There are many excellent specialised texts and articles that describe the physical principles of cardiovascular magnetic resonance (CMR) techniques. There are also many texts written with the clinician in mind that provide an understandable, more general introduction to the basic physical principles of magnetic resonance (MR) techniques and applications. There are however very few texts or articles that attempt to provide a basic MR physics introduction that is tailored for clinicians using CMR in their daily practice. This is the first of two reviews that are intended to cover the essential aspects of CMR physics in a way that is understandable and relevant to this group. It begins by explaining the basic physical principles of MR, including a description of the main components of an MR imaging system and the three types of magnetic field that they generate. The origin and method of production of the MR signal in biological systems are explained, focusing in particular on the two tissue magnetisation relaxation properties (T1 and T2) that give rise to signal differences from tissues, showing how they can be exploited to generate image contrast for tissue characterisation. The method most commonly used to localise and encode MR signal echoes to form a cross sectional image is described, introducing the concept of k-space and showing how the MR signal data stored within it relates to properties within the reconstructed image. Before describing the CMR acquisition methods in detail, the basic spin echo and gradient pulse sequences are introduced, identifying the key parameters that influence image contrast, including appearances in the presence of flowing blood, resolution and image acquisition time. The main derivatives of these two pulse sequences used for cardiac imaging are then described in more detail. Two of the key requirements for CMR are the need for data acquisition first to be to be synchronised with the subject's ECG and to be fast enough for the subject to be able to hold their breath. Methods of ECG synchronisation using both triggering and retrospective gating approaches, and accelerated data acquisition using turbo or fast spin echo and gradient echo pulse sequences are therefore outlined in some detail. It is shown how double inversion black blood preparation combined with turbo or fast spin echo pulse sequences acquisition is used to achieve high quality anatomical imaging. For functional cardiac imaging using cine gradient echo pulse sequences two derivatives of the gradient echo pulse sequence; spoiled gradient echo and balanced steady state free precession (bSSFP) are compared. In each case key relevant imaging parameters and vendor-specific terms are defined and explained. This review is the first of two that aim to cover the basic physical principles underlying the most commonly used cardiovascular magnetic resonance (CMR) techniques. There are numerous texts and journal articles that provide excellent, in-depth explanations of MR physics and in particular CMR physics -5. This o, defines the nominal operating field strength of the particular MRI system. Bo is measured in units of Tesla, (T) with 1 Tesla equal to approximately 20,000 times the earth's magnetic field. Nominal field strengths range from 0.2T to 3.0T for commercially produced clinical MR systems, with the most common field strength for cardiac imaging being 1.5T. A reference coordinate system of three orthogonal axes, x, y and z is used to define the magnetic field direction, with the z axis chosen to be parallel to the direction of Bo.A magnetic resonance imaging (MRI) system comprises three main electromagnetic components; a set of main magnet coils, three gradient coils and an integral radiofrequency transmitter coil Figure . These co but with a strength that changes with position along the x, y or z directions, according to which gradient coil is used. This gradient field is superimposed onto the Bo magnetic field so that its strength increases (or decreases) along the direction of the applied gradient field. The strength of the gradient magnetic field reflects the 'steepness' of its slope and is measured in units of millitesla per metre (mT/m).A gradient magnetic field that can be rapidly switched on and off is generated by each of the three gradient coils mounted inside the main magnet Figure . Each of1 field. The static magnetic field and radiofrequency field combine to generate magnetic resonance signals that are spatially localised and encoded by the gradient magnetic fields to create an MR image. For cardiac imaging, a separate rf receiver coil that is tailored to maximise signal from the heart is normally used to detect the emitted MR signals  magnetic field is generated by the rf transmitter coil mounted inside the gradient coil, closest to the patient Figure . It has s Figure .31P, 23Na, 13C, whose nuclei exhibit magnetic resonance properties but the high intrinsic sensitivity and natural abundance in the form of water and lipid molecules makes it particularly favourable for imaging. Hydrogen nuclei, (single protons) possess an intrinsic property known as nuclear spin that gives rise to a small magnetic field for each proton, known as a magnetic moment. Normally the