Development of wearable sensors to measure sweat rate and conductivity


Thèse de Doctorat, 2009

94 Pages, Note: none


Extrait


Contents

Introduction

Chapter 1 – Wearable sensors
1.1 BIOTEX project
1.2 Sweat
1.3 Applications and sensors requirements
1.4 Market innovation analysis and level of innovation
References

Chapter 2 – Sweat conductivity and temperature sensors
2.1 Definition and preliminary tests
2.2 Geometry and substrate of electrodes
2.3 Temperature sensor
2.4 Conductivity and temperature sensors
References

Chapter 3 - Sweat rate sensor
3.1 Measurement of flow
3.2 Humidity sensors
3.2.1 Resistive humidity sensors
3.2.2 Thermal conductivity humidity sensors
3.2.3 Capacitive humidity sensors
3.3 Wearable humidity sensors
3.3.1 Test system
3.4 Sensors based on conductive yarns coated with hydrophilic polymers
3.5 Sensors based on conductive polymer fibres
3.6 Sensors based on a layer of hydrophilic polymer between conductive fabrics
3.7 Test of the sweat rate sensor
References

Chapter 4 - Calibration of the sensors and results
4.1 Choice of body area for sweat sampling
4.2 Calibration of the sensors
4.3 Results
4.4 Conclusions
References

Acknowledgements

To my parents, for their love and support during these years.

To Prof. D. De Rossi, Dott. F. Di Francesco and Dott. D. Costanzo for their help and support.

To Institute of Clinical Physiology at CNR of Pisa, “Gruppo Mast”, where I did the Ph.D. thesis.

To the BIOTEX partners, for their excellent work.

To Charles Lutwidge Dodgson who has always been present.

Introduction

Wearable sensors are a new technology, which is rapidly spreading in the areas of sport and healthcare. This growth is mainly due to the athletes' need to have real time information regarding their physical status during training sessions and of course more importantly, a patient's need for a constant, low cost, non-invasive method of monitoring. In fact, detailed information is potentially available if close contact is ensured between the body and the sensors. One of the main advantages of this new technology is that the modified garment does not alter the normal activity of the user.

To be defined as wearable, a sensor has to:

- Be integrated onto clothing and specifically onto a textile substrate.
- Perform its tasks directly on the human body.

The first condition implies not only that the sensor has to be in direct contact with the garment but also that the textile substrate becomes a support to connect the body and the sensor.

The second condition defines an important constraint that is not always respected. The analysis of sweat is usually carried out by collecting the sample with a patch to be analyzed by another medical instrument. Our goal is to show that it is possible to measure several parameters regarding human sweat directly on the body, without the intermediation of other instruments. The data is promptly available for the user, by a wireless connection, on a PC. In fact, it is not necessary to directly connect the sensor to a PC since there are wireless connections available such as Bluetooth , which according to its latest specifications achieves a speed of 2.1 Mbits/sec up to about 100 meters with low power consumption.

Other properties are strictly related to the definition and use of wearable sensors. The garment has to retain all its properties of flexibility and washability, and so does the sensor. Moreover, there must be no discomfort so as to allow users to feel like they are wearing a normal garment and thus enable them to act normally. This freedom of movement is important if it means that users are no longer required to go to a medical or scientific laboratory in order to monitor certain parameters regarding their health.

Another desirable characteristic of wearable sensors is that they could be made on large scale, with cheap but high quality materials, and would only be of small dimensions.

Chapter 1 – Wearable sensors

1.1 BIOTEX project

The BIOTEX project is a Specific Targeted Research or Innovation Project, (STREP) which is part of the Sixth Framework Programme of the European Commission, Priority 2&3, joint call between IST (Information Society Technologies) and NMP (Nanotechnology and nanosciences, knowledge-based multifunctional materials and new production processes and devices). The consortium consists of eight partners from four countries and includes:

I. Centre Suisse d’Electronique et de Microtechnique (CSEM) in Switzerland which has a strong background in the field of micro and nanotechnology.
II. Commissariat à l’Energie Atomique (CEA) - Laboratory for Electronics & Information Technology (LETI) in France, which is skilled in developing electrochemical sensors.
III. Interdepartmental Research Center “E. Piaggio”, University of Pisa, Italy, which is a leader in the field of bioengineering.
IV. National Center for Sensor Research, Dublin City University, Ireland, which is well known for its activity in the field of health science, nanotechnology and mycrosystems.
V. Smartex s.r.l., Italy, a company active in the development of projects related to wearable instrumented garments.
VI. Penelope, Italy, is a leading fabric manufacturing company based not only on materials like wool and cotton but also on innovative ones like stainless steel and glass fibers.
VII. Sofileta, France, a specialist in integrated textile manufacturing.
VIII. Thuasne, France, is a producer of innovative products for the medical market and sports protection.

