**2. Magnetic sensors**

Magnetic sensors are based, with very few exceptions, on the same working principle: the change of magnetic moment that takes place in a magnetic material, (normally ferromagnetic), when submitted to a magnetic field, a change of temperature or, in the case of magnetoelastic materials, to a mechanical stress, generated by the medium, in which they are immersed. The measurement of this variation makes it possible to study the changes that occur in the surroundings of the sensor.

In the case of the biomedical applications, the medium may be a fluid like, for instance, blood, the cerebrospinal fluid or a culture medium or it may be organic tissue. In any case there will be an interaction between both elements, the magnetic material and the organic medium, which is undesirable. On the one hand, the organic media may be harmed since the most widely used magnetic materials, (transition metals and their alloys), are not biocompatible, except for iron which is very biocompatible; (human organs and tissues have a great affinity for iron). On the other hand, the above mentioned organic fluids have Cl- , Ca=, Na+, K+ ions and several free organic radicals which are, in general, corrosive for magnetic materials. The solution to this problem consists in coating the magnetic material with a thin layer (100 to 200 nm) of another biocompatible material, like gold, platinum, titanium oxide, silica or alumina. The most widely used coating methods are evaporation, sputtering, electrolysis and ionic implantation. The non metallic parts of the sensor also have to be made of biocompatible polymers or ceramics such as Teflon, medical silicones, and silica.

Another aspect that has to be taken into account regarding these sensors is the transmission and monitoring of the signal. Wireless transmission, which is one option in other application fields, is a compulsory one in biosensors. This is for obvious reasons in the case of internal implants, while in the case of the external ones wireless transmission is convenient so as not to restrict the patient's movement. Magnetic sensors and actuators offer a great advantage from the start: the magnetic field is itself a wireless transmission. The advances that have taken place in the past decades in the field of cellular phones, combined with magnetic sensors and biosensors, open the door to the final development of "telediagnosis".

The sensors that are presented in this section are based on the magnetoelastic properties of several magnetostrictive ferromagnetic alloys (Chikazumi, 1964). As is well known, a magnetostrictive material is characterized by a change of its macroscopic dimensions when its magnetization changes, getting longer or shorter (positive or negative magnetostriction respectively) along the direction of the magnetization. In other words, the energy of the

In the development of these magnetic devices, as well as others not described here, there are some aspects that are common to the magnetic devices used in other very different fields as, for example, railway sensors, automotive sensors or aerospace vehicles. These may apply the basic magnetic properties or the signal acquisition and control process. Nevertheless, there are some aspects, as for instance, biocompatibility, corrosion resistance, size limitation and patient comfort, in the case of a human implant, that are specific to this application. We

Magnetic sensors are based, with very few exceptions, on the same working principle: the change of magnetic moment that takes place in a magnetic material, (normally ferromagnetic), when submitted to a magnetic field, a change of temperature or, in the case of magnetoelastic materials, to a mechanical stress, generated by the medium, in which they are immersed. The measurement of this variation makes it possible to study the changes that

In the case of the biomedical applications, the medium may be a fluid like, for instance, blood, the cerebrospinal fluid or a culture medium or it may be organic tissue. In any case there will be an interaction between both elements, the magnetic material and the organic medium, which is undesirable. On the one hand, the organic media may be harmed since the most widely used magnetic materials, (transition metals and their alloys), are not biocompatible, except for iron which is very biocompatible; (human organs and tissues have a great affinity

and several free organic radicals which are, in general, corrosive for magnetic materials. The solution to this problem consists in coating the magnetic material with a thin layer (100 to 200 nm) of another biocompatible material, like gold, platinum, titanium oxide, silica or alumina. The most widely used coating methods are evaporation, sputtering, electrolysis and ionic implantation. The non metallic parts of the sensor also have to be made of biocompatible

Another aspect that has to be taken into account regarding these sensors is the transmission and monitoring of the signal. Wireless transmission, which is one option in other application fields, is a compulsory one in biosensors. This is for obvious reasons in the case of internal implants, while in the case of the external ones wireless transmission is convenient so as not to restrict the patient's movement. Magnetic sensors and actuators offer a great advantage from the start: the magnetic field is itself a wireless transmission. The advances that have taken place in the past decades in the field of cellular phones, combined with magnetic

The sensors that are presented in this section are based on the magnetoelastic properties of several magnetostrictive ferromagnetic alloys (Chikazumi, 1964). As is well known, a magnetostrictive material is characterized by a change of its macroscopic dimensions when its magnetization changes, getting longer or shorter (positive or negative magnetostriction respectively) along the direction of the magnetization. In other words, the energy of the

sensors and biosensors, open the door to the final development of "telediagnosis".