magnetic moments (spins) are randomly oriented but in the presence of the externally applied Bo field, they tend to align either toward or against the externally applied magnetic field. An equilibrium state is quickly attained where there is a small excess of spins aligned with the field  as this is the more energetically favourable direction of alignment. The excess of proton magnetic moments combines to form a net magnetic field or net magnetisation. This is often given the symbol M and at equilibrium it is aligned along the positive z axis  with the value, Mo. It is often shown as an arrow or vector  contained within free water or lipid molecules Hydrogen is one of a number of elements, including r Figure .o, the greater the excess of protons aligned with the magnetic field and the greater the size of the net magnetisation.The size of this net magnetisation is one of the key determinants of the maximum signal intensity that can be generated and used to form images. The greater the applied magnetic field strength, Bo that is determined by the equation:In order to generate a MR signal from the net magnetisation, the radiofrequency (rf) magnetic field described earlier is generated by the integral rf transmitter coil and used to deliver energy to the population of protons. This field is applied at a particular frequency, known as the Larmor frequency, ωThis equation is known as the Larmor equation. The constant γ is called the gyromagnetic ratio and has a value of 42.6 MHz/Tesla for the proton. The Larmor frequency is therefore proportional to the strength of the magnetic field and for 1.5 Tesla, the Larmor frequency is approximately 64 MHz. This is also known as the resonant frequency, as the protons only absorb energy (or resonate) at this characteristic frequency. The rf field is normally applied as a short pulse, known as an rf pulse.o, is at equilibrium, aligned along the z-axis in the same direction as Bo  towards a rotational motion in the plane of the x and y axes.Before the rf pulse is switched on the net magnetisation, Mo Figure . When tho field (the z axis). This depends upon both the amplitude and duration of the pulse. The rf pulse is switched off once the angle of precession has reached a prescribed value. This is known as the flip angle of the rf pulse  they will produce a net magnetisation that is rotating. The greater the amount of energy applied by the rf pulse, the greater the angle that the net magnetisation makes with the Be Figure .z, also know as the longitudinal component. The other component lies at right angles to the z axis within the plane of the x and y axes and is known as the x-y component of the net magnetisation, Mxy, or the transverse component. The transverse component rotates at the Larmor frequency within the xy plane and as it rotates, it generates its own small, oscillating magnetic field which is detected as an MR signal by the rf receiver coil. Radiofrequency pulses are commonly classified by both their flip angle and by their effect.Once the rf pulse has caused the net magnetisation to make an angle with the z-axis, it can be split into two components Figure . One comRadiofrequency pulses that generate an MR signal by delivering energy to the hydrogen spin population, causing the magnetisation to move away from its equilibrium position are known as excitation pulses. The 90° rf excitation pulse delivers just enough energy to rotate the net magnetisation through 90° Figure . This trLow flip angle rf excitation pulses rotate the net magnetisation through a pre-defined angle of less than 90° Figure . A low fThe 180° refocusing pulse is used in spin echo pulse sequences after the 90° excitation pulse, where the net magnetisation has already been transferred into the x-y plane. It flips the direction of the magnetisation in the x-y plane through 180° as it rotates at the Larmor frequency Figure . This puo field  and transverse (xy) components. The first relaxation process, longitudinal relaxation, commonly referred to as T1 relaxation is responsible for the recovery of the z component along the longitudinal (z) axis to its original value at equilibrium. The second relaxation process, transverse relaxation, is responsible for the decay of the xy component as it rotates about the z axis, causing a corresponding decay of the observed MR signal. Longitudinal and transverse relaxation both occur at the same time, however, transverse relaxation is typically a much faster process for human tissue. The signal decays away long before the spin system returns to its equilibrium state.T1 relaxation is an exponential process with a time constant T1. For example, if a 90° pulse (a saturation pulse) is applied at equilibrium, the z-magnetisation is saturated (reduced to zero) immediately after the pulse, but then recovers along the z-axis towards its equilibrium value, initially rapidly, slowing down as it approaches its equilibrium value Figure . The shoTransverse relaxation can be understood by remembering that the net magnetisation is the result of the sum of the magnetic moments (spins) of a whole population of protons. Immediately after the rf pulse they rotate together in a coherent fashion, so that as they rotate they continuously point in