EVALUATION OF AN OPTICAL METHOD FOR THE REVELATION OF HEMOLYSIS IN VIVO

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UNIVERSITÀ DI PISA

FACOLTÀ DI INGEGNERIA

Corso di Laurea Magistrale in Ingegneria Biomedica

TESI DI LAUREA

EVALUATION OF AN OPTICAL METHOD FOR

THE REVELATION OF HEMOLYSIS IN VIVO

Relatori: Candidato:

Prof. ssa Arianna Menciassi Giulia Gerboni Dr.ssa Monica Vatteroni

Dr.ssa Maria Giovanna Trivella

Anno Accademico 2014/2015 23 Settembre 2014

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“The human body has approximately 25 trillion red blood cells flowing through its network of vessels at any given time. They converge at one main point:

the Heart.” TEDMED, “Imaging the Future of Medicine”

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INTRODUCTION

As indicated by a series of works and studies available in literature [1], cardiac diseases and failures are the principal cause of death in Europe as well as in other world countries. This leads to the increasing and continuous quest for painless diagnostic and therapeutic devices in order to treat cardiac pathologies or to detect them in their early stage. In this context, an intensive use of prosthesis and artificial devices, in order to replace heart functionalities or to monitor the blood conditions is performed, such as Ventricular Assistive Device (VAD), extracorporeal circulation therapies, dialysis devices. The artificial devices above mentioned have one negative outcome, as all the synthetic apparatus in contact with biological tissues: the induction of a response by the organism. So, in case of instrument in contact with the bloodstream, a consequence is the damage of the blood cellular part, in particular of the red blood cells. Indeed, this event is mainly related to the mechanical injury caused by high and non physiological shear stresses for blood fluid and in particular for its cellular component, associated with tube kinking and pump malfunctions. The principal outcome of this phenomenon is the decrease in blood capacity of oxygen carriage, due to the rupture of erythrocytes. Indeed, the red blood cells compose the main cellular component of human blood, representing the 40-45% of the total volume and they contain hemoglobin, a protein principally responsible for oxygen binding in the cardiocirculatory system. Moreover, in case of hemolysis, free plasma hemoglobin interacts with a series of metabolites, which are firstly toxic for kidneys and could also activate the coagulation cascade. Optical devices for the continuous and non invasive monitoring of hematic parameters have been proposed in literature, which are based on Near Infrared (NIR) Spectroscopy or Plasma Surface Reflectance Spectroscopy. However, up to date, the proposed devices do not have enough sensitivity to allow the detection of low hemolysis levels, which are the ones useful for the monitoring of biomechanical systems malfunctioning and failure, before the advent of serious consequences for the patients. So, to prevent them, it is needed to detect hemolysis in its early stage, when the percentage of hemolyzed blood is low. Studies report on a difference in the absorption coefficient , the scattering

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coefficient and the anisotropy factor , for whole and hemolyzed blood, in visible and NIR optical windows, however results are pour and related to high blood dilutions. This thesis is focused on the development of a device, minimally

invasive, in order to carry on an early diagnosis of the hemolysis induced by the artificial instruments above mentioned. The sensor functional principle is an optical one, in order to reduce the invasivity. Therefore, to conceive a device with

enhanced sensitivity is mandatory to start from making a precise optical characterization of whole and hemolyzed blood, at different levels of concentrations, starting from low ones. It is worth mentioning that, theoretically, in the NIR range these hypothesis are consistent because of the hemolytic process, and the consequent red blood cell lysis, lead to a remarkable reduction of blood scattering. As concern the visible range, a less pronounced phenomenon is predictable in whole blood, due to a possible different optical behavior among plasma free hemoglobin and that one contained into the erythrocytes. So, the first step for the development of this experimental work is the execution of a spectrophotometric analysis of whole and hemolyzed blood specimens, to find wavelengths in which the optic behavior of these two types of blood shows clear variations. After that, the exploitation of the results obtained should bring to the design of an appropriate device, which has to be minimally invasive, as previous mentioned, as well as miniaturized, biocompatible and easily implementable in an existing VAD for the cardiac support.

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CHAPTER I

HEMOLYSIS ISSUE

1.1 HUMAN BLOOD ANATOMY

Cardiovascular apparatus is responsible for the distribution of blood inside the human body and it is the core of a series of physiological processes, such as, for example, the oxygen and nutrients transport, the collection of catabolites, signaling and communication functions between different body districts through hormones and derivatives, defensive function and homeostasis maintenance.

Figure 1: Cardiovascular system.

Blood, which is a type of specialized connective tissue, constituted the ‘fluid vehicle’ through which the functions prior mentioned are carried out and it contains different components [2]:

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 Erythrocytes or red blood cells (RBCs): they represent the 40-45% of the total

blood volume. Their principal function is the oxygen transport from the lungs to the others tissues around the body and the collection of the greater part of carbon dioxide into the bodily fluid from the organism periphery to the pulmonary circle.

 Leucocytes or white blood cells (WBCs): they are a cellular population that occupy

the 1% of the total blood volume. Their fundamental function is to preserve the biological integrity of the human body, executing defensive mechanisms against pathogenic organisms of different origin and nature, such as viruses, bacteria and parasitics. Different types of leucocytes exist, among which granulocytes (neutrophils, basophils, eosinophils), monocytes and lymphocytes could be mentioned.

 Platelet or thrombocytes: they’re fragments of a cell originated from the bone

marrow, called megakaryocyte. They appear as biconvex discoid structures, with a diameter of 2-3 μm, and they are present only in the mammals blood. They are involved in the homeostatic process, in particular they’re a central element in the bleeding block during the coagulation cascade.

 Plasma: it’s a liquid which the blood cells are immersed in and it’s made up almost

exclusively of water, proteins and mineral salts. It constitutes the 55% of total blood volume and it includes among the principal proteic components albumin, bilirubin, lipids and hormones, necessary to maintain the blood osmotic pressure. The function of oxygen transport in blood is relatively low if compared to that of hemoglobin enclosed in the RBCs, but it increases in hyperbaric conditions. One of the principal function of blood is the storing and transport of the coagulation factors such as fibrin.

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Figure 2: Human blood components.

As mentioned above, the RBCs are the most diffused cells into the bloodstream (4.5-5 millions/mm3_{in women and 5-6 millions/mm}3_{in men). Erythrocytes remain}

confined in the hematic torrent for all their lifetime, which is 120 days, together with other cell forms not completely mature, such ad the Howell-Jolly corps and Cabot rings [3]. RBCs appear as biconcave discs with variable thickness, typically 0.8 μm at the center and 1.9 μm at the periphery; the average diameter is 7.5 μm, but they could reach 9 μm (macrocytes) or 6 μm (microcytes).

