aims to gain insight into the process of dehydration of skin, especially water will be discussed.
In the absorption spectrum of water, a peak is present at 1440nm (Fig. 2). Around this wavelength the absorption in tissue is almost entirely due to water; although there may be other absorbing elements at this wavelength, their contribution to the loss of light intensity is so small it can be neglected. From this spectrum the absorption coefficient (𝜇𝑎(𝜆)
in mm-1) can be determined per wavelength.
Fig. 2. Absorption spectrum of water, from Hale & Querry (1973) [36]
Scattering also determines how light will behave in skin, and is dependent on the anisotropy (𝑔) of tissue [37]. Scattering will cause a photon to change direction, mainly due to interaction with collagen and other cells present in skin [9]. Consequently, some photons will not be able to hit the detector and will be lost, while other photons may have travelled a longer distance compared to the ones travelling straight through the tissue. The scattering coefficient (𝜇𝑠) defines the probability of a scattering event.
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which light will be scattered. When a medium has a𝑔-value of 1, there will be forward-directed scattering. With a 𝑔-value of -1 the scattering will be in the backward-direction. Skin has a high 𝑔-value (>0.9), and therefore mainly forward scattering is present. Putting these variables together, gives us the reduced scattering coefficient (µ𝑠’):
µ𝑠’ = (1 − 𝑔)𝜇𝑠 (1.1)
2.3.2 NIR spectroscopy
The optical properties of skin, the absorption coefficient and the reduced scattering coefficient, are of importance when measuring skin samples with NIR-spectroscopy. In the current study, the tissue is illuminated with a 1475nm laser, which is a wavelength close to the absorption peak of water, and with a 1540nm laser. The absorption of light at these wavelengths is mainly due to water present in the skin. Zang et al. [38] and Verdier-Sévrain & Bonté [8] have already introduced NIR spectroscopy as a new method for measuring the absorption of NIR light by water in living tissue. Zang et al. [38] compared the NIR imaging technique to visual assessment of the state of skin hydration as well as electrical methods and concluded that the NIR technique was more consistent and was shown to be a better tool for the assessment of skin hydration. However, both these studies used only reflection based NIR spectroscopy which limits the penetration depth of light into the skin. Therefore, transmission based NIR spectroscopy is used for this study, which gives the possibility to measure through all the skin layers, since the light transmitted through the tissue will be measured, instead of the light reflected back.
2.1.3 Lambert-Beer Law
To quantify the amount of water present in skin, a formula adjusted from the Lambert-Beer Law is used:
𝐼(𝜆) = 𝐼0(𝜆) ∙ 𝑒−𝑑(𝑓𝑣∙𝜇𝑎(𝜆)·𝑑𝑝𝑓(𝜆,𝜇𝑠 ′)+𝑙𝑓 (𝜇
𝑠′(𝜆),𝑜𝑔) ) (1.2)
The fraction of light that is detected by a photodiode, 𝐼(𝜆), depends on the initial amount of light which illuminated the tissue, 𝐼0(𝜆). Secondly,
since the light will be absorbed per unit length, the fraction of light reaching the detector depends on the distance it has to travel in the skin, 𝑑; on the volume fraction of water (𝑓𝑣), the absorption coefficient of
water, 𝜇𝑎(𝜆) and on the differential pathlength
factor, 𝑑𝑝𝑓(𝜆, 𝜇𝑠′) which is a ‘scaling factor for how
many times farther than 𝑑 the detected light has travelled’ [39] and is expressed as a function of the reduced scattering coefficient (𝜇𝑠′). Furthermore, it
depends on the loss factor 𝑙𝑓(𝜆) as a function of the reduced scattering coefficient, 𝜇𝑠′(𝜆) and losses due
to the optics and geometry of the system (𝑜𝑔). The losses due to the optics and geometry of the system are still unknown. However, when measuring at two wavelengths the losses due to the optics and geometry will cancel out. When measuring at one wavelength the assumption can be made that the majority of the losses are caused by the reduced scattering coefficient since the transmitting and receiving fibre both have a low numerical aperture and measurements are performed at small distances between these fibres. To calculate the volume fraction of water (𝑓𝑣)
we derive an expression for 𝑓𝑣 from formula 1.2 (see
Appendix I). The intensity of light coming through the tissue 𝐼(𝜆, 𝑑), is measured over increasing distances (Δ𝑑). This will result in an exponential drop-off in intensity of the light. Using the logarithmic version of formula 1.2, gives a linear drop-off in the light coming through tissue, Δ ln(𝐼(𝜆)). This results in the following: Δ ln(𝐼(𝜆)) = −Δ𝑑(𝑓𝑣∙ 𝜇𝑎(𝜆) · 𝑑𝑝𝑓(𝜆,𝜇𝑠′) + 𝑙𝑓 (𝜇𝑠′(𝜆), 𝑜𝑔)) (1.3) A decay-factor (𝐷𝐹), defined as 𝐷𝐹 = Δln (𝐼(𝜆)) 𝛥𝑑 , can be determined: −(𝑓𝑣∙ 𝜇𝑎(𝜆) · 𝑑𝑝𝑓(𝜆, 𝜇𝑠′) + 𝑙𝑓 (𝜇𝑠′(𝜆), 𝑜𝑔)) = 𝐷𝐹 (1.4)
From equation 1.4 a formula for the water volume fraction in skin can be derived, using one wavelength. Additionally a formula for the water volume fraction in skin can be derived when two wavelengths are combined, since we are measuring on 1475nm as well as on 1540nm. The derivation can be found in Appendix I. This gives the following formulas: One wavelength: 𝑓𝑣𝑤𝑎𝑡𝑒𝑟= −𝐷𝐹 − 𝑙𝑓 (𝜇𝑠′(𝜆),𝑜𝑔) 𝜇𝑎(𝜆)·𝑑𝑝𝑓(𝜆,𝜇𝑠′) (1.5) Two wavelengths: 𝑓𝑣𝑤𝑎𝑡𝑒𝑟= 𝐷𝐹2−𝐷𝐹1−𝜇𝑠′(𝜆1)(1−0.97) 𝜇𝑎(𝜆1)·𝑑𝑝𝑓(𝜆1,𝜇𝑠′1)−𝜇𝑎(𝜆2)·𝑑𝑝𝑓(𝜆2,𝜇𝑠′2) (1.6) These formulas (1.5 & 1.6) can be used to calculate the water volume fraction in skin, by measuring the absorption of light at two wavelengths and without knowing the exact value of scattering. This will be explained further in section 3.5.