The kind of wearable sensors that are commonly studied in research laboratories or sold by companies mainly regard ECG, heart rate, skin temperature and resistance. None have implemented a biochemical sensing technique capable of measuring fluids such as sweat and blood. The BIOTEX project is the first attempt to move towards this goal, analyzing, in particular, human sweat.

Chemical sensors are complex systems since their reactive layer has to be exposed to the target sample in order for the reaction to occur. Thus, how to deliver the sample to the sensor is one of the most critical aspects involved.

Artifacts caused by movement and a sufficient amount of uncontaminated fluid are very important, therefore tests that can determine the behavior of the system are absolutely essential.

The final goal is to create a patch able to carry out a multi-parametric analysis of various physiological targets including:

- Sweat monitoring: sweat rate (perspiration), sweat conductivity, specific ions like Na+, pH.
- ECG (electrocardiogram)
- Oxygen saturation of blood.

1.2 Sweat

The analysis of biological fluid underlies much of modern medicine. Blood is rich in information but there are a large number of pathologies that require frequent monitoring, sometimes for long periods or for a person's whole life. In these cases, blood sampling is too invasive for patients. It often requires long waiting times, it must be done in specialized laboratories or clinical structures, performed on an empty stomach and can cause infections.

One possible way out may be to strengthen the analysis of other biological fluids whose sampling is less invasive and which are less chemically complex. Easy-to-use, fast response sensors would allow both doctors and patients to get important information, thus improving prevention and cutting costs.

Sweat, in particular, seems very promising. It is composed of 98 per cent water and about 2 per cent is made up mainly of sodium, chloride, potassium, bicarbonates, urea, lactic acid, glucose and traces of other organic compounds.

The sodium concentration depends on the sweat rate, which while in normal conditions is about 20 mM, can reach 100 mM for higher rates [1]. Potassium ranges from 5 to 6 mM [2] while chloride is about 35 mM [3]. However, in the presence of cystic fibrosis, which affects the lungs, pancreas, liver and intestines sometimes leading to infections, poor growth or infertility, sodium concentration can increase to 200 mM [3] (see table 1 for more details about concentrations). It should be noted that an increase in chloride is just an indication and not certain proof of the presence of cystic fibrosis. Other diseases may also be responsible, such as Addison’s syndrome or a renal dysfunction.

Table 1. Sweat composition: main electrolytes and compounds.

illustration not visible in this excerpt

pH is about 5 for low sweat rates while it reaches 6.5-7 for higher rates [1].

There are two types of sweat gland: eccrine and apocrine (Fig. 1). Eccrine glands are smaller, active from birth and produce sweat. On the other hand, apocrine glands, which have the same structure as hair follicles and sebaceous glands, are active only at puberty and they do not have any role in thermo-regulation. The dimensions of eccrine glands can be very different - some people have eccrine glands five times bigger than other people do.

illustration not visible in this excerpt

Fig. 1. Sweat glands under the skin

Together with the skin’s capillary blood vessels, sweat glands regulate the temperature of the human body. In fact, the evaporation of water, which is the main component of sweat, controls the body cooling at a concentration of 0.6 cal per milliliter of evaporated sweat [4]. The body sweats when skin temperature rises over 32-34 °C. The maximum sweat rate is roughly 2 or, for a short time, 4 l/h in normal and extreme conditions, respectively.

What happens is that when the body is too warm, the flow of perspiration from the sweat glands to the ducts on the surface of the skin increases.

The two main forms of perspiration are perspiratio insensibilis and sensibilis. Perspiratio insensibilis is an incessant process caused by the diffusion of water between the derma and epidermis. It is strictly dependant on the hydration of skin and has little relation to body thermoregulation. At 31 °C, perspiratio insensibilis has a water flux of 6-10 g/m2∙h from the skin of legs, trunk and arms; up to 100 g/m2∙h from the feet, the palms of hands and from the skin of the face.