Figure 3: Erythrocytes dimensions and principal form variations

This particular structure improves the ratio between surface and volume of the cell, so facilitates the gaseous exchanges and it bestows on erythrocytes an elevated deformability that allows them to turn, to twist, to squeeze and to bend so that they

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are able to pass through really thin blood vessel. In humans, the mature RBCs contain almost exclusively hemoglobin, a globular protein which bounds oxygen weakly and in a reversible way and it gives to these hematic cells their typical coloring. As a matter of fact, the nucleus and mitochondria [4] are excreted during the differentiation of the progenitor cells, while the other cythoplasmic organelles are disintegrated or expelled.

1.2 HEMOLYSIS

Erythrocytes membrane rupture, which causes the release of hemoglobin and of the other cellular component into the blood plasma, is called hemolysis.

Figure 4: Erythrocyte breakage.

The fundamental consequence of this event is the decrease of erythrocytes capability to transport oxygen. Furthermore, after the hemolytic process, free plasma hemoglobin (fHb) interacts with a lot of metabolites and it is associated with a bilirubin enhancement, conjugated and not conjugated, and also an increase of lactate dehydrogenase (LDH). The levels of haptoglobin, a mucoprotein of the electrophoretic group of the alpha-globulin (Hp), are maintained low. As a matter of fact, the plasmatic haptoglobin has the properties to combine with the extraglobular hemoglobin to form a complex haptoglobin-hemoglobin (Hp-Hb), that is rapidly captured and eliminated by the cells of the reticulo-endothelial system (RES). After an hemolytic crisis, the excessive release of free hemoglobin in blood plasma brings to the fast consumption of plasmatic haptoglobin and the clearance of the Hp-Hb complexes mediated by the SRE takes to a pathologic condition in few hours, linked to a decrease of the haptoglobin in the bloodstream, which generally endures for several

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days. In cronical hemolysis cases, for example in pernicious anemia, the plasmatic haptoglobin absence is the standard. Other consequences of hemolysis could be an activation of the coagulation cascade and the free plasma hemoglobin toxicity for kidneys, especially in elevated concentrations.

Figure 5: Principal consequences of intravascular hemolysis.

The hemolytic process could happen for different causes, in-vivo and in-vitro. Physiologically this event takes place in the spleen, for erythrocytes natural turnover (1-2% of the total RBCs’ population a day), but above these reference values it becomes pathological, bringing to various anemic forms, at different degrees of gravity.

1.2.1 In-vitro hemolysis

In vitro hemolysis derived principally from problems during the collection and/or mechanical manipulation of the specimen and it’s also linked to the use of mechanical devices that submit the sample to elevated shear stresses, as happened during the extracorporeal circulation procedures. The current standard techniques for

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hemolysis degree revelation are principally related to the visual inspection of the sample color after collection and the use of a color card after blood centrifugation. As a matter of fact, in the second procedure mentioned, prior to analyze the sample. a blood centrifugation is performed, to separate the liquid and the corpuscolated part in order to quantify, even if grossly, free hemoglobin distributed in human blood plasma and/or in serum. These methods involved a limited precision, linked to the operators experience and subjectivity and they often bring to the analysis of contaminated samples, with consequent inaccurate results.

Figure 6: Color levels for the identification of hemolysis in serum and blood (numeric values indicate Hb concentrations [mg/dL]).

Alternatively, for the hemolysis degree control in the specimens after collection, as happened for the revelation of other hematic parameters, automatic

instrumentations could be used, based on impedance, spectroscopic, laser ( flow cytometry) or photometric methods. Also these techniques involved the blood sample

centrifugation, to separate the different components and, particularly, it’s useful to isolate blood plasma, in order to discriminate the free hemoglobin percentages.

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In several cases the device report an “hemolytic index” (HI), not useful for diagnostic methodologies rather than for the determination of the sample conditions. Sometimes to quantify the hemolysis level, instead of considering the evaluation of the presence and the quantity of free plasma hemoglobin, it is convenient to proceed with a complementary approach, that is to count the number of erythrocytes in the specimen. As a matter of fact, after the hemolytic event we have both the phenomena: RBCs rupture and the consequent release of free hemoglobin in blood plasma.

Figure 8: Chamber for the cells count.

To effectuate the counting process, the starting point is the count performed by the operator, using specific chamber’s structure (Fig. 8). This approach has a strong percentage of variability, so it has been progressively replaced by an automatic counter of cells, among which the ultimate models use a laser principle. In-vitro methodologies for the quantification of the content of free plasma hemoglobin are implemented in the above cited hematological analyzer as additional feature, but they could also be utilized as single specimen [5].

For example, a test used in clinical procedures is the Cyanomethemoglobin or Drabkin

test: the optical characteristics of the compound, formed after the reaction among

methemoglobin and hydrogen cyanide in a standard solution containing an appropriate reagent [6], are exploited for the spectrophotometric evaluation of the hemoglobin content.

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Figure 9: Correlation between absorbance and hemoglobin content in the specimen treated with the Drabkin test’s procedure.

An interesting trend is point-of-care tests (POCTs), a series of analysis performed in proximity of the care and assistance site, in the most comfortable and immediate way for the patient. These procedures are often realized with transportable devices, laptops, palmtops and kit tests and they allow to take diagnostic and therapeutic decisions with greater immediacy, as well as to permit a greater cheapness and to use a reduced amount of blood for the analysis. Together with glycemic test, hemogasanalysis, rapid coagulation test, the various types of POCTs include also test for the evaluation of the hemoglobin content. At the South Florida university, researchers are developing an “Hemolysis Sensor”: the device could be included in a syringe for the blood sample collection and in a lab-on-chip, to permit the evaluation of the patient blood hemolysis, after the standard collection procedure [7] .

1.2.2 In-vivo hemolysis

Intravascular hemolysis, which is the hemolysis that takes place into the blood vessels, could be caused by a series of factors, such as medical conditions, parasitic, autoimmune disorders, generic disorders or blood with low solutes concentration. Other principal causes are also related to chemical, thermal and mechanical events. The chemical phenomena that could originate the erythrocytes breakage are:

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 Poisons, toxins or also drugs;

 Differences in osmotic pressure, which cause the entering of water into the cells and the consequent cells breakage;

 Blood transfusions with donors not compatible, that bring to the ‘labeling’ of the transfused erythrocytes with antibodies so that these blood cells are attacked by immune defenses of the receiving.