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3. Materials & Methods3.1 NIR spectroscopy set-up
The transmission measurements of this study are performed using near infrared spectroscopy, illuminating the tissue with light at 1475nm and 1540nm. A ‘1-to-4 fan-out fibre’ (Ø 0.6 mm, NA 0.39, Thorlabs) connected to a single core fibre (Ø 1.5 mm, NA 0.50, Thorlabs) is used to illuminate the tissue; the transmitted light will travel through a single core fibre (Ø 1.5mm, NA 0.50, Thorlabs) to reach the photodiode for detection. The tissue to be measured is placed between these fibres (Fig. 3). The distance between the fibres, and thus the thickness of the tissue the transmitted light travels through, is measured and registered by MINISCALE (Schneeberger; resolution 1µm, accuracy < +/- 4µm). An AFE4404 device and AFE4404 EVM GUI software (Texas Instruments) are used to register and evaluate the detected light of both wavelengths by the photodiode. The lasers are switched rapidly (133Hz) so that the photodiode can isolate one wavelength at a time.
Fig. 3. Optical set-up. A: picture of the real set-up. B: 3D picture from the Zemax optical simulation suite, the blue lines visible in the tissue represent the pathlengths of the photons of light.
Several changes were made to reach the optimal set-up for the measurements. The distance between the two fibres can be changed using a turning wheel, giving the possibility to change the distance up to 1µm accurately. A drop of index
matching fluid (with an index of refraction (1.46) equal to the glass in the core of the fibre) is placed on the laser tip of the fibres before measuring to realise full optical contact between the tissue and the fibres, without any air present to cause discontinuity and reflection of light at the interfaces. 3.2 Phantom studies
Intralipid® 20% (Fresinius kabi) was used as a liquid phantom for validation of the method. Intralipid® 20% contains 22.7 vol% intralipid and 77.3 vol% H2O [40]. According to literature, 2%
intralipid is a suitable phantom, mimicking skin at wavelengths lower than 1900nm [21]. It should have similar characteristics compared to human skin and therefore we should be able to measure a water volume fraction of approximately 98%.
For these measurements, a dilution series was made of Intralipid® 20% and demi water, corresponding to concentrations of respectively 1.99, 2.27, 3.405 and 4.54 vol% intralipid. The protocol can be found in Appendix II.
3.3 Human cadaver studies
Permission was received from the department of anatomy and embryology of the Academic Medical Centre in Amsterdam, to perform studies on human cadavers received via their body donation programme. The protocols which received permission can be found in Appendix III.
Four human cadavers were measured. In total six skin biopsies were taken per day, using an 8mm disposable biopsy punch (Kai medical). One biopsy was taken per body site, namely the chest, belly and upper leg at the front and back sites of the body, see Fig. 4.
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The subcutaneous fat layer was cut away and thebiopsies were placed in small petri dishes to be weighed on a microbalance (Mettler AJ50). Thereafter, the biopsies were placed in between the fibres from the optical set-up (Fig. 3) and the light transmission was measured along seven distances using increments of 0.025 mm, mainly between 1.5 and 3.5 mm, depending on the thickness of the biopsy. The different distances were achieved by very slightly squeezing the biopsy between the fibres. Biopsies were taken on the first day the body arrived in the mortuary as well as on the second day, 24 hours later. Between measurements the body rested in a fridge at a temperature of approximately 4°C. The skin biopsies were kept in the fume hood at room temperature, under constant air flow (20-22°C, 52-56% humidity; measured on a Cresta thermos-hygro sensor). The weight loss of the skin biopsies was followed until a stable weight was achieved. It is assumed that the weight loss corresponds to the evaporation of water, and thus the water volume fraction present in the biopsy. This should be close to the water volume fraction measured with the NIR spectroscopy set-up.
The measurement protocol can be found in Appendix IV and an example of the weight measurement in Appendix V.
3.4 Pig skin studies
Since the human cadavers could only be measured over 24 hours and the supply of cadavers was minimal, pig skin was used additionally to investigate the dehydration of skin over time.
Pig skin was received from the surgical laboratory of the Academic Medical Centre. Biopsies were taken from the skin while it was resting in a fume hood for dehydration. At several time points multiple biopsies were taken. The biopsies were weighed first and then measured using the optical set-up, according to the measurement protocol found in Appendix VI.
Two studies were performed. In the first study the skin (Fig. 5) was wrapped in cling film with a square cut out on top (next to the skin) to ensure the tissue would dry via the skin. This tissue was measured over 6 days at five time-points, taking three biopsies at once per time-point. For the second study the skin was placed on a sponge (Fig. 5), to allow the fluids the possibility of draining down and away from the skin. The sponge together with the tissue was wrapped in cling film, leaving a square cut out to allow dehydration. This tissue was measured over 12 days, taking 3 or 4 biopsies at once, once a day. During the measurement period, the tissue was resting in the hood, at room temperature and constant air flow (20-22°C, 52-56%
humidity; measured on a Cresta thermos-hygro sensor).
Fig. 5. Pig skin studies. Above: pig skin study 1, below: pig skin study 2
3.5 Data analysis
To process the data, MatLab has been used. The MatLab scripts written for the data analysis can be found in Appendix VII.