the same direction as each other within the xy plane. The angle of the direction they point at any instant is known as the phase angle and the spins having similar phase angles are said at this initial stage to be 'in phase' Figure . Over tio is constant, it is however possible for the magnetic moment of one proton to slightly modify the magnetic field experienced by a neighbouring proton. As the protons are constituents of atoms within molecules, they are moving rapidly and randomly and so such effects are transient and random. The net effect is for the Larmor frequency of the individual protons to fluctuate in a random fashion, leading to a loss of coherence across the population of protons. i.e. the spins gradually acquire different phase angles, pointing in different directions to one another and are said to move out of phase with one another (this is often referred to as de-phasing). The resultant decay of the transverse component of the magnetisation (Mxy) has an exponential form with a time constant, T2, hence this contribution to transverse relaxation is known as T2 relaxation  relates to local static variations (inhomogeneities) in the applied magnetic field, Bl Figure . T2* relT1 relaxation involves the release of energy from the proton spin population as it returns to its equilibrium state. The rate of relaxation is related to the rate at which energy is released to the surrounding molecular structure. This in turn is related to the size of the molecule that contains the hydrogen nuclei and in particular the rate of molecular motion, known as the tumbling rate of the particular molecule. As molecules tumble or rotate they give rise to a fluctuating magnetic field which is experienced by protons in adjacent molecules. When this fluctuating magnetic field is close to the Larmor frequency, energy exchange is more favourable. For example, lipid molecules are of a size that gives rise to a tumbling rate which is close to the Larmor frequency and therefore extremely favourable for energy exchange. Fat therefore has one of the fastest relaxation rates of all body tissues and therefore the shortest T1 relaxation time. Larger molecules have much slower tumbling rates that are unfavourable for energy exchange, giving rise to long relaxation times. For free water, its smaller molecular size has a much faster molecular tumbling rate which is also unfavourable for energy exchange and therefore it has a long T1 relaxation time. The tumbling rates of water molecules that are adjacent to large macromolecules can however be slowed down towards the Larmor frequency shortening the T1 value. Water- based tissues with a high macromolecular content (e.g. muscle) therefore tend to have shorter T1 values. Conversely, when the water content is increased, for example by an inflammatory process, the T1 value also increases.J-coupling) that cause a reduction of the T2 relaxation time constant to an intermediate value. Rapidly repeated rf pulses, such as those used in turbo or fast spin echo techniques, can have the effect of reducing J-coupling, resulting in an increased T2 relaxation time and higher signal intensity from fat [T2 relaxation is related to the amount of spin-spin interaction that takes place. Free water contains small molecules that are relatively far apart and moving rapidly and therefore spin-spin interactions are less frequent and T2 relaxation is slow (leading to long T2 relaxation times). Water molecules bound to large molecules are slowed down and more likely in interact, leading to faster T2 relaxation and shorter T2 relaxation times. Water- based tissues with a high macromolecular content (e.g. muscle) tend to have shorter T2 values. Conversely, when the water content is increased, for example by an inflammatory process, the T2 value also increases. Lipid molecules are of an intermediate size and there are interactions between the hydrogen nuclei on the long carbon chains . Gradient echo imaging is however more affected by the presence of magnetic field inhomogeneities caused by iron and so is useful, for example, in the assessment of patients with increased iron deposition within the heart and liver.The MR echo signals produced above can be localised and encoded by applying magnetic field gradients as they are generated to produce an image. This is because the application of a magnetic field gradient causes the strength of the magnetic field and hence, the Larmor frequency to depend on position along that direction. The sections that follow describe the most commonly used method to build up a cross-sectional 2-dimensional image (or image slice) using a combination of rf pulses and gradient magnetic fields.S. The orientation of the slice is determined by the direction of the applied gradient known as the slice selection direction , each time applying the same slice selection and frequency encoding gradient, but a different amount of phase encoding Figure . This isP. The spatial resolution of the image therefore also depends on the number of phase encoding steps, and as a consequence is often limited by the image acquisition time, asThe repetition time, TR is another important parameter that can be set by the operator in milliseconds. As we will see later it not