The temperature is another factor which influences strongly the RBCs’ membrane deformability. As a matter of fact, hemolysis is related to:

 Temperature over 40°C;

 Low temperatures: as the human cells in general, the red blood cells could lyse if cooled down under the freezing point, without the use of a cryopreserving agent or a strict temperature;

 Rapid temperature variation.

Also elevated mechanical stresses on the cell membranes could induce hemolysis. As a matter of fact, for their structure and conformation, the RBCs are resistant to compression stresses but they are really sensitive to the traction ones: pressures under the atmospheric value and shear stresses elevated on hematic cells bring to hemolysis [8]. To evaluate the entity of the hemolytic process, not only the tangential stress must be considered but also the time during which the erythrocytes are subject to these stresses: the RBCs’ breakage is related both to the stress value and the time for which this fatigue has been applied. Particularly, the red blood cells, and the hematic cells in general, are submitted to non physiological stress conditions when mechanical devices in contact with blood are used for assistance or therapies, such as in extracorporeal circulation procedures, dialysis or cardiac pump implant.

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1.2.3 Non invasive techniques for the monitoring of the blood

properties

Instrumentation for the rapid and accurate evaluation of the hemoglobin content have a lot of applications, especially in emergency ward or pre hospital trauma care and/or to take treatment and rapid triage decisions, based on a few informations on the patient. The use of non invasive techniques is fundamental to reduce the patient trauma and procedure costs [9].

Among these, we found:

 Methods based on conductance phenomena: the monitoring of hematocrit values

with electrical admittance plethysmography, in which, during the pulsation, the modification of blood volume in the finger is related to the modification of the conductivity properties of the medium. The finger is immersed in an electrolytic solution, whom admittance is equal to that of the finger itself so that the conductivity variation in the electrolytic solution could be correlated to the conductivity of arteries and also to hematocrit. Difficulties associated to this method are linked to temperature variations, different intra- and extra-cellular ions percentages and to the presence of other compounds in the bloodstream;

 Use of spectrophotometric imaging: a combination of optical non-invasive techniques, for the evaluation of hematocrit, by considering the hemoglobin properties as chromophore. For example, the use of devices that combine NIR imagers for the identification of blood vessels and that estimate the concentration of hemoglobin by means of the absorption characteristics of vessels;

 NIR spectroscopy in transmission, based on the transcutaneous illumination of the

finger. Experiments based on the use of a NIR impulse at a single isosbestic wavelength (805 nm), coupled with a sound micrometer, are useful to monitor the pulsatile changes in the optical path through the finger and to correct the diameter variation of the finger inter-patient;

 Reflectance spectroscopy, that measures quantitatively the colour and the intensity

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 Ultrasounds and optoacustic spectroscopy: the rapid thermal expansion of the

tissue related to the laser beam absorption creates an optoacustic pressure wave, whom characteristics depend on the analytes.

Non invasive optical devices are developed for hemolysis evaluation, which function in visible and near infrared. These are utilized mostly for the monitoring of biomedical instrumentation related to the extracorporeal circulation, dialysis or to identify complications deriving from the use of cardiac pumps.

1.2.4 Examples of optical devices for the hemolysis

monitoring

Various optical systems for blood monitoring have been proposed, among which we could mention the multiple scattering spectroscopy, photoacustic spectroscopy and Raman spectroscopy [10].

Especially in patients subject to extracorporeal therapies, the Plasma Surface

Reflectance Spectroscopy (PSRS) [11] have been proposed for the analysis and the

quantitative optical and non invasive diagnosis of blood abnormalities. It deals with a reflectometry based on optical fibers with oblique incidence on the hematic surface, in order to extract only the optical characteristics of the blood plasma. The basic principle of this procedure is made up on two types of combinated analysis:

 Reflected light in the range 450-600 nm changes, related to the free hemoglobin content in plasma, which value is not influenced by the hematocrit variation;

 Instead, in the wavelength range 600-800 nm, the spectrum obtained in reflection is influenced both by hematocrit variation and by hemolysis degree.

The development of this system permits the extraction of optical characteristics of blood plasma and RBCs separately, without the centrifugation step.

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Figure 10: Variations on blood optical density related to the content of free plasma hemoglobin (upper) and hematocrit (lower).

Other studies consider the use of the Near Infrared Reflectance Spectroscopy (NIRS) to reveal hemolysis [12]. An example for a set-up is made up of an integrated optical sensor that works at three wavelengths (660nm, 730nm and 830nm), measuring the reflected light.

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Figure 11: NIRS devices outline.

From experimental results, it is verified that there is an enhancement of free plasma hemoglobin in blood, related to the mechanical pumping process, and it brings to a decrease of the reflected light relevated for all the three selected wavelength (Fig. 12).

Figure 12: Reflected light variation revealed from NIRS sensor, considering the variation of plasma fHb.

This system could be useful also for in-vitro detection of blood saturation, which is another important parameter for patient monitoring.

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1.3 MECHANICAL DEVICES IN CONTACT WITH

BLOODSTREAM

Heart diseases, term with whom a general heart muscle pathology is indicated, could be grouped in macro areas, such as congenital heart diseases, valvular heart diseases, infective endocarditis, cardiomyopathy. As indicated in various study in literature,

heart muscle problems are one of the prior causes of death in Europe and in the USA [1]. The elevated incidence of these types of pathologies have brought to the increase of the use of artificial devices, in order to replace the natural heart functionalities. These systems could be used for extracorporeal circulation or as implantable devices which partially or entirely substitute the pumping function of blood.

Figure 13: Device for extracorporeal circulation (ECMO).

In the first category, extracorporeal circulation systems, it is included the heart lung machine that, by substituting temporary the cardiopulmonary functions, is used in cardiosurgery environment to guarantee the surviving of patients during operations or, less frequently, it gives a cardiocirculatory support to patients affected by heart failures. In the second one, artificial heart or cardiac pumps are included.

1.3.1 Cardiac pumps

Heart assistive apparatus are mechanical devices that have gained more and more importance as instruments for heart failure and disease treatment. Their principal outcome is the maintenance of blood circulation, to permit a sufficient oxygen supply to organs and body tissues when the heart is not able to perform this necessary

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function autonomously. These devices are based on a series of physical principles of pumping and they include simple instrument as the intra aortic balloon pump to arrive to entirely artificial heart, with time of implantation and use that varies from few hours to chronically [13].

Figure 14: Types of cardiac pumps.