Simulations were performed with Zemax optical simulation suite to investigate the effect of different reduced scattering coefficients, 𝜇𝑠′(𝜆), on the
differential pathlength factor, 𝑑𝑝𝑓(𝜆). This has been simulated for five distances, respectively 1.5, 2, 2.5, 3, and 3.5mm thickness. For every thickness a relationship is established between the 𝜇𝑠′(𝜆) and
𝑑𝑝𝑓(𝜆). These simulations were done in a manner very similar to a Monte-Carlo calculation.
Measuring at two different wavelengths gives the opportunity to find the correct 𝜇𝑠′(𝜆) to plug into
the loss factor. In the formula with two wavelengths (1.6), the 𝜇𝑠′(𝜆) will almost cancel out, meaning that
the estimation from the water volume fraction will be independent of the initial guess of the reduced scattering coefficient. Using a wrong initial guess will therefore not majorly influence the value of the water volume fraction. However, when using the one wavelength formula (1.5), the 𝜇𝑠′(𝜆) will not cancel
out. Ideally, applying this one wavelength formula on the data of both wavelengths, should give similar outcomes for the water volume fraction, and should also be identical to the outcome of the combined two wavelength formula (1.6), if the guess for the amount of scattering is correct. Unfortunately, the scattering in skin changes significantly at different locations. Every skin sample has its own reduced scattering coefficient and thus we cannot use one value for the reduced scattering coefficient for all data analysis. Therefore, an iteration has been performed for every skin sample, using the formula for the two single wavelengths, to find a 𝜇𝑠′(𝜆) which
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gives identical outcomes. This 𝜇𝑠′(𝜆) issubsequently used to approximate the related 𝑑𝑝𝑓(𝜆). The calculation is repeated until an optimum is achieved. An example of the iteration procedure on raw data can be found in Appendix VIII.
Data containing intensities below 0.020 volt were excluded, as well as data with an R-squared value below 0.999 for the exponential fit between the intensities reached over the multiple distances.
4. Results
4.1 Optimization of the NIR spectroscopy set-up and measuring method
It was confirmed that the change in amplification is linear to the change in voltage coming from the photodiode, and that measuring over several distances gives an exponential drop-off in voltage (Appendix IX).
To optimize the measuring method, skin fold measurements were performed on volunteers. Multiple measurements were taken using the skin flap between the thumb and index finger. The best measurement direction was found to be from a lower to a higher distance to ensure fluids are not pushed away during the measurements. It was decided to increase the distances by increments of 0.025 mm to minimise the effect of pressure changes on the scattering properties of the tissue. Much variation was present in the measurements despite the changes in the set-up and measurement method. Due to the lack of control over the thickness of the skin and subcutaneous fat layer, the major result from the optimization of the method was to measure skin biopsies instead of skin folds, which gives us the opportunity to cut away the fat layer.
The process of optimizing the set-up and measuring method and the data from these measurements can be found in Appendix X.
4.2 Zemax simulations
Zemax simulations were performed to estimate the distance travelled through tissue by the photons that have been scattered and the effect of the presence of water as absorbing medium. An intensity vs. pathlength distribution was generated (Fig. 6). It can be observed that the pathlength travelled by the photons is longer compared to the intital distance between the fibres (3mm). A differential pathlength factor is thus present.
A second simulation was performed to test the effect of different reduced scattering coefficients on the differential pathlength factor. For a tissue thickness of 2mm, the result is shown in Fig. 7 on the next page. The graphs for the remaining tissue thicknesses are added in Appendix XI. Table 1 shows the formulas resulting from these graphs; these are used for the data analysis to find the related 𝑑𝑝𝑓(𝜆) given the 𝜇𝑠′(𝜆) obtained from the
iteration.
4.3 Phantom studies
Intralipid® 20% contains 22.7 vol% intralipid and 77.3 vol% H2O [40]. A dilution series of
respectively 1.99, 2.27, 3.405 and 4.54 vol% Intralipid was measured, completed with a measurement of the stock solution itself, Intralipid® 20%. Fig. 8A shows the vol% Intralipid against the obtained decay factor. Fig. 8B shows the linear relationship between the first four data points.
Fig. 6. Intensity distribution. No absorption present (blue line), absorption due to the presence of 60% water (green line). A: one y-axis. B: two y-axis, 60% water on the right axis. Transparent medium, 𝜇𝑠′(𝜆): 1.35(1475nm) and 1.31 (1540nm), tissue thickness: 3mm.
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Fig. 7. Reduced scattering coefficient vs. differential pathlengthfactor. Tissue thickness: 2mm
Table 1. Formulas to approximate the related differential pathlength factor by a given reduced scattering coefficient (x), for a specific distance.
Thickness (mm) Formula 1475nm Formula 1540nm 1.5 0.0502x + 0.9883 0.0510x + 0.9883 2.0 0.0884x + 0.9697 0.1342x + 0.9364 2.5 0.0899x + 0.9761 0.1744x + 0.9159 3.0 0.1271x + 0.9722 0.1127x + 0.9745 3.5 0.1059x + 0.9885 0.0942x + 0.9998
Fig. 8. Vol% Intralipid vs. decay factor. A: all data points. B: linear relationship between the first four data points
4.4 Human cadaver measurements
Table 2 shows an overview of the human cadavers measured.
Table 2.Overview measured human cadavers
# Sex Age Time of
death Time of first measurement 1 Male 61 yr 17:45h 05-04-2016 15:25h 06-04-2016 2 Female 99 yr 02:45h 19-04-2016 11:30h 19-04-2016 3 Male 79 yr 03:45h 11-05-2016 10:30h 11-05-2016 4 Female 94 yr 12:30h 06-07-2016 11:30h 07-07-2016
Fig. 9 shows the results of the NIR spectroscopy measurements compared to the amount of water loss due to weight loss of the biopsies, taken at the body’s arrival (day 1) and 24 hours later (day 2). It can be seen that the best correlation between the NIR spectroscopy measurements and the weight measurements is gained in subject 3. For the other subjects a lot of variation is present.