only determines how fast MR images can be acquired but also affects the image contrast. The number of pixels in the phase encoding direction of the reconstructed image is determined by the number of phase encoding steps used, NIf a greater spatial resolution is required in the phase encoding direction (for a fixed field of view), the number of pixels in that direction (sometimes referred to as the acquired image matrix size) must be increased. This requires a greater number of repetitions, and therefore a longer image acquisition time.x and ky. The value of each point in k-space represents how much of a particular spatial frequency is contained within the corresponding image.The way that the MR signals are generated and encoded by the use of magnetic field gradients gives rise to a particular relationship between the data points in the signal and those in the image. A single data point in an MR signal contributes a particular attribute to the whole image. Conversely, a single pixel in the image may have contributions from all of the MR signals collected. Just as each pixel occupies a unique location in image space, each point of an MR signal echo belongs to a particular location in a related space known as k-space . There ix direction. This is known as a Cartesian acquisition , or primarily dependent on the differences in T2 relaxation times (T2 weighted). If the parameters are chosen so that the image contrast is influenced by neither the T1 or T2 differences, the tissue signal is said to be primarily 'proton density' weighted. The TR controls the T1 weighting, while the TE controls the T2 weighting.xy, when the next rf pulse is applied. Tissues that have recovered less quickly will have a smaller longitudinal magnetisation before the next rf pulse, resulting in a smaller transverse magnetisation after the rf pulse. The short TE limits the influence of the different T2 decay rates. The resultant contrast is therefore said to be T1-weighted. T1 weighted spin echo images are typically characterised by bright fat signal and a low signal from fluid and are useful for anatomical imaging where high contrast is required between, fat, muscle and fluid. For cardiac imaging the pulse sequence is synchronised with the cardiac cycle and so the TR is determined by the patient's heart rate. For T1-weighted imaging the TR is set to one RR interval and the TE is set to a short value to minimise T2 weighting.The parameter choice for T1-weighted spin echo is a short TR and short TE Figure . The choThe parameter choice for T2-weighted spin echo is a long TR and long TE Figure . The choThe parameter choice for proton density-weighted spin echo is a short TR and short TE Figure . The chothrough the slice, this 'black blood' appearance provides high intrinsic contrast between the blood pool and the heart and blood vessel walls, which, in the early days of cardiac MR, made spin echo the pulse sequence of choice for anatomical imaging. The spin washout effect is reduced, however, where blood moves either slowly through or within the plane of the image slice. This results in a loss of dark blood contrast and a high residual blood signal that can lead to significant ghosting artefacts. The spin echo-based approach has therefore been modified for widespread clinical use by the addition of a black blood magnetisation preparation scheme [The spin echo pulse sequence generates images that have intrinsic black blood contrast when imaging fast moving blood flowing through the image slice . This isn scheme  which prThere are a number of types of gradient echo pulse sequence, each having quite different contrast behaviour . The twoFast Low Angle ShotSiemens:   FLASH   T1-weighted Fast Field EchoPhilips:   T1 FFE   Spoiled GRASS Gradient echo pulse sequences in cardiac imaging typically use very short TR values (<10 milliseconds) which gives rise to a more complex contrast behaviour. The TR values used are much shorter than the T2 relaxation times of blood and myocardium. This means that unless the transverse magnetisation generated by each rf pulse is destroyed after it has been sampled, it would still exist when the next rf pulse is applied. This can potentially contribute to, or interfere with, the signal during the following TR. In spoiled gradient echo, this signal is de-phased (or spoiled) either using a spoiler gradient at the end of each TR period, or by using a technique known as rf spoiling  so that Spoiled gradient echo pulse sequences follow a similar contrast behaviour to that described for spin echo, however there are some key differences. For gradient echo pulse sequences the absence of a 180° refocusing pulse determines that the amplitude of the gradient echo at the TE, is influenced by T2* relaxation. Furthermore, a variable flip angle for the excitation pulse, as well as the TR and TE, is used to control image contrast. These three parameters can be chosen to weight the image contrast so that it is either primarily dependent upon the differences in T1 relaxation times (T1-weighted), or primarily dependent on the differences in T2* relaxation times (T2*-weighted). The use of a low flip angle is important for spoiled gradient echo techniques ,13 as itFor spoiled gradient echo, T1-contrast