Principally, the cardiac pumps could be divided in two groups: displacement or rotary pumps.

Rotary pumps have a series of theoretical and practical advantages in terms of a smaller blood damage degree, limited dimensions, limited post-operatory progress. The use of displacement pumps instead is restricted to a few hours, because of the blood damage induced and the elevated dose of anticoagulant administered to the patients during the implant period. Other deteriorations of the cardiac function deserved more efficient instrument of support, as microaxial centrifugal pumps or pulsating flux ones, as well as pneumatically driven devices.

Microaxial pumps have the advantage to be minimally invasive and easily implantable. For intervention periods of mean duration, variable from few days to months, pneumatically devices with positive displacement are preferred, used as single or biventricular support.

For longer period of treatment, from months event to the two years, because of the common lack of heart donors or to extended recovery times, electromechanical

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assistive devices are used, completely implantable, called Ventricular Assistive Devices (VADs), in clinical use in the USA since 1984 and in Europe since 1993.

1.3.2 Ventricular Assistive Devices (VADs)

A ventricular assistive device [14] is an electromechanical instrument used to support partially or totally the cardiac function and to maintain the blood stream in people with heart diseases. The ventricular system apparatus is made up by a principal unit, that simulate the artificial ventricle, and that is placed in the abdomen; there is also a draw blood zone constituted by a duct placed at the top of the ventricle and an insertion zone represented by a duct in which the blood is pushed from the artificial ventricle directly to the aorta. Differently from what happened with the use of totally artificial hearts, which replace entirely the cardiac functionality and could deserve the complete removal of the natural heart, VADs could assist the right ventricle (RVAD) or left (LVAD) or both the lower cardiac chambers working in parallel with the heart muscle. The LVAD is the most used device for the blood pumping from the left ventricle to the aorta, so towards the peripheral circulation.

Figure 15: Types of VADs and implant examples.

These devices could be used for restricted times, as recovery bridges after heart attacks or cardiac surgery operation, or as ‘destination therapy’, as an alternative to the transplant, in a general context of lacking of donors and compatibility problems. Mostly, as bridge for a myocardial recovery, the use of these devices as therapeutic instruments is quite diffused: as a matter of fact, it has been demonstrated that

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putting an organ to rest could facilitate the rehabilitation and the improvement of the lost performances and, besides, by letting an effective and extended decompression of the left ventricle, which is discharge from a lot of work without the loss of the right values of flux and pressure, it is possible to expect an improvement of the right ventricle and the pulmonary circulation as well. Pumps used in VADs could belong to two principal categories, pulsating or positive displacement devices. Pulsating VADs mime the pulsating action of natural heart, while the devices with continuous flux pumps are smaller and more enduring as well as equipped with both centrifugal pumps and axial ones.

1.3.3 Complications deriving from the VADs implant

In case of employment of these mechanical devices in contact with the bloodstream, the continuous monitoring of the chemical composition of blood is fundamental, to evaluate and to prevent anemia, infection, infarction and to control possible malfunctioning events. As a matter of fact, there are a series of complications related to the use of artificial devices which enter in contact with the systemic blood flow, connected to a lot of factors, such as:

 thrombogenicity of the material used in contact with the blood, responsible for the elevated incidence of bleeding and thromboembolitic consequences;

 infections incidence, especially in case of implantable materials, related to limited biocompatibility;

 bleedings, mainly in the period immediately after the surgical implant.

 Hemolysis [15].

This excessive fatigue derived principally from the blood rubbing on the pipes of the mechanical device or from general pump malfunctioning. As principal consequence of hemolysis there is the decrease in blood capability of oxygen transport and, moreover, the hemolytic process is autocatalytic. Therefore, prior to have serious consequences for the patient, it seems to be fundamental the early diagnosis of small

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hemolysis percentages, using minimally invasive methods in order to reduce patient pain and time of intervention.

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CHAPTER II:

EXPERIMENTAL SESSIONS

2.1 BLOOD OPTICAL PROPERTIES

Blood properties, in particular the rheological and optical ones, are strictly related to red blood cells characteristics. Optically, blood behavior varies accordingly to different factors, such as different flux conditions, oxygenation, the considered wavelength range, hematocrit. Moreover, the modalities of sample preparation as well as the measuring conditions, influence the obtained optical coefficients. In general, the interaction of light with tissues, especially in the visible and infrared (IR) ranges, is characterized by two phenomena: absorption and scattering.

2.1.1 Absorption

The absorption process is defined as the set of events in which the photon energy interacts with a molecule without the emission of a second photon, and it’s correlated to the wavelength of the incident radiation and to the presence of specific substances, responsible for the absorption by the analyzed tissues: the chromophores. In blood, the fundamental chromophore is represented by the heme functional group (Figure 16) . In this molecule iron is contained and its concentration, together with its oxidation state, determinate the intensity and the position of the absorption band of blood, in the visible range.

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In blood, the absorption is also influenced by the presence of other substances, such as proteins and molecules in the UV, while it’s strongly related to the water absorption properties in the IR range [16].

Figure 17: Absorption coefficient of the principal biological tissues.

2.1.2 Scattering

As concern scattering phenomenon, the direction of the photon changes respect to that of the incident one, after the interaction with an object, defined as ‘scatterer’. Two scattering types are identifiable:

 Elastic scattering: photons don’t change their energy during the scattering process;

 Inelastic scattering: in this case the energy and, consequently, the incident photon wavelength, change when the particle is scattered.

Moreover, scattering theory includes three different types of this phenomenon, related to the wavelength λ and the particle radius :

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Tipologia

Raleigh Scattering

Mie Scattering

Reflective Scattering

Table 1: Types of scattering.

Considering blood in visible and near IR ranges (400-1000 nm), the behavior of the scattering coefficient is obtained typically referring to the Mie theory. This theoretical approach, called also Lorenz-Mie or Lorenz-Mie-Debye, derives from an analytic solution of Maxwell equation for the scattering of the electromagnetic radiations, considering a spherical approximation of the RBCs shape [17]. For more complex erythrocytes shapes, extensions and corrections of the classical theory are performed, and the solution is expressed in series of infinite terms.

2.1.3 Optical blood parameters

To proceed to the optical characterization of a substance or, more specifically, of a biological tissue, the parameters and coefficients that characterize its interaction with light spectrum are given. Principally, these are the absorption coefficient , scattering coefficient and anisotropy coefficient .