Fig. 10 shows the results of biopsies taken from human cadaver legs, buried in taphonomic ground for two months. Two biopsies have been taken from the top of the leg, and two from the bottom of the leg.
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Fig. 9. Human cadaver measurements. Four subjects were measured. Graph A-D represent subject 1-4. The blue bars aremeasurements of day 1, the yellow bars measurements of day2.
Fig. 10. Human cadaver leg measurements. Four biopsies taken, two of the back side and two of the front side of the leg.
4.5 Pig skin measurements
Fig. 11A shows the result from the first pig skin study performed. A drop-down in water volume fraction was seen during the first day, the water volume fraction went up again slightly during the last days. The trend in the NIR spectroscopy
measurements is similar to the trend in weight loss measurements.
The result from the second pig skin study is shown in Fig. 11B.A lot of variation is present in the NIR spectroscopy measurement. However, the measurement does follow the same trend as the weight loss measurement.
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Fig. 11. Pig skin measurements. Change in water volume fraction over time; measurements by NIR spectroscopy and weight loss. A: study 1, measured over 6 days at five time-points; the average and standard deviation over three biopsies taken simultaneously are shown. B: study 2, measured over 12 days at 11 time-points.5. Discussion
5.1 Zemax simulations
The intensity distribution obtained from the Zemax simulations shows that scattering causes the pathlength of the photons in skin to be longer than the distance between the fibres (Fig. 6). This simulation is performed for a tissue thickness of 3mm. At the maximum intensity peak, the detected rays travel approximately 3.5mm, which indicates therefore that a differential pathlength factor is present. However, the differential pathlength factor is related to the reduced scattering coefficient of the tissue (Fig. 7). Measuring two wavelengths allows us to find the best reduced scattering coefficient via an iteration procedure, from which the result can be used to approximate the related differential pathlength factor. Using this method makes it possible to perform the calculations without knowing the exact value of the reduced scattering coefficient.
Besides the presence of the differential pathlength factor, it can also be noted that absorption due to the presence of water is causing a drop in intensity and a decrease in the amounts of longer pathlengths and therefore a decrease in the differential pathlength factor (Fig. 6B).
5.2 Phantom studies
The method was validated with use of Intralipid® 20% as a phantom. The iteration method has not been used for the calculations. This method makes use of the results from the Zemax simulation, which uses the 𝑔-value of skin. The 𝑔-value for intralipid is a lot lower compared to skin [41], causing the right 𝜇𝑠′(𝜆) and 𝑑𝑝𝑓(𝜆) not to be found using this
method. Nevertheless, different volume percentages of intralipid were measured, and a change in slope was expected. Fig. 8 shows a linear relationship between the first four data points of the graph. The last data point, representing pure Intralipid® 20% doesn’t match with this linear relationship, which can be explained by the presence of much more dependent scattering in pure Intralipid® 20% [40].
When the calculation is performed without the presence of the 𝜇𝑠′(𝜆) and 𝑑𝑝𝑓(𝜆), values of 99.75
and 99.36% are obtained. Because the 𝜇𝑠′(𝜆) and
𝑑𝑝𝑓(𝜆) are not taken into account in the calculation, these water volume fractions are overestimated and thus do not reach the expected 98.01 and 97.73%. However, the difference between these values comes close to what it should be and together with the difference in slopes between the intralipid measurements it can be said that the NIR spectroscopy set-up is able to measure the differences in water volume fractions.
5.3 Human cadaver measurements
Four human cadavers were studied over 24 hours. For none of the subjects clear differences are visible between the days and between the top and bottom of the body. It can therefore be stated that the measurement range of 24 hours is too small to see any differences. The first two subjects should be excluded. The biopsies taken from the first subject (Fig. 9A) were not well executed which resulted in messy measurements. The belly of day 1 and back leg of day 2 from the NIR spectroscopy measurements are excluded due to a low R-squared value (<0.999), considered unreliable, of the
11
exponential relationship between the distance andintensity or low intensity value (<0.020). The NIR spectroscopy measurement of the back chest of day 2 was negative and is therefore not displayed in the figure, this is due to the fact that it reaches the exclusion criteria because of a too low R-squared value.
The second subject measured (Fig. 9B) was a women of 99 years old and had a very thin skin, which forced us to measure the biopsies including the fat layer. For this subject three NIR spectroscopy measurements were excluded based on a too low R-squared value or intensity value, namely the leg of day 2 and the back chest of day 1. Again The NIR spectroscopy measurement of the back chest of day 2 was negative and is therefore not displayed in the figure, due to the fact that it reaches the exclusion criteria because of a too low R-squared value.
The third subject (Fig. 9C) was the first subject where neat biopsies with a thick enough skin layer could be taken. Sufficiently high R-squared values were reached for the NIR spectroscopy measurement (>0.9998). The data that should be excluded based on a too low R-squared value or too low intensity value are the back belly of day 1 and the chest and belly of day 2. A good agreement between the NIR spectroscopy measurements and the weight measurements is present as well as a trend for the leg, where the water volume fraction at day 2 is lower compared to day 1. All the other locations stayed about the same over the two days.
The last subject measured (Fig. 9D), also had a thin skin. Therefore not all measurements were possible and are thus not visible in the graph. However, all the measurements that could be taken did reach the inclusion criteria. The fat layer was not present in the biopsies taken on the first day which made some of them impossible to measure. However, from the weight measurements it can be seen that the back leg and back belly do have larger water volume fractions compared to the biopsies taken at the front of the body. This is what was expected due to gravity. It should be noted that this subject came in 23 hours after death, and was therefore measured in a later time frame compared to the other subjects. From the biopsies taken at the second day, only the back leg and back belly were without fat. The water volume fractions of these biopsies stayed about the same at the second day. No conclusions can be drawn from the other biopsies since it is not known whether the change in water volume fraction is due to the presence of fat in the biopsy or due to dehydration.