is controlled by both the TR and the flip angle.Cardiac cine imaging requires very short repetition times to be used and so resultant spoiled gradient echo sequence, with both a short TR(<10 ms) and TE (<5 ms), combined with a flip angle of around 30° essentially behaves as a T1-weighted pulse sequence. As a very short TR is used, myocardial tissue or blood that remains in the slice becomes saturated. This sequence thus relies on the flow of blood to generate contrast.T2* weighting with spoiled gradient echo pulse sequences is achieved by increasing the TR and TE to relatively long values. As the T2* values for tissues are shorter than the T2 values, the echo times chosen to achieve T2* weighting with gradient echo are also much shorter than the echo times required to achieve T2 weighting with spin echo sequences. For T2*-weighted gradient echo, the image contrast is strongly influenced by the presence of magnetic susceptibility effects and can be used to detect the presence of iron, for example where there is haemorrhage or iron loading of tissue .Fast Imaging Employing Steady sTate AcquisitionGE:   FIESTA   balanced Fast Field EchoPhilips:   bFFE   Fast Imaging with Steady PrecessionSiemens:   True FISP   True Balanced SSFP gradient echo sequences are designed to ensure that the transverse magnetisation is not spoiled but brought back into phase at the end of each TR period when the next rf pulse is applied. This then carries over into the next repetition and is superimposed onto the to the transverse magnetisation generated by that rf pulse. After a number of repetitions this gives rise to a steady state condition where the transverse magnetisation from two or three successive repetition periods combine to give a much greater signal ,16.The contrast behaviour of bSSFP sequences is very different to that of the spoiled gradient echo sequences. SSFP contrast is related to the tissue's T2/T1 ratio, with fluid and fat in particular appearing as brighter than other tissues. Because the transverse magnetisation originating from several TR's are combined, the MR signal amplitude for bSSFP is much greater compared to spoiled gradient echo. The increased signal allows a higher receiver bandwidths to be used, resulting in a shorter TE and TR compared to spoiled gradient echo pulse sequences and therefore improved imaging efficiency. However, if the magnetic field is not uniform, the transverse magnetisation from different TRs can destructively cancel rather than add together in areas of magnetic field inhomogeneity, making the SSFP technique prone to dark banding artefacts across the image . It is tIn contrast to the spin echo sequence, the gradient echo sequence only uses one rf pulse to generate the signal and so the spin washout effect does not apply and the signal from flowing blood is usually visible. Indeed, rather than suffering from a reduction in signal, flowing blood often appears with an apparently increased signal, compared to the surrounding tissues . The graThe very short TR (TR < 10 ms) employed for the purpose of fast imaging means that the magnetisation of tissue that remains in the image slice becomes partially saturated as rf pulses are rapidly applied to the same tissue, as there is little time for recovery of the z-magnetisation between pulses Figure . This haThe 90° excitation pulse used by the spin echo pulse sequence transfers all of the available z magnetisation into the transverse plane. This combined with the 180° refocusing pulse gives the largest possible signal provided the magnetisation is allowed to recover sufficiently between repetitions. These two attributes make the spin echo technique ideally suited when the primary goal is to achieve images with a high signal-to-noise ratio and a reduced sensitivity to artefacts caused by magnetic field inhomogeneities. Fast gradient echo pulse sequences are used where imaging speed is more important than image quality. The absence of the 180° refocusing pulse in the gradient echo sequence leads to signal loss in the presence of magnetic susceptibility effects and at the boundaries between water and fat-based tissues. Flowing blood also appears differently between the two sequences, with spin echo giving an intrinsic black blood appearance and gradient echo pulse sequences giving an intrinsic bright blood appearance. The key differences between gradient echo and spin based techniques are summarised in Table To capture an image of the heart that is unaffected by motion requires an image to be acquired in just a few tens of milliseconds. This means both limiting the number of phase encoding steps  and making the TR as short as possible. Whilst this can be done, it is at the cost of accepting a significant reduction in image quality. On the other hand, to achieve acceptable image quality, the image acquisition time becomes too long to 'freeze' heart motion. For routine CMR therefore, the MR signals are acquired over multiple heart beats, synchronising the pulse sequence and therefore the signal acquisition to a particular time point in the cardiac cycle. Cardiac synchronisation is achieved by using the patient's ECG signal, obtained by applying ECG pads and leads onto the patient's chest Figure . SoftwarFor