Blood flow and changes on blood volume are one of most closely reflects the primary measurements of concentration of O2 and nutrients on cells. In this work are presented some of the major blow flow measurements techniques and methods.
There are many blood flow measurements techniques, but this work will focus only on four of them: Ultrasonic flowmeters and Electromagnetic flowmeters that can correct for varying pressure and temperature (i.e. density) conditions, non-linearities, and for the characteristics of the fluid.; Plethysmography is a widely used method in basic and preclinical research to study respiration and Photoplethysmography that uses a pulse oximeter which illuminates the skin and measures changes in light absorption .
Chapter 2 - Ultrasonic flowmeters
An ultrasonic flow meter is a device which measures volumetric flow and is non invasive. Based on the principle of the amount of time a acoustic wave, sent by a transducer, interacts with blood red cells, and returns to the transducers. Transit time ultrasonic flow meters send and receive ultrasonic waves between transducers in both the upstream and downstream directions in the vessels.
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At no flow conditions, it takes the same time to travel upstream and downstream between the transducers. Under flowing conditions, the upstream wave will travel slower and take more time than the (faster) downstream wave. When the fluid moves faster, the difference between the upstream and downstream times increases linearly. The electronic transmitter processes upstream and downstream times to determine the flow rate. 
The ultrasound transducer has a dual function - it is a transmitter that produces ultrasound by converting electrical energy into mechanical energy and then it becomes the receiver, detecting returning ultrasound waves by converting mechanical into electrical energy. The active component in most ultrasound transducers is a piezoelectric crystal.
Certain crystals change their physical dimensions when subjected to an electric field, and change back when the field is removed. When compressed, they also have the property of generating electric potentials. Changes in polarity of a voltage applied to a transducer cause the transducer to change in thickness, expanding and contracting as the polarity changes.
These results, in increases and decreases pressure, produce ultrasound waves that can be transmitted into the body. Pressure changes caused by the returning ultrasound echoes are converted back into electrical energy signals, which are transferred to a computer to create an ultrasound image. These small events are the source of all ultrasound images. 
The region located near the transducer surface is called the near field. In the near field, the acoustic field is basically cylindrical, with a diameter slightly less than the diameter of the emitter, and the intensity of the acoustic waves oscillates along the axis of the transducer. As the characteristic distances of these oscillations are much smaller than the dimensions of the measured volumes, they do not significantly affect Doppler information collected in this region. The length of the near field,, is determined by the position of the last maximum of the acoustic intensity.
Figure 1- Near and far fields for various transducer diameters and frequencies.Beams are drawn to scale, passing through a 10mm-diameter vessel.Transducer diameters are, 5, 2, and 1 mm. Solid lines are for 1.5 MHz, dashed lines for 7.5 MHz.
The near field extends about, where D is the transducer diameter and λ is the wavelength. During this region, the beam is mostly cylindrical (with little spreading), however with no uniform intensity.
In the far field, the beam diverges with an angle, where, but the intensity uniformly attenuates proportional to the square of the distance from the transducer.
There are various types of ultrasonic flowmeters in use for discharge measurement:
Transit time: This is today's high technology and most widely used type. This type of ultrasonic flowmeter makes use of the difference in the time for a sonic pulse to travel a fixed distance; first against the flow and then in the direction of flow.
Transmit time flowmeters are sensitive to suspended solids or air bubbles in the fluid.
Doppler: This type is more popular and less expensive, but is not considered as accurate as the transit time flowmeter.
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It makes use of the Doppler frequency shift caused by sound reflected or scattered from suspensions in the flow path and is therefore more complementary than competitive to transit time flowmeters. 
Transit time Flowmeter
A pair (or pairs) of transducers, each having its own transmitter and receiver, are placed on the pipe wall, one (set) on the upstream and the other (set) on the downstream. The time for acoustic waves to travel from the upstream transducer to the downstream transducer td is shorter than the time it requires for the same waves to travel from the downstream to the upstream tu. The larger the difference, the higher the flow velocity .
Figure 2- Illustrated transit time technique
The acoustic method of discharge measurement is based on the fact that the propagation velocity of an acoustic wave and the flow velocity are summed vectorially.
This type of flowmeter measures the difference in transit times between two ultrasonic pulses transmitted upstream td and downstream tu across the flow as refereed above.