Beside the human cadaver measurements, one measurement was performed on legs which had been buried for two months in taphonomic ground,
for another research program. Two biopsies were taken at the upper side of the leg and two at the bottom. The NIR spectroscopy measurements deviate a lot from the weight measurement (Fig. 10). This can be explained by the poor R-squared values for three of the four biopsies (back side#1, front side#1 and front side#2). However, the trend seen in Fig. 10 between the NIR measurements and the weight measurements is similar. The biopsies taken at the bottom side of the legs do clearly have a larger water volume fraction compared to the biopsies from the upper part of the leg.
5.4 Pig skin measurements
Since the measurement range of 24 hours was too small to see any major changes in the biopsies from the human cadavers, and the supply of human cadavers was minimal, pig skin studies were performed as well. In Fig. 11Ait can be seen that the NIR spectroscopy measurements have a similar trend compared to the weight measurements. However, the first two points of the NIR spectroscopy measurements deviate much more in comparison to the last three data points. Three biopsies were taken at each time point and for the first time measurement, all three measurements should be excluded because they have too low R-squared values (<0.999). This is also the case for the second time measurement, where two of the three measurements can be excluded due to low R-squared values. Taking this into account it can be said that the NIR measurement follows the weight measurement with a difference of about 5% and that the skin slightly hydrates again after three days.
The second pig measurements shows more variation compared to the previous measurement (Fig. 11B). The pig skin was placed on a sponge to make sure the fluids were able to drain down, and to see whether the skin would still hydrate at a later time point. The trend of the NIR measurements and the weight measurements show both some dehydration first, and hydration again of the skin after a week. However, the changes in water volume fraction are of a minimum amount. After a week skin slippage was noted as well as sliminess of the skin.
6. Conclusion
From this study we can conclude that using NIR spectroscopy to measure the hydration of skin, shows promise. Although the quantitative accuracy shows large variation relative to the weight loss measurements, averaging multiple/repeating measurements shows that the optical method can follow the same trends observed in the weight loss measurements. A possible improvement to
12
overcome the problem of wide variation might be theuse of homogenizing rods in the optical set-up. This should allow the sampling of a larger area of the biopsy cancelling out local heterogeneity and hence a potential source for inconsistency. Furthermore, the possibility of using reflectance spectroscopy should be investigated in the future. This could potentially generate a hand held device and a non-invasive method, easy to use outside a laboratory at a crime scene.
The results from the human cadaver measurements show clearly that 24 hours is too small a time frame to register any change in the hydration of skin and can therefore not be used to estimate a time of death. However, the last subject did show a clear difference between the top and bottom of the body for two of the biopsies. This subject came in at a later time point (23 hours after death), which indicates that changes might be seen at a later time point than 24 hours. This is also visible in the pig measurements. A small decrease in hydration was seen after 1-4 days. However, the skin hydrating again and the occurrence of the sliminess, although perhaps counter-intuitive (it was expected that the skin, being the part of the body most exposed to the air, would dehydrate continuously), could also potentially serve as a marker/indication of PMI or environmental conditions that the skin has been exposed to. It is of importance to reach a better understanding of the decaying processes of skin, especially what happens inside the skin with the interstitular and intercellular water.
Altogether, it can be concluded that the post-mortem hydration state of skin has interesting potential as an indicator of post-mortem interval estimation. This research has made an important first step.
7. References
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15
Appendices16
APPENDIX I – Derivation formulasIn this appendix a derivation of the formulas presented in section 2.1.3 is provided. The relevant variables are introduced in this section. Starting from the adjusted Lambert-Beer law (1.2): 𝐼(𝜆) = 𝐼0(𝜆) ∙ 𝑒−𝑑(𝑓𝑣∙𝜇𝑎(𝜆)·𝑑𝑝𝑓(𝜆,𝜇𝑠
′)+𝑙𝑓 (𝜇 𝑠 ′(𝜆),𝑜𝑔) )
(1.2)
The intensity (𝐼(𝜆)) of light coming through the tissue is measured over multiple distances. When taking two arbitrary distances 𝑑1 and 𝑑2, the following can be derived:
𝐼(𝜆,𝑑2) 𝐼(𝜆,𝑑1) =
𝐼0(𝑑2)·𝑒−𝑑2(ℎ(𝜆)) 𝐼0(𝑑1)·𝑒−𝑑1(ℎ(𝜆)) = 𝑒
−𝑑2(ℎ(𝜆))+𝑑1(ℎ(𝜆))
were we denote the exponent, _(𝑓𝑣∙𝜇𝑎(𝜆)·𝑑𝑝𝑓(𝜆,𝜇𝑠′)+𝑙𝑓 (𝜇𝑠′(𝜆),𝑜𝑔)), as ℎ(𝜆).