, Ca=, Na+, K+ ions

for iron). On the other hand, the above mentioned organic fluids have Cl-

polymers or ceramics such as Teflon, medical silicones, and silica.

nanoparticles

**2. Magnetic sensors** 

occur in the surroundings of the sensor.

will try to describe them through our work in this area.

Hyperthermia HeLa cell treatment with silica-coated manganese oxide

magnetizing field is used not only in the magnetization process but also in elastically deforming the material. The opposite phenomenon also takes place. When the material is deformed due to an external stress, not all the mechanical work is used in deforming the material, a part of the stress is used in magnetizing the material. In the free energy of the solid, a third term has to be added to the terms of elastic and magnetic energy that is called the magnetoelastic energy term. It takes into account the energy transfer between the elastic system and the magnetic one:

$$F = F\_{al}(\varepsilon) + F\_{mg}(m) + F\_{mgal}(m, \varepsilon) \tag{1}$$

As a consequence, in these materials the magnetic susceptibility changes with the deformation (and consequently with stress) of the material and, inversely, the elastic constant of the material changes with its magnetization (and thus the applied magnetic field). The magnetic coupling term, being the one that takes into account the energy exchange between both systems, shows a resonance phenomenon: it has a maximum for a particular frequency that depends on the magnetic and elastic properties of the material.

The materials that are most widely used are the amorphous magnetostrictive alloys, in which the absence of magnetocristalline anisotropy makes it easy to control the resonance frequency, acting on the magnetic anisotropy of the material by means of appropriate thermal treatments. The amorphous magnetic materials with positive magnetostriction constant, made by the Taylor technique (Marín & Hernando, 2004), are well known due to their availability for use in wireless sensors based on magnetoelastic resonance (Vázquez & Hernando, 1996). Some recent works show the possibility of using these materials as magnetoelastic biosensors(Shem et al., 2009; Xie et al., 2009). Other works show a detailed study of the magnetoelastic coupling phenomenon in ribbons (Hernando 1983). Recently, there has been published a development, for monitoring in situ the mass of a cell culture, based on the magnetoelastic resonance of ribbon shaped metallic glasses (Rivero et al., 2008). On the other hand, magnetic amorphous microwires coated with Pyrex have attracted much interest due to their particular properties and their simple manufacturing process based on the Taylor technique. The use of these materials can reduce the dimensions of the set-up and the Pyrex cover makes them appropriate for many applications in the medical field.

### **2.1** *In situ* **measurement of the mass evolution of cell culture**

Cell cultures constitute one of the most frequently used assays in biology and also one of the diagnostic methods most used in Medicine. The growing of several microorganism strains, like cells, bacteria and virus etc., under conditions in which atmosphere, temperature, humidity and nutrients are controlled have been studied.

On the other hand, the research on the treatment of tumours by hyperthermia, in the last decade, has been focused on the different behaviour of normal and tumour cells over temperature. Generally, normal cells show better temperature resistance than the tumour ones. Consequently, it is very important to determine the optimum temperature for hyperthermia treatments.

The monitoring of the progress of a cell culture is conventionally done by direct observation of the evolution that takes place on a culture plate, (the support on which the cells are

Magnetic Sensors for Biomedical Applications 129

frequency of the applied electromagnetic field as well as receiving the answer of the sensor

Fig. 1. Experimental set-up to measure the mass evolution of cell culture.