Perspiratio sensibilis depends on the eccrine glands, which are already developed in the body from birth. Typically, on average, there are 2.6 million eccrine glands (in the skin, ranging from 1.6 to 4 million. They are unevenly distributed over the entire body with the exception of the external genital organs, lips and nipples [5][6]. They are embedded in the dermis, which is the layer of connective tissue lying under the epidermis. Their ducts penetrate the epidermis and excrete sweat.

The average eccrine glands density depends on the anatomic area. It is reported 108 glands/cm2 on the forearm, 64 glands/cm2 on the back, 181 glands/cm2 on the forehead and 600-700 glands/cm2 on the palms of hands and feet [6][7]. The maximum sweat-rate ranges from 2 to 20 nL/min/gland [8].

Sweat sampling is critical. Collection is not easy since people sweat in different ways, so there are cases where the amounts are too low. It is reported that the minimum flux has to be 1 g/m2∙min and the collection time does not have to exceed 30 minutes. Sampling methods also present some difficulties [3,9]. A typical collection procedure involves placing an absorbent material in contact with the skin from which the sweat is then drawn. This method has a critical drawback regarding the amount of sweat, which may not always be sufficient. In fact, to draw the sweat from the patch, it is necessary to make use of a vessel filled with at least 2 cc of pure water, which greatly dilutes the sample.

These considerations show that the continuous monitoring of a person may only be done by designing a system that can deliver the sweat to the sensors without being affected by any contamination nor by movements of the body. In BIOTEX, the solution is to use a fabric pump that collects the sweat and delivers it to the sensors which are located directly on the fabric pump, as will be explained in detail the following chapters.

Important applications of sweat analysis include the diagnosis of cystic fibrosis, against the use of illicit drugs (e.g. cocaine) and against doping in sports, but these are not the only ones.

BIOTEX applications are mainly aimed at people involved in sports, but they could also have significant advantages for obese and diabetic patients who do sports.

1.3 Applications and sensors requirements

One of the main reasons for the fast development of wearable sensors is due to their high demand in the military field e.g. helmet-mounted IR imaging systems that enhance the user's vision when visible light sensors are inadequate, and which also free the user's hands in hazardous or potentially hazardous military operations. Investment in this sector is considerably high and the interaction with other fields of application is a great opportunity for knowledge exchange. This interaction has led to the diffusion of wearable sensors in sectors like sports and clinical medicine.

An exhaustive evaluation of physiological functions may help in planning the best training program, for example deciding on the correct duration and kind of exercises that will improve an athlete’s fitness and health. An opportunity to test an athlete’s performance in his/her typical training environment, wherever that may be, is clearly an added value.

Sports people aim to constantly improve their athletic condition and often use several devices that provide them with information about their training session, e.g. heart rate or ECG. This is true not only for professional sportsmen and women but also for all those who like to train seriously.

Being able to monitor physiological parameters in real-time for an athlete is important in terms of their health and in order to adjust the training activity to improve performance.

During physical training, sweat evaporation is the body’s most effective resource to dissipate excess heat which, otherwise, might damage the tissues and cause dysfunctions in the heart or lungs. However, an athlete must avoid dehydration since the human body needs fluids to correctly maintain normal physiological conditions.

Sweat rates depend on environmental conditions, such as temperature and relative humidity, as well as the athlete’s physical condition. While there are athletes who can tolerate fluid losses of 4-5% of body mass [10], in some subjects even a 2% loss of fluid can cause a dysfunction of thermoregulation leading to a significant alteration in physical performance. The critical point is reached when the fluid deficit approaches 7% [11] of the total amount while a 10% loss can lead to heatstroke. In any case, water loss is not the only target of the BIOTEX wearable system. In fact, there are not only volume losses, but also losses of electrolytes, primarily sodium, chloride and potassium, which are lost in the sweat.

Low electrolyte levels can cause some gastrointestinal discomfort and in extreme cases, hyponatraemia, caused by low sodium concentrations in blood, which is potentially life threatening.

At present, there are no wearable systems that monitor electrolyte concentrations in sweat. Moreover, wet patches that need to be analyzed in laboratories are impractical for frequent monitoring.

The usual method to quantify sweat loss is an estimation of the athletes’ weight before and after exercise sessions, but this does not provide any information about the electrolyte balance.