The absorption coefficient for a compound with a certain concentration c _is

obtained by:

,

where is the extinction coefficient or specific absorbance [ _{, which}

corresponds to the absorption coefficient for concentration unit. Instead, procures informations about the behavior of the tissue in absorption. The reciprocal of this value ( ) gives the absorption length, that is to say the value of the distance after which lights that crosses the body is attenuated by a factor of with respect to its initial value, measured in millimeters. As concern scattering, in blood this

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phenomenon is fundamental and related to the RBCs presence. As a matter of fact, the difference among the refraction index of blood plasma and the one of hemoglobin contained in erythrocytes (Figure 18) as well as RBCs form, volume and orientation, promote the scattering phenomenon.

Figure 18: Refraction indexes of hemoglobin (left side) and plasma (right side).

To understand the scattering phenomenon it is useful to resort to two coefficients:

or scattering coefficient and the anisotropy coefficient g, which, in particular, specifies the type of predominant scattering in the tissue. This second parameter varies between -1 (backscattering) and +1 (forward scattering), assuming zero value if an isotropic scattering is present, so without a preferential direction. Sometimes it could be given a reduced scattering coefficient, which summarizes in a unique value all the information related to the process, identified by the following formula:

Scattering event is more complex to analyze than absorption; so, there’s the need to draw upon a phase function to characterize the biological tissue behavior. There are various types of this function analyzed in literature, for example the Mie one, related to the famous theory, the one of Henyey-Greenstein, obtained as a particular case of the Gegenbauer two-parameters scattering function [18], or other functions[19].

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Figure 19: Comparison among different phase functions for red blood cells.

In case of Mie function, considering a physiological hematocrit value of 0.41, typical values of optical coefficients obtained at 665 nm are

, _, _.

By using Henyey-Greenstein function and by considering an hematocrit of 0.45-0.46 and a blood oxygenation of 98%, at 633 nm we obtain:

, _, _.

Even if the optical behavior of blood is strictly related to hemoglobin properties and spectra, relevant differences between the optical characteristics of blood and of an hemoglobin solution are present. For example:

 Absorption flattening, that brings to an increase of the absorption coefficient for solution containing hemoglobin if compared to those ones with whole blood. These

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differences are clear mostly at the maximum hemoglobin absorption band, called also

Soret Band (420-450nm) and the mentioned effect is negligible at physiological

hematocrit;

 Sieve effect, which appears when light doesn’t encounte the strong absorbing RBCs

while it crosses the blood. This phenomenon predominates at low hematocrit values and it involves a low luminous flux attenuation;

 Detour effect, which is characterized, in antithesis with the previous one, by a light

refraction into the red blood cells. This effect is more pronounced at physiological hematocrit and it brings to an increase of blood absorption, mostly in the hemoglobin maximum absorption band.

Figure 20: Absorption flattening effect.

Beyond the heme group contained in hemoglobin, which is the principal chromophore in blood and influences the blood spectra trend, directly as concern absorption and indirectly scattering, there are also other substances in blood plasma that have to be considered in order to completely understand the optical behavior of this biological fluid. As concern absorption, especially in the visible range (400-700 nm), we have the influence of a series of molecules and proteic plasmatic compounds, such as bilirubin, albumin, icterus, lipemia, which provoke systematic errors, especially in the laboratory procedures [20].

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Figure 21: Absorption spectra of interfering substances in blood plasma.

For example, bilirubin, which is a yellow-red pigment that is formed by the senescent red blood cells rupture in the reticuloendothelial system for the 80% and, by the serum hemoproteins catabolism for the remaining 20% , it has an absorption spectrum included between 340-500 nm, as bilirubin and peroxidases. Lipemia, visible as the plasma samples turbidity, is principally due to the increase in triglycerides number. The lipemia influence is different from that of icterus and bilirubin and it is concentrated principally on the alteration of the scattering parameters, which disturb light transmission through the sample. The scattering degree produced depends on the number, dimension and refraction index of the suspended lipidic particles. Among all these causes of influence, as concern the blood sample analysis as well as more specific analysis of serum and plasma specimens, it’s important to consider also the hemolysis factor, that directly influences the modification of scattering and absorption parameters. In literature, we could find a lot of material related to the revelation of blood optical properties, using different techniques, direct and indirect. One of the most extensive study on the macroscopic optical properties of RBCs suspended in a phosphate buffer saline solution (PBS), in different physiological and biochemical conditions (such as hematocrit value, oxygen saturation, flux velocity, osmolarity and hemolysis) has been conducted by Roggan et al. [21], who has worked with a technique of double sphere integration to obtained optical coefficients with the Inverse Monte Carlo method. Bosschaart [22] has described the optical properties of blood, by considering various physical and methodological factors of influence, in the range 250-2500 nm. This characterization

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has been performed with direct measuring methods, sided by theoretical approaches, mostly as concern the scattering properties of blood. In particular, the calculated optical spectra are given by combining the Kramer Kronig analysis together with the analytic scattering theory, extended by the Percus-Yevick factors, which consider the dependent scattering effect in whole blood.

Figure 22: Flux diagram about inverse Monte Carlo Simulation (IMCS).

Moreover, in this work, mathematical formulas obtained analyzing a blood sample with physiological hematocrit are presented, which are useful to scale the numeric values given for the optical coefficients in case of different hematocrit values. A similar approach has been followed by Friebel [23], who has determined the blood optical properties in the range 250-1100 nm, considering this time a new algorithm for the phase function determination, in order to create a model for the scattering process.

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Figure 23: Absorption coefficients (upper) and scattering ones (lower) of blood with 45% hematocrit value [22].

The best results have been obtained with the Reynolds-McCormick phase function:

,

with , and , which represents the probability that a photon which travels in s direction is scattered in the direction, with θ angle between and

.

This equation, respect to the values obtained with the Mie model, permits to keep under consideration the non spherical shape of erythrocytes, the coupling among the

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absorption and the scattering phenomena, multiple scattering events and other interferences.

Figure 24: (a) absorption coefficient, (b) scattering coefficient, (c) anisotropy coefficient, (d) RBCs reduced scattering coefficient in flux condition (shear rate 600 _{), with hematocrit value of 0.84, compared to the}

absorption coefficient of an hemoglobin solution with note concentration (0.27g/dL) , all values calculated using the Mie theory together with values found in literature [23].

Moreover, considering that RBCs are deformable cells that assume a specific conformation if subjected to shear stresses of different entity, the greater part of optical characterization of this species is carried out focusing on the importance of the flux conditions. As a matter of fact, Klosb et al. [24] have demonstrated that in whole blood samples we have a minimum in light transmission when cells are dispersed and randomly oriented, while aggregation produces an increase in incident light transmission.