*t)* and *cos(*

To perform the measurement an electronic system is used. Its flowchart is shown in figure 2. By means of a DDS (1) (Direct Digital Synthesizer) device the values of two sinusoidal

difference is generated that is used by the D/A (Analogical/Digital) (3) and A/D (8)

signal by the D/A converter. This signal is amplified by means of a power amplifier (4). The amplified signal feeds the excitation/pick up system (5) that is made up by two opposite series connected coils, which generate an alternating magnetic field that energizes the magnetostrictive ribbons (6) and that also enables answer from the magnetoelastic sensor

The variations in the induced voltage created in the pick up system are converted into electric current variations by the voltage/current converter (7). By means of the analogical/digital converter we can obtained the digital measurement of the electric current that flows through the exciting coils. The digital signal processor (9) permits us to extract the in phase and in quadrature components of the current measured by (8) and by (10) we obtain, for each frequency, the magnitude of the impedance of the coil system, which makes it possible to measure the resonance frequency of the coils / magnetoelastic

*t*) are obtained. By means of (2) a fixed voltage

*t)* generated by (1) is transformed into an analogical

in function of the frequency.

signals in quadrature, *sin(*

to be picked up.

sensor setup.

converters. The sinusoidal signal *sin(*

placed), using a microscope. It is essential to have perfect control over the microenvironment in which the culture is developing to ensure that any change in the behaviour and multiplication of the cells is only ascribable to the cell behaviour in a given situation and not to poor culture conditions. For this reason, the cultures are carried out inside incubation chambers where it is possible to control factors such as humidity, pH and temperature. Among all these factors, probably the most important one is strict control of the temperature since it is a critical factor in the majority of the experiments performed with cells, particularly in mammalian ones. However when the evolution of the cells is observed using a microscope, it is necessary to extract the cells from the chamber, submitting them with what may result in undetermined damages due to changes in temperature, aside from the mechanical damages that take place in each measurement.

So a system that makes it possible to continuously quantify the mass evolution of a cellular culture "in situ", that is, without extraction from the incubation chamber would be very useful and to our knowledge, it does not exist. This sensor would enable the cellular growth to be studied accurately under different temperatures, without the periodical mechanical damage and the cooling-heating processes produced by the extraction and movement of the culture from the chamber to the microscope where the counting of the cells is performed.

One solution is a system sensor based on the magneto-elastic resonance of ferromagnetic amorphous ribbons. Other systems based on the same principle have been developed before for detecting other biological agents (Lakshmanan et al., 2007; Wan et al., 2007)

The system consists of the following elements (Fig.1):


The working of the device is as follows. Inside the culture plate designed for the device two ribbons of an amorphous magnetostrictive material with the same dimensions are placed in the compartments designed for them immersed in the culture environment. One of the ribbons acts as a reference, in order to evaluate the changes on the magnetoelastic resonance frequency due to possible changes of temperature or other factors that are not directly related to the evolution of the cell culture. So, it is immersed in one of the baths containing the culture environment but without cells. A seed of the cells, whose evolution and growth is being studied, is placed in the bath containing the other ribbon. By means of the coils system (excitation-pick up system) an electromagnetic field of frequency is applied over the whole set-up and the variations in the magnetic flux density, created by the sensor system, are collected. The designed electronic system makes it possible to change the

placed), using a microscope. It is essential to have perfect control over the microenvironment in which the culture is developing to ensure that any change in the behaviour and multiplication of the cells is only ascribable to the cell behaviour in a given situation and not to poor culture conditions. For this reason, the cultures are carried out inside incubation chambers where it is possible to control factors such as humidity, pH and temperature. Among all these factors, probably the most important one is strict control of the temperature since it is a critical factor in the majority of the experiments performed with cells, particularly in mammalian ones. However when the evolution of the cells is observed using a microscope, it is necessary to extract the cells from the chamber, submitting them with what may result in undetermined damages due to changes in temperature, aside from

So a system that makes it possible to continuously quantify the mass evolution of a cellular culture "in situ", that is, without extraction from the incubation chamber would be very useful and to our knowledge, it does not exist. This sensor would enable the cellular growth to be studied accurately under different temperatures, without the periodical mechanical damage and the cooling-heating processes produced by the extraction and movement of the culture from the chamber to the microscope where the counting of the cells is performed.

One solution is a system sensor based on the magneto-elastic resonance of ferromagnetic amorphous ribbons. Other systems based on the same principle have been developed before

 A culture plate that has been designed with two separate baths, each one containing an amorphous magnetoelastic ribbon with an iron based composition of area 40 x 4 mm2 and 15 microns in thickness, coated with 250 nm of TiO2 immersed in a culture medium. Only one bath is seeded with cells. So we have a continuous reference

An arrangement of two coils and a permanent magnet under the plate to apply the bias

A scanner impedance meter (Fig. 2), connected to the coils, which measures the coils