Regarding sport, sweat analysis against doping deserves special mention. The use of illicit drugs is one of the most terrible plagues of our society. It destroys the drug-taker's health, it is a risk for people who are in contact with users, it is a source of income for criminality and governments spend considerable sums combating it. Non- invasive tests might help in the fight against illicit drugs by providing a fast and easy method to detect habitual drug users. There are several studies regarding the presence of drugs in sweat (it seems that skin is a tank for drugs) and although there is still a lot to do, in particular in developing reliable detection techniques, sweat analysis is a very promising tool to monitor habitual users of illicit drugs.

For example, if a threshold is overcome, a sound or visual alarm like a beep or a red LED may be activated. Other options are possible, like employing different sensors to monitor several health levels. If data is stored or transmitted to a PC, a specialist might provide his feedback and intervene when it is necessary (Fig. 2).

illustration not visible in this excerpt

Fig. 2. Working principle of wearable sensors.

Obesity could be another strong contender for a BIOTEX application and, since it is strictly related to normal physical activity, it has many points in common with sport. It is commonly associated with an excess of body fat but it is more correctly related to a body mass index (BMI) equal or higher than 30 Kg/m2 [12]. BMI is a statistical measurement that compares a person's weight and height, and is defined as the individual's body weight divided by the square of their height.

Obesity is often linked to hypertension, diabetes mellitus, high blood pressure, cardiovascular and neurologic dysfunctions, and also to some types of cancer.

It is caused by not only by a sedentary lifestyle and a poor diet but it is also related to genetic mechanisms, the metabolism or medicine abuse. The number of obese people is dramatically increasing in the western world and national governments have started several information campaigns to reduce its high socioeconomic impact.

Common therapies are based diets and pharmacotherapy that are specific for each patient, but which have side-effects and may only have a short period of applicability. Another option is bariatric surgery mainly based on reducing stomach size. In general, weight reduction can be accomplished, but there are operative risks (including mortality) and side effects.

All these therapies are often ineffective and the best solution is prevention, by constantly monitoring the evolution of obesity over time. An indirect analysis of a person's health from their sweat composition and production is highly relevant not only in terms of monitoring but also prevention. This is extremely important when children are obese since it is very probable they will be obese as adults. As with sports applications, a wearable sensor can help not only the patient but also the doctor to constantly monitor the patient's health status.

The third possible application regards diabetic patients [13]. Diabetes is a disorder of the metabolism. Most of the food we eat is broken down into glucose, the form of sugar in the blood. Glucose is the main source of fuel for the body.

After digestion, glucose passes into the bloodstream, where it is used by cells for growth and energy. For glucose to get into cells, insulin must be present. Insulin is a hormone produced by the pancreas, a large gland behind the stomach.

During eating, the pancreas produces insulin to move the glucose from the blood into our cells. Unfortunately, in patients affected by diabetes, the pancreas is either not capable to produce the right amount of insulin, or the cells do not respond appropriately to the insulin. Glucose builds up in the blood, overflows into the urine, and passes out of the body in the urine. Thus, the body loses its main source of fuel even though the blood contains large amounts of glucose. The two main types of diabetes are a) type 1 diabetes and b) type 2 diabetes.

Type 1 diabetes is an autoimmune disease. An autoimmune disease is when the body’s system to fight infection (the immune system) turns against a part of the body. In diabetes, the immune system attacks and destroys the insulin-producing beta cells in the pancreas. The pancreas then produces little or no insulin. A person who has type 1 diabetes must take insulin daily to live.

At present, scientists do not know exactly what causes the body’s immune system to attack the beta cells, but they believe that autoimmune, genetic, and environmental factors, possibly viruses, are involved. Type 1 diabetes accounts for about 5 to 10 per cent of diagnosed diabetes in the United States. It develops most often in children and young adults, but can appear at any age.

Symptoms of type 1 diabetes usually develop over a short period, although beta cell destruction can begin years earlier. Symptoms may include increased thirst and urination, constant hunger, weight loss, blurred vision, and extreme fatigue. If not diagnosed and treated with insulin, a person with type 1 diabetes can lapse into a life-threatening diabetic coma, also known as diabetic ketoacidosis.