ln (𝐼(𝜆, 𝑑2) 𝐼(𝜆, 𝑑1) ) = −𝑑2(ℎ(𝜆)) + 𝑑1(ℎ(𝜆)) = −ℎ(𝜆)(𝑑2− 𝑑1) ln(𝐼(𝜆, 𝑑2)) − ln(𝐼(𝜆, 𝑑1)) = −ℎ(𝜆)(𝑑2− 𝑑1) 𝛥 ln(𝐼(𝜆)) = −ℎ(𝜆) · 𝛥𝑑 𝐷𝐹 ≝ 𝛥 ln(𝐼(𝜆)) 𝛥𝑑 = −ℎ(𝜆) −(𝑓𝑣∙ 𝜇𝑎(𝜆) · 𝑑𝑝𝑓(𝜆, 𝜇𝑠′) + 𝑙𝑓 (𝜇𝑠′(𝜆), 𝑜𝑔)) = 𝐷𝐹 (1.4) Single wavelength − (𝑓𝑣∙ 𝜇𝑎(𝜆) · 𝑑𝑝𝑓(𝜆, 𝜇𝑠′) + 𝑙𝑓 (𝜇𝑠′(𝜆), 𝑜𝑔)) = 𝐷𝐹 (1.4) 𝑓𝑣𝑤𝑎𝑡𝑒𝑟= −𝐷𝐹 − 𝑙𝑓 (𝜇𝑠′(𝜆),𝑜𝑔) 𝜇𝑎(𝜆)·𝑑𝑝𝑓(𝜆,𝜇𝑠′) (1.5) Two wavelengths
When measuring at two wavelengths, 1475nm and 1540nm, and taking the difference between these wavelengths, the water volume fraction can be derived as follows:
𝐷𝐹1− 𝐷𝐹2= −(𝑓𝑣∙ 𝜇𝑎(𝜆1) · 𝑑𝑝𝑓(𝜆1, 𝜇𝑠′1) + 𝑙𝑓 (𝜇𝑠′(𝜆1), 𝑜𝑔)) + (𝑓𝑣∙ 𝜇𝑎(𝜆2) · 𝑑𝑝𝑓(𝜆2, 𝜇𝑠′2) + 𝑙𝑓 (𝜇𝑠′(𝜆2), 𝑜𝑔))
𝐷𝐹1− 𝐷𝐹2= −𝑓𝑣(𝜇𝑎(𝜆1) · 𝑑𝑝𝑓(𝜆1, 𝜇𝑠′1) − 𝜇𝑎(𝜆2) · 𝑑𝑝𝑓(𝜆2, 𝜇𝑠′2)) − 𝑙𝑓1+ 𝑙𝑓2
𝐷𝐹1− 𝐷𝐹2+ 𝑙𝑓1− 𝑙𝑓2= −𝑓𝑣(𝜇𝑎(𝜆1) · 𝑑𝑝𝑓(𝜆1, 𝜇𝑠′1) − 𝜇𝑎(𝜆2) · 𝑑𝑝𝑓(𝜆2, 𝜇𝑠′2))
𝑓𝑣𝑤𝑎𝑡𝑒𝑟= 𝐷𝐹2−𝐷𝐹1+𝑙𝑓2−𝑙𝑓1
𝜇𝑎(𝜆1)·𝑑𝑝𝑓(𝜆1,𝜇𝑠′1)−𝜇𝑎(𝜆2)·𝑑𝑝𝑓(𝜆2,𝜇𝑠′2)
𝑙𝑓(𝜆) = 𝜇𝑠′(𝜆) + 𝑜𝑔, hence 𝑜𝑔 cancels out, leaving:
𝑓𝑣𝑤𝑎𝑡𝑒𝑟= 𝐷𝐹2−𝐷𝐹1+𝜇′𝑠(𝜆2)− 𝜇𝑠′(𝜆1) 𝜇𝑎(𝜆1)·𝑑𝑝𝑓(𝜆1,𝜇𝑠′1)−𝜇𝑎(𝜆2)·𝑑𝑝𝑓(𝜆2,𝜇𝑠′2)
Since 𝜇𝑠′(𝜆
2) is approximately 3% lower compared to 𝜇𝑠′(𝜆1):
𝜇𝑠′(𝜆2) = 𝜇𝑠′(𝜆1) · 0.97
𝜇𝑠′(𝜆2) − 𝜇𝑠′(𝜆1) = −𝜇𝑠′(𝜆1)(1 − 0.97)
𝑓𝑣𝑤𝑎𝑡𝑒𝑟= 𝐷𝐹2−𝐷𝐹1−𝜇𝑠′(𝜆1)(1−0.97)
17
APPENDIX II – Protocol phantomsMaterials
Intralipid® 20% (Fresiunius kabi) Demi water
Pipette (tips) Vortex
10mL tubes with lid
Five different concentrations are made according to Table 3. The solutions should be well-stirred, using the vortex, before measuring.
Table 3. Dilution series of intralipid
mL IL20% mL H2O Vol% IL Vol% H2O Ratio IL20%:H2O
3.5 36.5 1.99 98.01 1:11.43
4 36 2.27 97.73 1:10
6 34 3.405 96.595 1:6.667
8 32 4.54 95.46 1:5
The following set-up is used for the liquid phantom measurements:
Fig. 12. Set-up for liquid phantom measurements
The liquid phantom is placed in the container, by use of a pipette. The upper fibre is placed into the liquid, with a distance around 3.0 mm between the fibres. If the fibre doesn’t reach the liquid, then more liquid should be added.
Measurements are taken at increments of 0.025 mm, for 7 distances, between 3.000 and 3.150 mm, starting with the 3.000 mm measurement.
The lights in the room should be turned off during the measurements to avoid a significant amount of background light being present. If it is not possible to turn off the light, aluminium foil should be wrapped around the measuring device.
18
APPENDIX III – Protocol human skin measurementsProtocol measurements department of Anatomy and Embryology – 25.02.2016
Jeltje van Esch (0638338450 / jeltjevesch@gmail.com)
Richelle Hoveling (sein (81)57454 / 64390 / 0645384484 evt voicemail / r.j.hoveling@amc.uva.nl) Maurice Aalders
Research goals
1. Gaining more insight into the process of dehydration of the skin after death, using near infrared spectroscopy.
2. Estimating whether the dehydration of the skin changes over time, post mortem.
3. Estimating whether the dehydration of the skin can be used to estimate the post mortem interval.
Measurements
The measurements will be performed in the mortuary/ department of Anatomy and Embryology of the AMC.
The optical properties of the skin are of importance for the measurements. From the absorption spectrum of water it is known that a high absorption peak exists around 1480 nm. To detect changes in skin hydration the measurements will be performed using near infrared spectroscopy, transmission-based. This technique allows us to measure skin hydration quantitatively and it will measure the absorption of water in the skin at 1480 nm as well as at a slightly greater wavelength, 1550 nm. The measurements can subsequently be used to calculate the percentage of water in the skin.
We would like to gain more insight into the change of skin hydration over time, post mortem. Therefore it is important to measure regularly over the maximum period of time. Preferably immediately after the body comes in until the body will be preserved.