A software program developed to extract the ribbons resonance frequency from the

The working of the device is as follows. Inside the culture plate designed for the device two ribbons of an amorphous magnetostrictive material with the same dimensions are placed in the compartments designed for them immersed in the culture environment. One of the ribbons acts as a reference, in order to evaluate the changes on the magnetoelastic resonance frequency due to possible changes of temperature or other factors that are not directly related to the evolution of the cell culture. So, it is immersed in one of the baths containing the culture environment but without cells. A seed of the cells, whose evolution and growth is being studied, is placed in the bath containing the other ribbon. By means of the coils system (excitation-pick up system) an electromagnetic field of frequency is applied over the whole set-up and the variations in the magnetic flux density, created by the sensor system, are collected. The designed electronic system makes it possible to change the

for detecting other biological agents (Lakshmanan et al., 2007; Wan et al., 2007)

impedance around the resonance frequency of the ribbons.

the mechanical damages that take place in each measurement.

The system consists of the following elements (Fig.1):

independent of temperature.

and the alternating field.

impedance measurements.

frequency of the applied electromagnetic field as well as receiving the answer of the sensor in function of the frequency.

Fig. 1. Experimental set-up to measure the mass evolution of cell culture.

To perform the measurement an electronic system is used. Its flowchart is shown in figure 2. By means of a DDS (1) (Direct Digital Synthesizer) device the values of two sinusoidal signals in quadrature, *sin(t)* and *cos(t*) are obtained. By means of (2) a fixed voltage difference is generated that is used by the D/A (Analogical/Digital) (3) and A/D (8) converters. The sinusoidal signal *sin(t)* generated by (1) is transformed into an analogical signal by the D/A converter. This signal is amplified by means of a power amplifier (4). The amplified signal feeds the excitation/pick up system (5) that is made up by two opposite series connected coils, which generate an alternating magnetic field that energizes the magnetostrictive ribbons (6) and that also enables answer from the magnetoelastic sensor to be picked up.

The variations in the induced voltage created in the pick up system are converted into electric current variations by the voltage/current converter (7). By means of the analogical/digital converter we can obtained the digital measurement of the electric current that flows through the exciting coils. The digital signal processor (9) permits us to extract the in phase and in quadrature components of the current measured by (8) and by (10) we obtain, for each frequency, the magnitude of the impedance of the coil system, which makes it possible to measure the resonance frequency of the coils / magnetoelastic sensor setup.

Magnetic Sensors for Biomedical Applications 131

Fig. 3. Evolution of the resonance of ribbons arrangement. In the initial state A, both ribbons have the same resonance frequency. The left peak increases and decreases its frequency with

The Time of Prothrombine (TP), and the values that derive from it, like the International Normalized Ratio (INR), are used for determining the tendency of the blood to coagulate in the presence of possible biological disorders like hepatic failure or K vitamin deficiency. It is also used to control patients that take anticoagulation drugs like warfarina or acenocumarol to prevent coronary thrombosis processes in cardiac pathologies: atrial fibrillation, and auricular fibrillation, etc. In addition, due to the increase in life expectancy, an ever growing percentage of the population needs to replace one or more cardiac valves with a mechanical prosthesis and, in some cases, more than once. All these people must be submitted to a lifelong treatment using anticoagulants. This entails a permanent risk for them. So it is not rare that the problem of controlling the appropriate level of the anticoagulation agent in the treatment of several pathologies may affect about 1 – 2 % of people in the European Community. The Food and Drugs Administration (FDA) of USA estimates that about two million people begin a treatment with warfarin every year. These patients need to be controlled periodically due to the side effects of the treatment. These controls must be done

the amount of mass on the corresponding ribbon.

**2.2 Test of blood coagulation** 

1) Direct Digital Synthesizer; 2) Voltage reference; 3) D/A Converter; 4) Power amplifier; 5) Exciting/Pick up coils; 6) Magnetoelastic sensor; 7) Voltage/Current Converter; 8) A/D converter; 9) Digital signal processor; 10) Acquisition

Fig. 2. Flowchart of the scanning impedance meter:

When the frequency of the electromagnetic field matches the frequency of the magnetoelastic resonance of any of the ribbons, the transformation of magnetic energy into an elastic one reaches a maximum. This resonance is detected by the coil system, showing a characteristic peak in the measurement of the coil impedance. The change of the magnetic resonance frequency when the mass of a magnetostrictive material changes by *m* is given by (Grimes et al, 1999):

$$
\Delta \, \phi = -\phi \, \frac{\Delta \, m}{2 \, m} \tag{2}
$$

Where is the initial resonance frequency, m is is the initial mass, *m* is the change of mass and is the resonance frequency variation. Thus, the resonance frequency of a magnetoelastic ribbon decreases when the mass on the ribbon increases. Before the cells are seeded, both ribbons have the same resonance frequency and only one resonance peak is detected. When the culture cells on the seeded ribbon grow, two different peaks appear, corresponding to both ribbons, as shown in figure 3. The frequency interval between the peaks determines the amount of culture mass.