The most common form of diabetes is type 2 diabetes. About 90 to 95 per cent of people with diabetes have type 2. This form of diabetes is most often associated with older age, obesity, family history of diabetes, previous history of gestational diabetes, physical inactivity, and certain ethnicities. About 80 per cent of people with type 2 diabetes are overweight.

Type 2 diabetes is increasingly being diagnosed in children and adolescents. However, nationally representative data on the prevalence of type 2 diabetes in youth are not available.

When type 2 diabetes is diagnosed, the pancreas is usually producing enough insulin, but for unknown reasons the body cannot use the insulin effectively, a condition called insulin resistance. After several years, insulin production decreases. The result is the same as for type 1 diabetes: glucose builds up in the blood and the body cannot make efficient use of its main source of fuel.

The symptoms of type 2 diabetes develop gradually. Their onset is not as sudden as in type 1 diabetes. Symptoms may include fatigue, frequent urination, increased thirst and hunger, weight loss, blurred vision, and the slow healing of wounds or sores. Some people have no symptoms.

All over the world, there are millions of people suffering from diabetes and it represents a substantial social and economic cost.

The fasting blood glucose test is the preferred test for diagnosing diabetes in children and non-pregnant adults. It is most reliable when done in the morning. However, a diagnosis of diabetes can be made based on any of the following test results, confirmed by retesting on a different day:

1. A blood glucose level of 126 milligrams per deciliter (mg/dL) or more after an 8-hour fast. This test is called the fasting blood glucose test.
2. A blood glucose level of 200 mg/dL or more 2 hours after drinking a beverage containing 75 grams of glucose dissolved in water. This test is called the oral glucose tolerance test (OGTT).
3. A random (taken at any time of day) blood glucose level of 200 mg/dL or more, along with the presence of diabetes symptoms.

The three previous monitoring methods are invasive since they measure the amount of insulin in the blood.

Sweat analysis can be helpful for monitoring hypoglycemic patients although what it really offers is a holistic evaluation of the unbalances in the physiological parameters that may be related to diabetes.

Knowing the applications and the targets, a wearable system should have specific electrical characteristics that can be divided into two main parts:

1. Pre-processing electronics for all the different sensors and specifically for physiological sensors. It is preferable to locate the circuitry as close as possible to the sensors.
2. A signal processing electronics responsible for data retrieving, signal multiplexing, conversion to digital, processing, and local or remote data storage. This part may be placed outside the garment for easy access, e.g. the battery and all those electronics that does not need to be washable or flexible.

This splitting renders the system more user-friendly since it is easier a) the replacement of the sensors and batteries and b) to wash the garment. The electronics, like patches, have to be as small as possible and should not be over 70 x 90 x 25 mm3 with a weight of 150 g, including the battery.

Low circuitry cost is another important aspect. The price of the electronic patch should be as low as possible and production costs should be comparable to the cost of the interfaced sensors, i.e. about or less than € 5 per interfaced sensor. The cost of the detachable electronics is less limiting, since these devices should preferably be reusable. However, a production cost of € 200 seems acceptable for this product, taking into account the cost of stand-alone monitoring devices that do not rely on textile sensors.

In order to have a system which can be used both by specialists, such as doctors and trainers, patients and athletes, the user interface needs to be water resistant and as simple as possible, e.g. operated using a single press button.

Power consumption has to be low since the system has to work for several days.

Close contact with the skin is obtained through soft, flexible patches, which need to be disposable and removable from the garment. Furthermore, the biosensor must never interfere with the sweat analysis or cause harm to the users.

1.4 Market innovation analysis and level of innovation

The market is not only ready for the diffusion of wearable sensors but demand is also increasing. Smart fabrics and interactive textiles (SFITs) are likely to exceed $ 640 US million by the end of 2008. Moreover, the compound annual growth rate (CAGR) was about 27% in the period 2004-2008.

According to BCC Research in 2007, the US market for smart textiles alone was worth about $ 79 million. Sales of conductive fabric products are expected to more than double each year through 2012, when the market is expected to reach $ 392 million.

BCC expects rapid growth in military, health care, vehicle safety and comfort applications, thus leading to a greater impact of wearable sensors in the global market for sensors. Very few products that were designed to monitor health have reached the market, but significant amounts of money are being invested in this technology. Most of the products already available were designed for use by athletes.