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Figure 25: Light transmission related to different shear rates.

The principal chromophore in blood is hemoglobin, which is responsible for its optical behavior. Hemoglobin is present in different forms and types, as methahemoglobin, ( ), carboxyhemoglobin ( ), reduced hemoglobin ( ), oxyhemoglobin ( ), with different trends of the optical coefficient, according to the variation of the considered wavelength [9], as we could verify by the trend of the absorption coefficient visible in Figure 26 [25].

Figure 26: Absorption spectra of water and hemoglobin derivatives, in wavelength range between 500 and 1300 nm.

Nowadays, hemolysis and its influence on the optical behavior of blood, in visible and IR ranges, is gaining more and more importance, especially related to the evaluation of the biomechanical devices functioning. Indeed, these systems enter in contact with

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the bloodstream because of they are more and more diffuse for the treatment of various pathologies or complications in the cardiocirculatory apparatus. In literature, there are several characterizations that indicate the variation in the absorption coefficient trend as well as in the scattering and the anisotropy one, related to the growing degree of hemolysis, even if data are still preliminary. Indeed, there are optical parameters values, which are gathered from blood sample with elevated degree of dilution [26], and the non linearity of the scattering process doesn’t permit to scale the values obtained in case of physiological hematocrit. Meinke et al. [27] gives a trend for absorbance curves for whole blood samples and completely hemolyzed ones. Tuchin reports ([28], [29]) an in-depth characterization of the optical properties of biological tissues, among which there is blood: particularly, it presents results of a theoretical model based on Mie theory, in the context of the optical clearing analysis and it shows the optical hematological coefficient variation in the spectral range of visible and near infrared [30]. As explained in this work, the scattering coefficient ( Figure 27) is 30-40% reduced for all the wavelength analyzed, for hemolysis percentages over the 20%, while the absorption coefficient (Figure 28) reduction is localized in the Soret Band, spectral range in which hemoglobin has the maximum absorption, around the 415 nm, while in the NIR range (700-1000 nm) we have a maximum decrease of the 8%.

Figure 27: Scattering coefficient variations for different hemolysis degrees.

Currently, studies are in progress at the Laser-und Medizin-Technology (LMTB) in Berlin [31], as concern the hemolysis impact on optical properties of blood and the

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preliminary results shows a different trend from those revealed by Tuchin with its theoretical model, mostly regarding the absorption coefficient. Indeed, in the study they have encountered a slightly increase of , correlated with the increase of hemolysis in the sample. Effect which could be explained considering that the absorbing hemoglobin, after the exit from the cell, has a more uniform distribution in the blood plasma.

Figure 28: Absorption coefficient variation related to different hemolysis percentages.

Instead, the reduced scattering coefficient decreases almost linearly: the exit of hemoglobin brings to a matching between refraction index of the RBCs inner part and the one of blood plasma. Moreover, in case of complete hemolysis, the scattering coefficient is non zero, and it is possible to find a residual scattering effect due to the ghost cells, so to the erythrocytes membranes, i.e. the disintegrated erythrocytes that remain in suspension [32].

Because of the presence of poor and contradictory data on several points, for the development of a sensor, in order to reveal low free hemoglobin levels in plasma, it is necessary to start from a complete optical analysis, which permits to identify the trend of the optical coefficients, according to different hemolysis percentages.

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2.2 FIRST EXPERIMENTAL SETUP

To make the experiments, the initial idea deals with the realization of different blood sample, with increasing and controlled hemolysis degrees, to analyze the differences in the optical behavior.

2.2.1 Hemolyzing agent identification

The first step for the identification of the suitable setup concerns the determination of the modality of preparation of hemolyzed samples. In literature, different processes to create hemolysis in vitro are presented, utilizing chemical and physical procedures. For example, rapid variations of temperature over 42°C create hemolysis, temperatures under the freezing ones as well as the vigorous agitation of the sample have the same effect. As soluble compounds that have to be added to blood to create hemolysis, there are amphoteric surfactants and compounds of the nitrous acid, sodium azide (0.5g/L) and ad hoc reagents for hemolyzed preparations. The drug induced hemolysis is quite rare and it happens consequently to two phenomena:

 Toxic hemolysis, related to a direct toxicity of the drug, of its metabolites or of a

bulking agent present in the formulation;

 Allergic hemolysis, caused by an immunological reaction in patients, sensitized to

a drug.

For example, the saponine parietally injection [33] determinates hemolysis, while its oral assumption doesn’t produce this poisonous effect, considering that their hemolytic activity is carried out only if the molecule remains intact. Distill water and its hypotonic solutions bring to osmotic hemolysis: a greater concentration of water is present in the solution with respect to that one into the RBC, so water tends to enter into the hematic cell which first blows up and then explodes.

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Figure 29: Red blood cells suspended in isotonic solution (A), hypertonic (B) and hypotonic one (C).

Among the hemolyzing solutions there are also the Hemolysins [34], proteins and lipids that cause RBCs lysis, by damaging the cellular membrane. As hemolizing agent for the experiment, the TritonX-100 [35] has been used, which is an amphoteric non-ionic surfactant that contains an hydrophilic group of polyethylene glycol and a lipophilic or hydrophobic group.

Figure 30: Chemical formula of TritonX-100.

This detergent is commonly used in laboratories and in biological analysis procedures, principally to permeabilize the eukaryotic cell membrane or in conjunction with other substances, to solubilize the membrane proteins in their native state. Other applications predict the use of TritonX-100 as part of the tampon solution for DNA extraction or, exiting from the biological context, among the pasty liquid compounds or the dried ones, into industrial products and delicate detergents. In the different experiments, hemolyzing solutions have been prepared adding different percentages of TritonX-100 to a basis of PBS, a tampon compound frequently used in the biological research for its isotonic properties and no toxicity

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for cells [36]. It deals with an aqueous saline preparation, containing sodium chloride, sodium phosphate and, in certain formulations, potassium chloride, that is often used for dilutions. The tampon helps to maintain a constant pH, while concentration and osmolarity are related to the isotonic range, according to that of human body.

2.2.2 Preparation of TritonX-100 solutions

Initially, we decided to test an hemolytic scale found in literature, to verify the hemolysis percentages created in the blood sample. These hemolyzing solutions are PBS based and contain TritonX-100 in the following quantities:

TritonX-100 in solution(%)

TritonX-100 quantity(μL)

PBS quantity (μL) Total volumeof

the solution (cc)

0 0 2 2

0.03 150 1350 1.5

0.3 150 1350 1.5

3 60 1940 2

Table 2: Hemolyzing solutions in the first setup.