Preliminary experiments have been made with a human cervical cancer cell line (HeLa) in Dulbecco's modified Eagle medium, supplemented with 10% fetal bovine serum (FBS) and 1% (v/v) antibiotic solution. Changes in the mass culture of less than 1% have been detected.

1) Direct Digital Synthesizer; 2) Voltage reference; 3) D/A Converter; 4) Power amplifier; 5)

Digital signal processor; 10) Acquisition

by (Grimes et al, 1999):

been detected.

Fig. 2. Flowchart of the scanning impedance meter:

peaks determines the amount of culture mass.

Exciting/Pick up coils; 6) Magnetoelastic sensor; 7) Voltage/Current Converter; 8) A/D converter; 9)

When the frequency of the electromagnetic field matches the frequency of the magnetoelastic resonance of any of the ribbons, the transformation of magnetic energy into an elastic one reaches a maximum. This resonance is detected by the coil system, showing a characteristic peak in the measurement of the coil impedance. The change of the magnetic resonance frequency when the mass of a magnetostrictive material changes by *m* is given

2

*m* (2)

 

*<sup>m</sup>*

Where is the initial resonance frequency, m is is the initial mass, *m* is the change of mass and is the resonance frequency variation. Thus, the resonance frequency of a magnetoelastic ribbon decreases when the mass on the ribbon increases. Before the cells are seeded, both ribbons have the same resonance frequency and only one resonance peak is detected. When the culture cells on the seeded ribbon grow, two different peaks appear, corresponding to both ribbons, as shown in figure 3. The frequency interval between the

Preliminary experiments have been made with a human cervical cancer cell line (HeLa) in Dulbecco's modified Eagle medium, supplemented with 10% fetal bovine serum (FBS) and 1% (v/v) antibiotic solution. Changes in the mass culture of less than 1% have

Fig. 3. Evolution of the resonance of ribbons arrangement. In the initial state A, both ribbons have the same resonance frequency. The left peak increases and decreases its frequency with the amount of mass on the corresponding ribbon.

### **2.2 Test of blood coagulation**

The Time of Prothrombine (TP), and the values that derive from it, like the International Normalized Ratio (INR), are used for determining the tendency of the blood to coagulate in the presence of possible biological disorders like hepatic failure or K vitamin deficiency. It is also used to control patients that take anticoagulation drugs like warfarina or acenocumarol to prevent coronary thrombosis processes in cardiac pathologies: atrial fibrillation, and auricular fibrillation, etc. In addition, due to the increase in life expectancy, an ever growing percentage of the population needs to replace one or more cardiac valves with a mechanical prosthesis and, in some cases, more than once. All these people must be submitted to a lifelong treatment using anticoagulants. This entails a permanent risk for them. So it is not rare that the problem of controlling the appropriate level of the anticoagulation agent in the treatment of several pathologies may affect about 1 – 2 % of people in the European Community. The Food and Drugs Administration (FDA) of USA estimates that about two million people begin a treatment with warfarin every year. These patients need to be controlled periodically due to the side effects of the treatment. These controls must be done

Magnetic Sensors for Biomedical Applications 133

A signal generator that provides a sinusoidal voltage signal in a range of 10 – 50 KHz.

 Two power amplifiers, driven by the signal of the generator, which feed two equal coils with the microwire arrangements. The gain of amplifiers can be adjusted to obtain zero

A differential amplifier that gives the difference between the rectified voltages in the

A temperature controlled chamber in which the sensor system is introduced to perform

 A temperature sensor (8) that measures the temperature in the temperature controlled chamber. The signal of the temperature sensor is sent to a temperature controller device

Fig. 5. Study of the influence in the coagulation of blood with different amounts of coagulant agent. The amount of blood is 200 l, and was mixed with 5l of coagulant (curve A), 1l of

It can be observed that blood, in the presence of the greatest quantity of coagulant agent, coagulates in a time 10 times faster than the blood without the coagulant agent*.* The output potential, *VOUT*, of the differential amplifier shown in figure 4 is the difference between *VREF* (Voltage difference in the circuit of the reference coils) and *VBLOOD* (Voltage difference in the

Tests with blood samples that coagulate at different rates are illustrated in figure 5.