conventional spin echo and gradient echo imaging techniques, the phase encoding gradient is incremented with each successive heart beat, acquiring a single line of k-space each heart beat and resulting in imaging times of several minutes. This means that images using these techniques are degraded by respiratory motion. Image degradation caused by respiratory motion can be reduced by using one of three possible approaches, namely respiratory compensation methods (respiratory gating), cardiac synchronised fast imaging techniques combined with patient breath-holding or ultra-fast (single-shot) imaging techniques . In practice, most cardiac imaging is performed with patient breath-holding combined with fast imaging techniques and these are described in the following section.Conventional imaging techniques acquire only one phase encoding step (one line of k-space) per heart beat. Thus the TR for those pulse sequences is defined by the patient's heart rate and is equal to the R-R interval. It therefore invariably takes several minutes to acquire an anatomical image dataset with conventional spin echo (SE) or a cine image dataset with conventional gradient echo sequences (spoiled gradient echo or bSSFP pulse sequences). In order to overcome this limitation to achieve shorter image acquisition times, fast imaging techniques acquire more than one line of k-space in each heart beat . This fiThe ECG synchronisation technique used for still imaging is known as triggering. The synchronisation pulse is used as a trigger to initiate the pulse sequence at a particular time point after the R-wave in each cardiac cycle. This time point is known as the trigger delay and is selectable by the system operator to determine the point in the cardiac cycle at which the heart is to be imaged. This still imaging approach can be used for myocardial viability assessment or coronary angiography anatomical imaging, but the most routine application is to use it in combination with a fast or turbo spin echo pulse sequence to acquire black blood images for anatomical imaging.Turbo Spin EchoPhilips, Siemens   TSE   Fast Spin EchoGE   FSE   J-coupling that is present between the hydrogen nuclei in molecules with long carbon chains. This interaction has the effect of reducing the T2-relaxation time and therefore the signal intensity in conventional spin echo images. For cardiac imaging, turbo or fast spin echo pulse sequences are commonly used in combination with a double inversion 'black-blood' magnetisation preparation scheme to acquire anatomical images of the heart and major vessels.The conventional spin echo (SE) pulse sequence generates a single spin echo signal by the use of an excitation pulse followed by a 180° refocusing pulse. The turbo or fast spin echo pulse sequence ,21 generReliance on the spin washout effect alone to produce dark blood contrast often leads to inconsistent results due to insufficient blood flow. In order to improve the effectiveness of black blood imaging it is common to use a black blood magnetisation preparation scheme in combination with the spin echo pulse sequence ,22. The The most commonly-used pulse sequence for anatomical imaging combines the black-blood preparation scheme with the turbo or fast spin echo pulse sequence Figure . The blaA common problem with this pulse sequence is loss of signal from the myocardium due to motion of the re-inverted myocardial tissue out of the image slice between the time of the black-blood preparation scheme and the time of the turbo or fast spin echo data acquisition. This effect can be reduced by increasing the thickness of the slice of tissue that is re-inverted by the second 180° pulse of the black-blood preparation scheme. While the image slice thickness may be typically 6-8 mm, a more appropriate value for the black blood inversion preparation pulse is 20 mm. The exact choice depends on how much displacement of the myocardium there is through the slice and it requires some adjustment depending on the trigger delay, slice orientation and location within the heart.Cine imaging requires very short repetition times to be used and therefore can only be achieved using gradient echo-based pulse sequences. It involves the acquisition of data at multiple time points, known as cardiac phases, throughout the cardiac cycle Figure . The triFor cine imaging, cardiac synchronisation can be performed in either of two ways: ECG triggering or ECG Gating Figure . With ECsmall beat-to-beat variations in RR interval. The method acquires data from the whole of each heart beat, so that heart beats of different lengths will have different numbers of data points recorded. At the end of the data acquisition, an average heart beat interval is calculated from the whole acquisition. The time intervals between data points acquired from shorter heart beats are stretched and data from longer heart beats are compressed to fit the average heart beat interval, ensuring that all points in the cardiac cycle are imaged. The use of retrospective gating is essential for applications such as imaging mitral or tricuspid valve function or atrial contraction.A consequence of this approach is that there is a 'blind spot' where no data is acquired at the end of the