The near-infrared spectroscopy technique is a rapid and non-invasive technique, since only two lasers are used to measure the absorption. The personal data (name, medical data) of the bodies on which we are performing the measurements, will not be documented or published. Nevertheless, we will make use of the age, gender, body weight, body dimensions, skin temperature, time of death, skin diseases or infections which may be present at time of death, and the measured water concentration of the skin.
Plan of action:
The researchers need to be contacted at the moment a patient comes in. Thereafter the measurements can be started.
Near infrared spectroscopy
From previous research it is known that the flap of skin between the thumb and the index finger is a suitable location to measure the hydration of the skin. Furthermore, assuming that the body fluids/water descends by gravity, the following locations will be measured:
- Thumb-index finger skin flap - Chest (non-dependent trunk)
19
Protocol measurements department of Anatomy and Embryology – 11.04.2016Jeltje van Esch (0638338450 / jeltjevesch@gmail.com)
Richelle Hoveling (sein (81)57454 / 64390 / 0645384484 evt voicemail / r.j.hoveling@amc.uva.nl) Maurice Aalders
Research goals
1. Gaining more insight into the process of dehydration of the skin after death, using near infrared spectroscopy.
2. Estimating whether the dehydration of the skin changes over time, post mortem. 3. Estimating whether the dehydration of the skin can be used to estimate the post mortem
interval.
Biopsies and measurements
The measurements will be performed in the mortuary/ department of Anatomy and Embryology of the AMC and multiple biopsies need to be taken from the body.
The optical properties of the skin are of importance for the measurements. From the absorption spectrum of water it is known that a high absorption peak exists around 1480 nm. To detect changes in skin hydration the measurements will be performed using near infrared spectroscopy, transmission-based. This technique allows us to measure skin hydration quantitatively and it will measure the absorption of water in the skin at 1475 nm as well as at a slightly greater wavelength, 1540 nm. The measurements can subsequently be used to calculate the percentage of water in the skin.
We would like to gain more insight into the change of skin hydration over time, post mortem. Therefore it is important to measure over the maximum period of time. Preferably, skin punch biopsies are taken immediately after the body comes in, and just before the body will be preserved. The skin punch biopsies will be measured using the near-infrared spectroscopy technique.
The personal data (name, medical data) of the bodies on which we are performing the measurements, will not be documented or published. Nevertheless, we will make use of the age, gender, body weight, body dimensions, skin temperature, time of death, skin diseases or infections which may be present at time of death, and the measured water concentration of the skin.
Plan of action:
The researchers need to be contacted at the moment a patient comes in. Thereafter the skin punch biopsies can be taken.
We are aware that the body might be used for multiple projects. Therefore we are flexible on the locations the biopsies can be taken to accommodate other studies. Preferably, assuming that the body fluids/water descends by gravity, a skin punch biopsy is needed from the following locations:
- Chest (back & front ) - Belly (back & front) - Leg (back & front)
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APPENDIX IV – Protocol human skin measurementsMaterials
Small petri dishes
Mettler AJ50 balance (4 decimal places) Disposable biopsy punch 8mm
Scalpel Tweezers Gloves
Index matching gel Fume hood
NIR spectroscopy device
o 1475nm laser & 1540nm laser, 1.5mm diameter transmitting and receiving fibre o Detector
o Distance measurement Software
o Miniscale
o AFE4404 EVM GUI o MatLab
Human cadaver measurements
Six skin punch biopsies will be taken from the following locations: - Chest (back & front)
- Belly (back & front) - Upper leg (back & front)
The skin punch biopsies will be taken immediately after the body comes in and 24 hours later, next to the one already taken.
Steps to follow:
In the lab:
1. Label six empty petri dishes (small) and weigh them before going to the mortuary. (Weigh in triplet.)
In the mortuary:
2. Register the time of death, the time the body came in into the mortuary, the age and gender of the body and the time of measurement.
3. Take six skin punch biopsies from the mentioned sides, using a disposable skin puncher with a diameter of 8mm minimum and a scalpel and tweezer to cut out the biopsy. Place the biopsies in the labelled petri dishes.
In the lab:
4. Cut off the fat layer from the biopsies.
5. Weigh the biopsies in their petri dish (weigh in triplet.)
6. Measure the biopsies using the NIR spectroscopy device. Make sure a little drop of index matching fluid is placed on top of the fibres.
7. Place the petri dishes with the biopsies in the fume hood and let them rest.
Repeat step 1-8 after 24 hours for a second run of measurements and biopsies. Try to measure and take the biopsies at, or close to, the same spot measured the day before.
8. Repeat the weighing of the petri dishes over time while drying out in the fume hood. Weigh until the weight is stable, using the microbalance.
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APPENDIX V – Weight tracking exampleBesides the NIR spectroscopy measurements, weight measurements were performed. After the biopsies were taken, they were weighed. The biopsies rested in the fume hood at room temperature and constant air flow. The weight of the biopsies was tracked over the following days until a constant weight was reached. It is assumed that the weight loss corresponds to the evaporation of water, and thus the water volume fraction present in the biopsy.
Fig. 13 shows an example of the weight tracking. These biopsies were taken from the first human cadaver measured, directly after the body arrived in the morgue.
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APPENDIX VI – Protocol pig skin measurementsMaterials
Small petri dishes
Mettler AJ50 balance (4 decimal places) Disposable biopsy punch 8mm
Scalpel Tweezers Gloves
Index matching gel Vaseline
Cling film Fume hood
NIR spectroscopy device
o 1475nm laser & 1540nm laser, 1.5mm diameter transmitting and receiving fibre o Detector
o Distance measurement Software
o Miniscale
o AFE4404 EVM GUI o MatLab
Pig measurements
Preparation:
1. Ensure the pig skin is only able to dry out via the skin (wrap in cling film and cut a square out next to the skin), and place the pig skin in a fume hood.
2. Take a photograph of the pig skin before taking the biopsies. 3. Label the petri dishes (small) and weigh them in triplet. Biopsies:
4. Take the chosen amount of biopsies (at least 3) from the chosen place of pig skin and place one biopsy in each petri dish.