Lifeshirt, manufactured by Vivometrics, was designed for respiratory monitoring and other physiological signals, such as heart rate, EEG, EOG. Users have to wear a cap and a thimble in order to have their EEG/EOG and blood oxygen saturation monitored, respectively. Lifeshirt correlates and makes indirect measurements to obtain blood pressure, body temperature, periodic leg movement, and end tidal CO2. In any case, its use is limited to research and military centres.

Sensatex, a U.S. company, is working on a Smart Textile Technology and on the SmartShirt System, which should be able to measure and/or monitor heart rate, respiration rate, body temperature, caloric burn, body fat, and UV exposure.

Wealthy is a system by Smartex, an Italian company, able to acquire physiological parameters like ECG, posture and temperature.

The most common products available are for heart monitoring by Polar, Reebok or Mio™, pedometers and pulse meters manufacture by, for example, Oregon Scientific and for diabetes monitoring such as GlucoWatch®, which shows glucose levels in blood.

The development of a wearable sensor, which can be integrated into textiles, for sweat analysis is a complete breakthrough and it is the subject of this Ph.D. thesis. This thesis is, in fact, what we believe to be the first attempt to correlate electrophysiological data with biochemical information.

The results should provide lead to a more effective system than any other currently on the market. At present, to the best of our knowledge there is no product on the market that can perform multiple physiological measurements using a portable wireless system.

Furthermore, although there are some devices that can monitor some physiological parameters, there are no chemical wearable sensors currently available.

This point needs emphasizing since it represents the most important strength of the project, providing a new useful non-invasive instrument and technique for trainers, doctors, patients and users.

Protection, safety, health and also fashion are sectors which will be greatly influenced by wearable sensors and it is certainly not farfetched to imagine a future where our life will be regulated by these new sensors.

References

[1] Sato K., Kang W.H., Saga K., Sato K.T., Biology of sweat glands and their disorders. I. Normal sweat gland function, J Am Academy of Dermatol, 20: 537-66, (1989).

[2] Sato K., Sweat induction from an isolated eccrine sweat gland. Am J Physiol, 225: 1147-51, (1973).

[3] Tietz, Fundamentals of clinical chemistry, Saunders Elsevier, (2008).

[4] Rindi G., Manni E., Fisiologia umana, Vol. 2, UTET (2001).

[5] Montagna W., Parakkal PF., The structure and function of the skin. 3rd ed. New York: Academic Press: 376-96 (1974).

[6] Kuno Y., Human Perspiration. Springfield, Illinois: Charles C. Thomas. Blackwell Scientific Publications: Oxford, (1956).

[7] Sato K., The physiology, pharmacology and biochemistry of the eccrine sweat gland. Rev. Physiol Biochem Pharmacol 79: 51-131, (1977).

[8] Sato K., Sato F., Individual variations in structure and function of human eccrine sweat gland, American J. Physiology, 245 (2): 203-208 (1983).

[9] NCCLS/Clinical and Laboratory Standards Institute. Sweat testing: sample collection and quantitative analysis; approved guideline, 2nd ed. CLSI/NCCLS Document C34-A2. Wayne, PA: Clinical and Laboratory Standards Institute, (2000).

[10] Brotherhood, J.R. 1984. Nutrition and sports performance. Sports Med. 1: 350-389.

[11] Epstein, Y. and Armstrong, L.E. 1999. Fluid-electrolyte balance during labor and exercise: concepts and misconceptions. Int. J. Sports Nutr. 9: 1-12.

[12] World Health Organization, Technical report series 894: Obesity: preventing and managing the global epidemic, (2000).

[13] NIH Publication No. 06–3873 (2006).

[...]

Fin de l'extrait de 94 pages

Résumé des informations

Titre
Development of wearable sensors to measure sweat rate and conductivity
Université
University of Pisa  (Faculty of Engineering)
Cours
Bioengineering
Note
none
Auteur
Année
2009
Pages
94
N° de catalogue
V199721
ISBN (ebook)
9783656323396
ISBN (Livre)
9783656326809
Taille d'un fichier
3148 KB
Langue
anglais
Mots clés
sweat rate, sweat conductivity, wearable sensors, textile sensors
Citation du texte
Dr. Ir. Pietro Salvo (Auteur), 2009, Development of wearable sensors to measure sweat rate and conductivity, Munich, GRIN Verlag, https://www.grin.com/document/199721

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