cardiac cycle while the system waits for the next trigger pulse. This is a disadvantage if imaging of diastolic function or mitral and tricuspid valve function is important. An alternative is to use retrospective ECG gating . Here thWhile retrospective gating works well for small beat-to-beat variations in the R-R interval, imaging of patients with large beat to beat variations is problematic. For occasional arrhythmias, there is usually an option for data points acquired from excessively long or short heart beats to be rejected and reacquired. This is known as arrhythmia rejection. In cases where there are many arrhythmias however, rejection of data is not practical and the only options are to revert to a triggered data acquisition if only systolic information is required, or to use a 'real-time' image data acquisition for which ECG synchronisation is not required -27. The Acceleration of cine gradient echo imaging is achieved simply by rapidly repeating the gradient echo pulse sequence a number of times to acquire a number of lines of k-space within each cardiac phase Figure . Each grThe parameter that defines the number of lines of k-space acquired in each shot is dependent upon the manufacturer as follows:Philips   turbofactorSiemens   no of segments*GE   views per segment. This determines the acceleration factor for a particular pulse sequence. For functional imaging it also determines the length of the acquisition window corresponding to each phase of the cardiac cycle. Increasing the 'turbofactor' decreases the scan time (shortens the length of breath-hold) but increases the acquisition window for each cardiac phase, thus limiting the number of cardiac phases that can be imaged, resulting in a lower cine frame rate or poorer temporal resolution. In order to maximise the number of cardiac phases and minimise the breath-hold period, the ability of an MR system to achieve very short TR values is therefore an advantage.For breath hold cine gradient echo imaging, this method of accelerated image acquisition can be applied to both spoiled gradient echo and bSSFP pulse sequences commonly used for cardiac imaging. The vendor-specific names for the 'turbo' or 'fast' versions of these sequences are given below:Fast spoiled gradient echo.TurboFLASHSiemens   TFL   T1-weighted Turbo Field EchoPhilips   T1-TFE   Fast SPoiled GRASSGE   FSPGR   Balanced Steady State Free Precession (bSSFP)Siemens   Segmented True FISPBalanced Turbo Field EchoPhilips BTFE Fast Imaging Employing Steady sTate AcquisitionGE   FIESTA   Imaging of cardiac function, including the assessment of wall motion and volumetric assessment is performed using a 'bright-blood' cine gradient echo technique that acquires images at multiple heart phases which are displayed as a movie. The most common approach to cine imaging is to combine retrospective gating with a turbo or fast gradient echo method Figure . This alA key parameter for cine pulse sequences is the number of lines of k-space acquired within each heart phase . Increasing the value of this parameter shortens the acquisition time, but also increases the time between cardiac phases. This reduces the number of cardiac phases within the cardiac cycle and therefore the cine frame rate or 'temporal resolution' of the image acquisition (the ability to resolve faster motion). 'Real-Time' imaging is achieved by selecting a very high turbofactor -27, suchThis review has outlined the key physical principles that underlie the most commonly used cardiac MR imaging techniques. The basic principles of MR signal generation and image production have been explained and key imaging parameters have been defined, explaining their influence on image contrast, resolution and acquisition time. It has been shown how fast spin echo and gradient echo imaging techniques can be combined with cardiac synchronisation methods to provide high quality anatomical and functional cine imaging of the heart within a single breath-hold period.The author declares that they have no competing interests.JPR drafted, read, revised and approved the final manuscript.Phase and frequency encoding. A PowerPoint animation showing steps 2 and 3 in the image formation process. Step 2 applies a magnetic field gradient in the phase encoding direction. This changes the resonant frequency of the spins along this direction, resulting in a phase shift that is related to position in this direction when the gradient is switched off. Step 3 applies a magnetic field gradient in the frequency encoding gradient, resulting in a resonant frequency that is related to position along this direction. The MR signal is measured during step 3 and is the sum of all the frequencies produced.Click here for file