5. After taking the biopsies, fill the holes with Vaseline to prevent drying out too quickly. 6. Cut off the fat layer from the biopsies.
7. Weigh the petri dishes with skin biopsies (in triplet.) 8. Measure the skin biopsies with NIR spectroscopy.
9. Leave the petri dishes in the fume hood, with the lid off, to let the biopsies dry out over time. Repeat taking the biopsies, step 1-8 in the chosen time frame (1x per 2 hours, 1x per day, ...) and record the weight of the biopsies over time, until a stable weight is reached.
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APPENDIX VII – MatLab scripts data analysis biopsies%Without iteration – biopsies calculations
clear all
load
D:\AMC_MatLabData\Pig_skin_measurements\2_pigskin_1606\pig_AMC_2306_morning.mat;
%Fit parameters
fo = fitoptions('method','LinearLeastSquares','Robust','On');
ft= fittype('poly1');
%absorption coefficients water per wavelength
mu1475 = 2.353; mu1540 = 1.082;
%reduced scattering coefficients per wavelength
mus_1475 = 1.5;
mus_1540 = mus_1475*0.97;
%average differential pathlength factor per wavelength
DPF_1475 = (1.08+1.15)/2; DPF_1540 = (1.09+1.17)/2;
%performing the calculation for every subject and measurement
count = 0;
for subject = 24:26 for meas = 1
count = count+1
this_sub_meas = find(pig_AMC_2306_morning(:,1)==subject &
pig_AMC_2306_morning(:,2)==meas) %Taking the right subject & measurement data out of the uploaded file (subject number in column 1, measurement number in column 2)
Distances=pig_AMC_2306_morning(this_sub_meas(1),3:9); %distances measured
Volt_1475=pig_AMC_2306_morning(this_sub_meas(2),3:9); %intensity measured
Volt_1540=pig_AMC_2306_morning(this_sub_meas(3),3:9); %intensity measured
% Correcting the distances measured with the differential pathlength factor
for lk=1:7 dpf_corrected_1475(lk)=((0.04392*Distances(lk)^2)+(0.9951*Distances(lk))); end for lk=1:7 dpf_corrected_1540(lk)=((0.05631*Distances(lk)^2)+(0.9754*Distances(lk))); end
% Taking the LN of the intensity measured
Ln_volt_1475 = log(Volt_1475); Ln_volt_1540 = log(Volt_1540);
% Linear fit of the intensities vs. corrected distances
[cf1475,gof1475] = fit(dpf_corrected_1475',Ln_volt_1475',ft,fo); [cf1540,gof1540] = fit(dpf_corrected_1540',Ln_volt_1540',ft,fo); myco1475 = coeffvalues(cf1475); myco1540 = coeffvalues(cf1540);
% R-squared of the fit
rsq1475 = gof1475.rsquare; rsq1540 = gof1540.rsquare;
% Slopes of the fit
slope1475 = myco1475(1); slope1540 = myco1540(1);
slope_slope = slope1475/slope1540;
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% Calculations water volume fractions (Two WL formula & One WL formulas)
water_concentration = ((slope1540-slope1475-1.5*(1-0.97))/((mu1475*DPF_1475)-(mu1540*DPF_1540))); water_1475 = (-slope1475-mus_1475)/(DPF_1475*mu1475); water_1540 = (-slope1540-mus_1540)/(DPF_1540*mu1540);
% Results for one subject
result_range = [subject meas slope1475 slope1540 rsq1475 rsq1540 water_concentration water_1475 water_1540 slope_slope];
% Results for all subjects
results(count,:) = result_range;
end end
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%With iteration – biopsies calculations
clear all
load D:\AMC_MatLabData\Pig_skin_measurements\2_pigskin_1606\pig_AMC_2306_noon.mat;
%Fit parameters
fo = fitoptions('method','LinearLeastSquares','Robust','On'); ft= fittype('poly1');
%absorption coefficients water per wavelength
mu1475 = 2.353; mu1540 = 1.082;
%starting points differential pathlength factors (dpf)
new_DPF1475 = 1.12; new_DPF1540 = 1.14;
% Iteration procedure
for iter=1:10 %number of iterations
DPF_1475 = new_DPF1475; %replacing the dpf with the new calculated dpf
DPF_1540 = new_DPF1540;
count = 0;
for mus_1475 = 0.5:0.01:3.0; %going through a range of mus' to find the best
mus_1540 = mus_1475*0.97; subject = 29; %subject number
meas = 1; %measurement number
count = count+1;
this_sub_meas = find(pig_AMC_2306_noon(:,1)==subject &
pig_AMC_2306_noon(:,2)==meas); %Taking the right subject & measurement data out of the uploaded file (subject number in column 1, measurement number in column 2)
Distances=pig_AMC_2306_noon(this_sub_meas(1),3:9); Volt_1475=pig_AMC_2306_noon(this_sub_meas(2),3:9); Volt_1540=pig_AMC_2306_noon(this_sub_meas(3),3:9);
% Correcting the distances measured with the differential pathlength factor
for lk=1:7 dpf_corrected_1475(lk)=DPF_1475*Distances(lk); end for lk=1:7 dpf_corrected_1540(lk)=DPF_1540*Distances(lk); end
% Taking the LN of the intensity measured
Ln_volt_1475 = log(Volt_1475); Ln_volt_1540 = log(Volt_1540);
% Linear fit of the intensities vs. corrected distances
[cf1475,gof1475] = fit(dpf_corrected_1475',Ln_volt_1475',ft,fo); [cf1540,gof1540] = fit(dpf_corrected_1540',Ln_volt_1540',ft,fo); myco1475 = coeffvalues(cf1475); myco1540 = coeffvalues(cf1540);
% R-squared of the fit
rsq1475 = gof1475.rsquare; rsq1540 = gof1540.rsquare;
% Slopes of the fit
slope1475 = myco1475(1); slope1540 = myco1540(1);
slope_slope = slope1475/slope1540;