 Coil with reference arrangement (capillary + microwire + fluid of reference) (3) Coil with measurement arrangement (capillary + microwire + blood) (4)

(1)

signal before the test. (2)

 Two precision rectifiers (5) Two non-inductive resistors (6)

non-inductive resistors. (7)

the test at constant temperature of 25 ºC.

(9) that keeps the chamber temperature at 25 ºC.

coagulant (curve B), and without coagulant (curve C).

in hospital. Nowadays, there are some portable devices (Neel et al., 1998; Askew et al., 2010) that enable the control to be done more conveniently, but the results are not very reliable. The main causes of error are usually the influence of temperature and the amount of blood involved in the test. Other methods based on the measurement of blood viscosity (Drobrovol'skii et al., 1999) need a large amount of blood.

A sensor, based on a magnetoelastic material, can be used to determine the TP and the INR in patients under anticoagulation treatment, without the need for specialized staff or installations. The method is based on the variation in the magnetic permeability of a magnetoelastic microwire induced by the change on the blood viscosity when it coagulates. When the blood coagulates, the viscosity force applied to the immersed wire dissipates, as heat, a portion of the magnetic energy supplied by the magnetic field. Therefore the apparent magnetic permeability of the microwire decreases due to the magnetoelastic coupling. The experimental set-up compares this permeability with that of a reference wire immersed in an inalterable fluid. The absolute value of the measured signal tends to a maximum when the blood coagulates. The time to raise this maximum enables the TP and the INR to be calculated.

The sensor consists of two identical microwires, with an iron base, that are placed into two capillaries with tenths of mm. inner diameter and around 5 cm in length. These capillaries are surrounded by one coil each, which are fed by two power amplifiers driven by a signal generator. The capillaries are filled with blood and with a fluid of reference, respectively. The difference between both signals increases when the blood coagulation process begins and its absolute value tends to a maximum when the blood is fully clotted. The scheme of the experimental set-up used to measure the blood coagulation is illustrated in figure 4.

Fig. 4. Scheme of the experimental setup used to measure the blood coagulation.

The sensor system consists of the following components (see figure):

in hospital. Nowadays, there are some portable devices (Neel et al., 1998; Askew et al., 2010) that enable the control to be done more conveniently, but the results are not very reliable. The main causes of error are usually the influence of temperature and the amount of blood involved in the test. Other methods based on the measurement of blood viscosity

A sensor, based on a magnetoelastic material, can be used to determine the TP and the INR in patients under anticoagulation treatment, without the need for specialized staff or installations. The method is based on the variation in the magnetic permeability of a magnetoelastic microwire induced by the change on the blood viscosity when it coagulates. When the blood coagulates, the viscosity force applied to the immersed wire dissipates, as heat, a portion of the magnetic energy supplied by the magnetic field. Therefore the apparent magnetic permeability of the microwire decreases due to the magnetoelastic coupling. The experimental set-up compares this permeability with that of a reference wire immersed in an inalterable fluid. The absolute value of the measured signal tends to a maximum when the blood coagulates. The time to raise this maximum enables the TP and

The sensor consists of two identical microwires, with an iron base, that are placed into two capillaries with tenths of mm. inner diameter and around 5 cm in length. These capillaries are surrounded by one coil each, which are fed by two power amplifiers driven by a signal generator. The capillaries are filled with blood and with a fluid of reference, respectively. The difference between both signals increases when the blood coagulation process begins and its absolute value tends to a maximum when the blood is fully clotted. The scheme of the experimental set-up used to measure the blood coagulation is

Fig. 4. Scheme of the experimental setup used to measure the blood coagulation.

The sensor system consists of the following components (see figure):

(Drobrovol'skii et al., 1999) need a large amount of blood.

the INR to be calculated.

illustrated in figure 4.


Tests with blood samples that coagulate at different rates are illustrated in figure 5.