For the synthesis of these preparations, a series of Gilson pipettes P100, P200 e P1000 has been used, according to the treated volumes and in order to guarantee the adequate precisions [37]. The obtained solutions, especially that one with a greater TritonX-100 percentage, appeared soapy: so the Vortexer Mixer has been used, in order to create a vortex and to assure a greater homogeneity of the solutions.

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Figure 31: Vortexer mixer (left side) and Gilson pipettes (right side).

2.2.3 Preparation of blood samples

For the collection of blood sample, standard test tubes with 3 cc volume have been used, containing as anticoagulant the ethylenadiaminetetraacetic acid, defined also with the acronym EDTA-K3[38] .

Figure 32: Standard test tubes, containing EDTA-K3 anticoagulant.

As concern the use of anticoagulant and their influence in an optical analysis of the specimen, a series of preliminary researches have been executed in scientific literature on EDTA, sodium citrate and heparin. Because of all the above mentioned compounds are found indiscriminately for the blood preservation after collection, even before the performing of an optical analysis [39], we decided to exclude their eventual optical influence in the revelation of hematological parameters.

Moreover, to verify the volumes obtained with the standard collection procedure, a weighing of the test tubes has been performed before and after the puffiness with the blood samples (Table 3), finding negligible imprecisions.

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SAMPLES WEIGHT BEFORE FILLING (g) WEIGHT AFTER FILLING (g)

1 5.902 9.103

2 5.962 9.118

3 5.951 9.169

4 5.960 9.228

Table 3: Test tubes weighing before and after blood filling.

These sample are centrifugated at 800 rpm for 10 minutes, to separate the corpuscolated parts from the liquid one. Subsequently, 1 cc of blood plasma has been substituted with 1 cc of hemolyzing solution, at different concentrations in the four samples, in order to maintain a proportion 1:3 in volume with respect to the total 3 cc of blood contained in the test tubes. To allow the hemolyzing agent action, test tubes have been mixed up using an hematological laboratory device called agitator roller (Figure 33 - upper), to obtain an homogenization between cellular and liquid parts in the sample. Then, the tubes have been inserted for 45 minutes in a static water bath at 37 °C (Figure 33 - lower), in order to reproduce a physiological environment.

Figure 33: Agitator roller (upper) and static water bath ( lower).

For the test tubes analysis and the evaluation of the hemolysis degree, we decided to use an hematological analyzer ADVIA 2120 hematology system [40], usually utilized for the routine hematological analysis. This device automates the hematological

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analysis laboratory and simplifies the workflow, by maximizing the productivity and by eliminating the greater part of the manual steps commonly executed.

Figure 34: ADVIA 2120 (left image) and screen containing the devices results (right side).

Among the different functionalities, such as the hematic cells counts, the evaluation of pathological states without adding reagents, the direct measurement of the erythrocytes morphology and of the intracellular hemoglobin, in order to effectuate a precise revelation of the sample condition, it gives also an index in percentage of the sample hemolysis degree, combining a series of evaluated optical parameters. From the analysis of the samples, treated with the TritonX-100 solutions, the following mean results have been obtained:

% TritonX-100 into the solution % hemolysis revealed with ADVIA 2120 % hemolysis expected 0 0 0 0.01 0 2 0.1 3 14 1 100 70

Table 4: Results obtained from the blood sample analysis, containing hemolyzing solution, effectuated with the

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2.2.4 Results discussion

As concern the hemolysis percentages, the obtained results are different from the expected values found in literature. Moreover, from visual inspection of the samples, a greater coarseness of the hemolysis scale with respect to the percentages obtain with the ADVIA 2120 is quite clear. So, we have supposed and, then, verified with the direct spectrophotometric analysis on the specimens supernatant, that the cited hematological analyzer doesn’t present an adequate precision and sensitivity for the revelation of low free hemoglobin degrees, so it doesn’t permit to effectuate an evaluation of small hemolysis percentages. While, for the development of an optical device, the determination of an hemolytic and repeatable hemolytic scale is important, mostly as concern small hemolysis percentages, useful for the correct monitoring of the patient condition, prior to have negative consequences for his health.

So we decided to modify the approach and to pass to a direct spectrophotometric analysis. To further overcome the lack of coarseness of the hemolytic scale, that passes from zero hemolysis to a very accentuated one, we modified the used TritonX-100 percentages, into the hemolyzing solutions, during the later experiments (Table 5).

TEST I TEST II TEST III TEST IV TEST V

0% 0% 0% 0% 0% 0.01% 0.02% 0.01% 0.025% 0.025% 0.1% 0.05% 0.03% 0.05% 0.05% 1% 0.15% 0.05% 0.075% 0.075% 0.3% 0.075% 0.1% 0.1% 0.1% 0.125% 0.125% 0.125% 0.15% 0.15% 0.15% 0.2% 0.2%

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Finally, we evaluated the homogeneity degree in the blood samples, after the addition of the TrintonX-100 solutions, discussing particularly the utility of the static water bath at 37 °C to obtain it. By searching in literature, rather than to privilege an exact temperature control, maintaining the samples at 37°C during the period of action of the hemolyzing solution, we choose to agitate gently the samples, in order to obtain the desired homogenization without provoking additional hemolysis and, consequently, we are able to reproduce a more uniformly distribute hemolyzing action.

2.3 SETUP EVOLUTION

2.3.1 Hemolyzing solutions composition

As previously implied, the choice of TritonX-100 percentages for the various hemolyzing solutions, has been partially modified in all the experimental sessions, in order to obtain an hemolytic scale more precise and more sensitive for the revelation of low hemolysis degree in the sample (Table 5). Moreover, in the following experiments, hemolyzing solutions have been prepared with the above mentioned dilutions, departing from a mother solution with the greater percentage of TritonX-100, in order to reduce more and more the possible variability and to reach the highest precision.

2.3.2 Instrumentation used

To overcome the limited sensitivity in revealing hemolysis of the ADVIA 2120

Hematology Analyzer, we passed to a direct spectrophotometric analysis of the

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Figure 35: Infinite M200 Pro spectrophotometer.

This instrument permits to visualize the spectra of variation of the optical density (OD) in the sample, in selected wavelength ranges, variable from the UV to the IR (380-2000 nm), with settable wavelength steps which have been chosen of 2-3 nm for this experimental work. The analysis procedure of this device is in reflection, using a technology called Quad4 Monochromators TM [42], that permits an accurate selection of the incident wavelength on the sample and also an accurate filtering of the reflected luminous flux, in the reading procedure. The spectrophotometric analysis have been obtained inserting 100-150 μl of blood and supernatant in the wells of a 96 multiwell (Figure 36).