If there are no transverse flow components in the conduit, these two transmit times of acoustic pulses are given by :
Where L= distance in the fluid between the two transducers
C= speed of sound at the operating conditions
angle between the axis of the conduit and the acoustic path
V= axial low velocity averaged along the distance Lw
The flow velocity can therefore be written as :
Continuous-wave doppler flowmeter
This is a technique in which the transducer emits and receives the ultrasound beam continuously, enabling the measurement of high velocity blood flow, such as occurs through heart valve stenoses.
The Doppler Effect describes the change in frequency of the received signal in relation to the transmitted signal when it is reflected by an object (blood cells).
The variation, or shifting, of the frequency is 
= frequency of the emitted signal
u = velocity of circulation of the blood ( ± 1.5m/s)
= angle between the incident signal and t blood flow
c = speed of sound on blood ( ±1500m/s)
An ultrasonic continuous wave blood flowmeter using Doppler effect analysis includes a filter having a cut-off frequency determined in part by a manually selected zero shift value. A traducing device, in the flowmeter includes a transmission element and a reception element that are similar. The oscillator transmit waves to the moving blood cells, that consequently reflects the waves conditioned by the Doppler effect, being received by the reception transducer. The signal is intensify in the RF transducer, producing an audio signal according to the frequency. A detecting circuit is operatively connected to the transducer device for orthogonally detecting the electric reception signal and outputting a Doppler detection signal. A filter circuit is operatively connected to the detecting circuit for cutting high frequency components of the Doppler detection signal based on the cut-off frequency and outputting an analogue signal. A converting circuit is operatively connected to the filter circuit for converting the analogue signal of the filter circuit to a digital signal based on a Doppler sampling frequency having a continuous wave. A transforming circuit is operatively connected to the converting circuit for analyzing the digital signal and obtaining a Doppler frequency spectrum. A control circuit is operatively connected to the filter circuit for controlling the cut-off frequency based on the Doppler sampling frequency and the zero shift value . The zero crossing detectors emits a signal whenever the signal crosses zero and is then filtered resulting in a number of pulses proportional to the velocity of blood 
Figure 3-Doopler ultrasonic blood flowmeter: Ultrasound is beamed through the vessels walls, backscattered by the red blood cells, and received by a piezoelectric crystal.
Chapter 3 - Electromagnetic Flowmeters
Electromagnetic flowmeters measures instantaneous pulsative blood flow, based on the principle that when a fluid containing electric charges flow in a magnetic field, an electromotive force is generated.
Having a particle with charge, q, that moves with a velocity U in a magnetic flux density, B, then a force, F, will be exerted on the particle, which is expressed in the vector form as
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As blood is a electrolyte solution, the ions with different charges (positive and negative) will move in different positions as flowing in a across a magnetic field creating a electric field, E, that will balance with the electric force, qE.
So faraday's law of induction gives the formula for the induce emf, measured between two electrodes.
B=magnetic flux density, T
L=length between electrodes, m
u=instantaneous velocity of blood
Figure 4- When blood flows in the vessel with velocity u, and passes through the magnetic field B, the induced emf e is measured at the electrodes shown. When a ac magnetic field is used, any flux lines cutting the shaded loop induces a undesired transformer voltage.
For a uniform magnetic field B and a uniform velocity profile u, the induce emf is :
In this expression, these three components are orthogonal.
Method and equipment
For example, the electromagnetic blood flowmeter is used during vascular surgery to measure the quantity of blood passing through a vessel or graft; before during or after surgery. A circular probe with a gap to fit the vessel is fitted around the vessel. This probe applies an alternating magnetic field across the vessel and detects the voltage induced by the flow via small electrodes in contact with the vessel (only used in arteries no in veins, since the veins during diastole are not in contact with the electrodes of the probe).
A number of probes are required to fit the various diameters of blood vessel that can cost up to 400 € each.
An alternative design carries the sensing device on the tip of a special catheter which passes inside the vessel and generates a magnetic field in the space around it and has the electrodes on its surface.
Electromagnetic flowmeters have existed for measurement of blood flow rate outside the body during open heart surgery. 
Figure 5- The toroidal-type cuff probe has two oppositely wound windings on each half of the core. The magnetic flux thus leaves the top of both sides, flows down in the centre of the cuff, enters the base of the toroid, and flows up through both sides.