Fig. 5. Study of the influence in the coagulation of blood with different amounts of coagulant agent. The amount of blood is 200 l, and was mixed with 5l of coagulant (curve A), 1l of coagulant (curve B), and without coagulant (curve C).

It can be observed that blood, in the presence of the greatest quantity of coagulant agent, coagulates in a time 10 times faster than the blood without the coagulant agent*.* The output potential, *VOUT*, of the differential amplifier shown in figure 4 is the difference between *VREF* (Voltage difference in the circuit of the reference coils) and *VBLOOD* (Voltage difference in the

Magnetic Sensors for Biomedical Applications 135

**Vout Experimental**

 **VoutTheoretical**

**0 20 40 60 80**

**Time (min)**

Fig. 6. The points with a green circle represent the experimental data of the coagulation of blood without coagulant. The line in red represents the proposed approximation adjusted to

Heart valves are widely used in cardiac diseases. For example in 2002 in Spain 9269 heart valves were implanted as against 310 heart transplants. There are two kinds of heart valves, mechanical and biological ones. Biological heart valves, currently made with calf pericardium, have a similar shape to that of the original ones and better hemodynamic conditions than the mechanical ones. Moreover they have the advantage that the patient does not need lifelong treatment with anticoagulants, as happens with the mechanical valves. On the other hand, biological cardiac valves, or bioprostheses, have the inconvenience of their limited durability (about 10 years on average). What is more troublesome is the fact that they have an important dispersion that may be estimated in

These bioprostheses fail for several reasons, similar to those of the original ones and there are many factors that may contribute to their deterioration. The most important are biochemical degradation and mechanical damage of the tissue. Mechanical fatigue is the result of the great number of opening and closing cycles (approximately 30 million per year), which the valve is submitted to. Their effects are cumulative, and are expressed by

This means that it is difficult to determine the best moment for replacing the valve. The problem of the user getting it done too late must be balanced against the economic costs to the Social Security system, if is carried out unnecessarily early. So, a sensor is needed that

**2.3 Sensor system for early detection of heart valve bioprostheses failure** 

**-0,014**

plus/minus 3 years (Kouchoukos et al, 2003).

lineal ruptures and/or perforations.

**-0,012**

**-0,010**

**-0,008**

**-0,006**

**VOUT(V)**

the experiment.

**-0,004**

**-0,002**

**0,000**

**0,002**

circuit we are measuring the blood in). Both are *RL* circuits and the inductance *L* and resistance *RL:* 

$$L = \mu\_0 \frac{N^2}{l} \left( S\_c + \mu\_W S\_W \right) \qquad \qquad R\_L = \frac{2N \sqrt{\pi S\_C}}{\sigma\_{Cu} S\_{Cu}} \tag{3}$$

Being *<sup>W</sup>*the relative permeability of the microwire*, μ0* the permeability of free space, *N* the number of turns, *l* the length of the coil*, Cu* the copper conductivity and *SC* and *SW the* sections of the coil and the microwire, respectively.

Since in this setup, when *R0* and *RL << w L* then:

$$V\_S = V\_0 \ e^{i\alpha t} \quad \Longrightarrow \quad V = V\_0 \frac{R\_0}{\alpha L} e^{i\left(\alpha t - \frac{\pi}{2}Q\right)} \tag{4}$$

Once they are rectified, the voltage differences are:

$$V\_{REF} = V\_0 \frac{R\_0 \sqrt{2}}{\alpha \, L\_{REF}} \qquad \text{and} \qquad V\_{R\_{LOAD}} = V\_0 \frac{R\_0 \sqrt{2}}{\alpha \, L\_{R\_{LOAD}}} \tag{5}$$

Where *LREF* and *LBLOOD* are the inductances of the reference and measurement coils, respectively. Thus the output of the differential amplifier (see figure 1):

$$V\_{OUT} = V\_{REF} - V\_{RLOAD} = V\_0 \frac{R\_0 \sqrt{2}}{oo} \left(\frac{1}{L\_{REF}} - \frac{1}{L\_{RLOAD}}\right) \tag{6}$$

This output is taken to zero at the initial moment, adjusting the gain of the feeding amplifiers. From this moment, the permeability*, <sup>W</sup>*, of the microwire immersed in blood begins to decrease because of the effect of the viscosity force the blood exerts on it while it clots. This makes *LBLOOD* decrease as well.