Figure 36: Multiwell with blood and supernatant specimens.

For an adequate homogeneity in the blood sample and in the hemolyzing solution, a custom agitator has been developed (Figure 37 Figure 38), which presents variable planes, according to the number of test tubes used for the analysis, in order to obtain a balanced structure. Moreover, this device permits to control the agitation velocity of

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the sample, that has been set to 10 rpm for the experiments, to avoid an induced additional hemolysis.

Figure 37: Custom agitator with four samples and control setup for temperature and velocity.

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2.3.3 Experimental procedure

The TritonX-100 and PBS based solutions have been prepared with the above mentioned dilution procedure, in the percentages previously described for the various tests. The samples have been collected in 3cc test tubes with EDTA-K3, then they have been centrifugated for 10 minutes at 800 rpm for the separation between corpuscolated parts and the liquid ones. After the sample homogenization with the Vortexer or the hemolyzing solution heating using a water bath, a rate corresponding to 1 cc of the preparations has been added to the blood sample, after the extraction of 1 cc of blood plasma. Then the test tubes have been positioned in the custom agitator for 30 minutes, checking that the temperature remained around 22-25 °C, to assure the repeatability of the procedure. In order to speed up the following analysis at the spectrophotometer and to avoid sample degradation, a series of Eppendorf has been prepared, to effectuate the various whole blood and supernatant dilutions. The dilution procedure is really important, to avoid the instrument saturation during the optical reading, especially in the spectral region which corresponds to the hemoglobin absorption peaks.

2.3.4 Spectrophotometric analysis of blood samples

Once that the agitation process ends, 500 μl of blood has been collected from the test tubes and they are inserted in the Eppendorf, to be firstly diluted and then analyzed with the spectrophotometer. In the first series of test, a low degree of dilutions of blood have been performed, in order to concentrate the attention on the revelation of optical differences between whole and hemolyzed blood in the wavelength range over 600nm, which could be imputable to differences in the scattering properties of the specimens. Indeed, in the spectral region between 600 and 1200nm, hemoglobin absorption properties are low and negligible with respect to the scattering influence. Above the 1200 nm, the water absorption properties become relevant (Figure 39), so it is difficult to extract information about hemolysis in the NIR.

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Figure 39: Absorption coefficients of oxyhemoglobin (left) and water (right).

Since there is not a monotonous trend of the curves of the absorption coefficients with the variation of hemolysis degree (Figure 40 - Figure 41), we proceeded to effectuate dilutions of the blood specimens, starting from low ones (1:3) to elevated ones (1:50), in order to obtain information on the optical density trend with the hemolysis variation, in all the sensitive silicon region (400-1000nm).

Figure 40: Blood optical density with different induced hemolysis percentages (indicated in the legend). Trend of OD related to hemolysis degree included between 0-98%.

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Figure 41: Diluted blood optical density, with the addition of hemolyzing solutions to obtain the hemolysis percentages indicated in the legend. Optical density trend for limited hemolysis degree (0-13%), in the wavelength

range 650-1000 nm.

As concern the dilutions 1:50 (Figure 42), we focus on the revelation of the changing of the absorption properties of the samples, considering that scattering is a strongly non-linear phenomenon.

Figure 42: Optical density of blood with dilution 1:50.

It’s important to underline that all the dilution in the studies effectuated have been realized using PBS, because it’s an agent that doesn’t modify the hemolysis degree and the osmolarity in the specimen. In addition, PBS is optically irrelevant, because it

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has an absorption spectra almost flat and constant, whose influence could be eliminated and subtracted as an offset (Figure 43).

Figure 43: PBS optical density.

2.3.5 Spectrophotometric analysis of supernatant specimens

For the hemolysis scale revelation, we proceed to the spectrophotometric analysis of the supernatant samples. Supernatant is the liquid part of blood, obtained after centrifugation and that contains plasma and, in case of hemolytic events, variable quantities of free plasma hemoglobin, uniformly distributed. The spectral analysis of these samples has been performed by inserting 150 μl of supernatant in a 96 multiwell, then placed in the Infinite M200 and we define the device parameters (Figure 44) such as the wavelength range between 450-1000 nm, with step length between two consecutive lectures of 3 nm. Obtained curves show a clear variation in optical density in the range 500-650 nm, also if low hemolysis percentages are present in plasma. It is important to underline that in this region the absorption peaks of hemoglobin are included. Departing from these observations, we have chosen a reference value of optical density (0.12) related to an hemoglobin concentration (10mM) corresponding to a wavelength of 543 nm, in order to quantify the hemoglobin content in the specimen under analysis.

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Figure 44: Spectrophotometric settings for supernatant analysis.

This wavelength has been chosen because it corresponds to an isosbestic point of hemoglobin spectrum, and this permits the absolute quantification of the concentration of this species in solution. As a matter of fact at 543 nm, curves corresponding to the different hemoglobin forms (carboxyhemoglobin, methahemoglobin, deoxyhemoglobin, oxyemoglobin) are superimposed, giving the same optical density value. Once identified the free hemoglobin percentage in plasma, using a simple proportion, the hemolysis degree has been evaluated, linking the value of optical density obtained to the hematological parameters find out from the laboratory analysis of the blood specimen. Particularly, the total hemoglobin value and the RBCs count in the sample have been used to obtain, proportionally, the broken erythrocytes number, corresponding to the hemolysis percentage in the specimen.

The quantities considered for the analysis are:

 ;



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Then the following formulas have been applied:

The hemolysis percentages have been obtained by relating the broken erythrocytes number, which corresponds to the free hemoglobin in the supernatant, to the total number of erythrocytes:

In the various experimental sessions, appears a monotonous ascending relation between the TritonX-100 percentages added to the hemolyzing solution and the hemolysis obtained in the sample (Figure 45).

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Figure 45: Hemolysis scale obtained, related to the different TritonX-100 percentages in the hemolyzing solutions.

2.3.6 Experiments discussion

As anticipated, supernatant analysis give stable and interesting results in the wavelength range 500-650 nm (Figure 46).

Figure 46: Supernatant optical density, with different percentages of free plasma hemoglobin.

Instead, considering the direct optical evaluation of blood specimens, we are not able to extract a repeatable relation between hemolysis and optical density trend, in the visible and NIR range. As a matter of fact, in the range above the 650 nm, where the