Direct-current / alternating current
Electromagnetic flowmeters can use direct-current magnetic field, so the output voltage continuously indicates the flow. Alternating magnetic fields (typically at 400 Hz) are used since the induced voltages are in the microvolt region and dc electrode potentials may cause significant errors with unchanging magnetic fields. So in dc magnet current some problems where found: the voltage cross the electrodes metal-to-solution interface is in with the flow signal; the ECG has a wave form and frequency content similar to the flow signal; in the frequency range of interest, 0 to 30 Hz, the 1/f noise in the amplifier is large which results in a poor SNR ( signal noise ratio).
The blood as a ionic and fluid tends to polarize at the electrodes, so the measurement suffers disturbances as stated above.
To avoid polarization and eliminate the problems of dc flowmeter it is used alternating magnet current like sin-wave flowmeter.
In the sin-wave flowmeter, the magnet is a electromagnet excited with a sinusoidal alternating current at 100 Hz .
Chapter 4 - Plethysmography Chamber
The Pletysmography determinates blood flow by measuring changes is the volume of the limb. For that is used a Pletysmography chamber that measures changes in the blood volume in the extremities.
There are many ways to measure methods but the example that is used is venous-occlusion pletysmography.
Prevents return of venous blood
Ensures that the volume changes in the given section of the limb is measured only
Figure 6- In a chamber plethysmography, the venous-occlusion cuff is inflated to 50 mmHg (6.7 kPa), stopping venous return. Arterial flow causes an increase in volume of the leg segment, which the chamber measures. 
The Venou-occlousin cuff is inflated to 50 mmHg to stop venous return.
The chamber has a rigid container that houses some a type of bladder full of liquid (water usually) or air, that is squeezed by the leg as the volume it increases due to arterial flow (the venous flow is occlude by the cuff).
The changes in volume/press ion can be measured using a pressure transducer or observing the rise of water in a calibrated tube.
As above mean venous-occlusion cuff is applied into the inferior limb and prevents the return of the blood flow, so the blood can't leave the limb. The arterial flow is not influence by the venous-occlusion so the increase of volume in the limb per unit time is equal to the arterial inflow. The reason why is used a arterial-occlusion cuff on the distal part of the limp is because if the chamber only encloses a segment of a limp, the arterial-occlusion must be inflated to 180mmHg to ensure that the changes in chamber volume measure only the arterial flow entering in to the segment of the limb.
Figure 7- After venous-occlusion cuff pressure is turned on, the initial volume-versus-time slope is caused by arterial inflow. After the cuff is released, segment volume rapidly returns to normal (A). If a venous thrombosis blocks the vein, return t normal is slower (B).
Chapter 5 - Photopletysmography
Photoplethysmography (PPG) is a simple and low-cost optical technique that can be used to detect blood volume changes in the microvascular bed of tissue but is not very accurate, PPG is simples method and indicates the timing of events such as heart rate.  It is often used non-invasively to make measurements at the skin surface. Light can be transmitted through a capillary bed. As arterial pulsations fill the capillary be, the changes in volume of the vessels modify the absorption, reflection, and scattering the light.
The principle of PPG, is simple, which employs a small light source and a photosensitive detector (photoelectric cell) applied to the skin. The emitted light is scattered in the tissue and partly absorbed. Part of the scattered light emerges again through the skin and is detected by the photoelectric cell, which can be placed either beside or opposite the light source (reflection and transmission mode, respectively). The intensity of the light detected by reflection or transmission is converted to the PPG signal.
For light source it can be used a small tungsten lamp, that transfers heat to the muscles and causes vasodilatation, which can be useful because a larger pulse is produce. So in the figure below are mention two phetoplysmogrophy methods in which sources generate light that is transmitted through the bone.
Figure 8 a) Light transmitted into the finger pad is reflected off bone and detected by a photosensor. b) Light transmitted through the aural pinna is detected by the photosensor.
The photoplethysmography waveform
The pulsatile component of the PPG waveform is the 'AC' component and usually has its fundamental frequency, typically around 1 Hz, depending on heart rate. This AC component is superimposed onto a large quasi-DC component that relates to the tissues and to the average blood volume. This DC component varies slowly due to respiration, vasomotor activity and vasoconstrictor waves, Traube Hering Mayer (THM) waves and also thermoregulation. These characteristics are also body site dependent. With suitable electronic filtering and amplification both the AC and DC can be extracted for subsequent pulse wave analysis.
It's a simple method and the cardiac pulsation is easily observed, although is very sensitive to the exterior and is a weak measurer to volume variations.