The output of the differential amplifier depends on time as follows:

$$V\_{\rm OUT}(t) = V\_0 \frac{R\_0 \sqrt{2}}{\alpha} \left( \frac{1}{L\_{\rm RLOAD}(0)} - \frac{1}{L\_{\rm RLOAD}(t)} \right) = \frac{V\_0 \ R\_0 \sqrt{2}}{\alpha} \left( 1 - \frac{S\_\odot + S\_\mathrm{w} \,\mu\_\mathrm{w}(0)}{S\_\odot + S\_\mathrm{w} \,\mu\_\mathrm{w}(t)} \right) \tag{7}$$

Figure 6 shows the curve obtained from human blood without coagulant agent and the theoretical *VOUT(t)* curve, following the equation *(7).* In this expression the best adjustment to experimental results is obtained assuming a relative permeability change of the microwire during the coagulation process as:

$$
\mu\_W(t) = \mu\_{W,\alpha} + \left(\mu\_{W,0} - \mu\_{W,\alpha}\right) \exp\left(-\frac{t^2}{\tau^2}\right) \tag{8}
$$

Being W,0 and W, the measured values of the initial permeability and the permeability when the blood is completely coagulated, respectively, and a time constant that depends on the coagulation properties of the blood sample. The value of for the best adjustment to the experimental values enables the TP and INR to be determined.

circuit we are measuring the blood in). Both are *RL* circuits and the inductance *L* and

*<sup>t</sup> V V*<sup>0</sup>

Where *LREF* and *LBLOOD* are the inductances of the reference and measurement coils,

This output is taken to zero at the initial moment, adjusting the gain of the feeding

begins to decrease because of the effect of the viscosity force the blood exerts on it while it

*LBLOOD* (*t*)

 ( ) exp

Figure 6 shows the curve obtained from human blood without coagulant agent and the theoretical *VOUT(t)* curve, following the equation *(7).* In this expression the best adjustment to experimental results is obtained assuming a relative permeability change of the microwire

*R*<sup>0</sup> 2 

 

 <sup>2</sup> , ,0 , 2

 *W W WW*

Being W,0 and W, the measured values of the initial permeability and the permeability when the blood is completely coagulated, respectively, and a time constant that depends on the coagulation properties of the blood sample. The value of for the best adjustment to

 *<sup>V</sup>*<sup>0</sup> *<sup>R</sup>*<sup>0</sup> <sup>2</sup> *LBLOOD* (0)

1 *LREF*

   <sup>1</sup> *LBLOOD*

*<sup>W</sup> SW RL* <sup>2</sup>*<sup>N</sup>*

*<sup>W</sup>*the relative permeability of the microwire*, μ0* the permeability of free space, *N* the

*R*0 *L e i t*

*and VBLOOD V*<sup>0</sup>

*SC*

*Cu* the copper conductivity and *SC* and *SW the*

*R*<sup>0</sup> 2 *LBLOOD*

> 

*<sup>W</sup>*, of the microwire immersed in blood

<sup>1</sup> *SC SW*

 

*t t* (8)

*SC SW <sup>W</sup>* (*t*)

*<sup>W</sup>* (0)  

(7)

<sup>2</sup> (4)

(6)

(3)

(5)

*Cu SCu*

*<sup>l</sup> SC* 

resistance *RL:* 

Being  *L* 0 *N*2

sections of the coil and the microwire, respectively.

Once they are rectified, the voltage differences are:

*VREF V*<sup>0</sup>

amplifiers. From this moment, the permeability*,* 

*R*<sup>0</sup> 2 

 

 

the experimental values enables the TP and INR to be determined.

clots. This makes *LBLOOD* decrease as well.

*VOUT* (*t*) *V*<sup>0</sup>

during the coagulation process as:

*VS V*<sup>0</sup> *e<sup>i</sup>*

> *R*<sup>0</sup> 2 *LREF*

respectively. Thus the output of the differential amplifier (see figure 1):

*VOUT VREF VBLOOD V*<sup>0</sup>

The output of the differential amplifier depends on time as follows:

1 *LBLOOD* (0) <sup>1</sup>

Since in this setup, when *R0* and *RL << w L* then:

number of turns, *l* the length of the coil*,* 

Fig. 6. The points with a green circle represent the experimental data of the coagulation of blood without coagulant. The line in red represents the proposed approximation adjusted to the experiment.