Among bacteria, we have previously shown that species that are capable of rapid growth have stronger selection on codon usage than slow growing species, and possess higher numbers of rRNA and tRNA genes. This suggests that fast-growers are adapted for fast protein synthesis. There is also considerable evidence that codon usage is influenced by accuracy of translation, and some authors have argued that accuracy is more important than speed. Here we compare the strength of the two effects by studying the codon usages in high and low expression genes and on conserved and variable sites within high expression genes. We introduce a simple statistical method that can be used to assess the significance and the strength of the two types of bias in the same sets of sequences. We compare our statistical measure of codon bias to the common used codon adaptation index, and show that the new measure is preferable for three reasons for the purposes of this analysis. Across a large sample of bacterial genomes, both effects from speed and accuracy are clearly visible, although the speed effect appears to be much stronger than the accuracy effect and is found to be significant in a larger proportion of genomes. It is also difficult to explain the correlation of codon bias in the high expression genes with growth rates and numbers of copies of tRNA and rRNA genes on the basis of selection for accuracy. Hence we conclude that selection for translational speed is a dominant effect in driving codon usage bias in fast-growing bacteria, with selection for accuracy playing a small supplementary role. Translation is the process by which ribosomes synthesize proteins in cells. Protein synthesis is essential to all organisms, and cells expend a large amount of energy and time on translation. For single celled organisms, such as bacteria, there is a direct relationship between the rates of cellular processes such as translation and the rate of cell growth and cell division. Therefore, improvements in translation should increase the fitness of the organism. The term ‘translational selection’ refers to selection to optimize the translation process itself rather than selection acting on the functions of the proteins produced by translation. One of the main pieces of evidence for translational selection is the observation that the choice of synonymous codons appears to be influenced by selection in many organisms. Synonymous changes in the gene do not affect the resulting protein but can affect the way that the mRNA is translated by the ribosome.E. coli, the concentrations of tRNAs are also found to vary with growth conditions The speed of translation is one of the key factors on which translational selection can act. Speed has the direct benefit that the proteins required are produced faster, and the secondary benefit that if a given ribosome finishes translation of one sequence, it can begin work on another. Hence, speeding up translation means that the same total protein production rate can be achieved with fewer ribosomes. Synthesis of the ribosomal proteins and RNAs themselves is costly to the cell, so getting the most out of a limited number of ribosomes is important for efficiency. The argument for translational speed/efficiency explains the observation that codon usage is most strongly biased in a relatively small number of genes that are highly expressed in conditions of rapid growth Ribosomal proteins and translational elongation factors are among the most highly expressed genes in bacteria, and are easily recognizable conserved genes in most genomes. These genes are often used as a reference set, and the codon frequencies in these reference genes are used to define measures of codon bias with which to compare the strength of translational selection in different genes. The first of these is the codon adaptation index (CAI), introduced by Sharp and Li Further evidence for the importance of translational speed in bacteria is the observation that codon bias is strongest in organisms that have fast growth rates are often duplicated attests to the importance of these genes. It is interesting to note that ribosomal proteins, which are required in cells in equally high numbers as ribosomal RNAs, usually have single-copy genes. High levels of proteins can be achieved by optimizing translation from a limited number of mRNAs, whereas high levels of rRNAs and tRNAs can only be achieved by duplicating the genes, and hence increasing transcription.Bacterial genomes usually do not have large non-coding regions and, in general, duplicated genes are rare. This suggests that the efficiency of DNA replication is also important to bacteria and this keeps genomes from becoming larger than necessary. The fact that tRNA and rRNA genes The other important aspect of translational selection is accuracy. Occasional mis-pairings between codon and anticodon may occur during translation, leading to errors in the protein sequence. This is wasteful, if the protein is no longer functional, and may actually be harmful, if mistranslated proteins misfold to structures that are toxic, as has been suggested There seems to be clear evidence that both the speed and accuracy of translation can differ between synonymous codons. We have previously discussed many of the specific details of codon-anticodon interactions that influence which codons are preferred as a function of which tRNAs are present in an organism et al.Escherichia coli were downloaded from the E. coli database. BLAST was used to find the orthologous protein sequences in each of the other genomes, where possible. We wished to include only sequences that are conserved across a large majority of genomes and that can be reasonably assumed to be high expression genes in all cases. Hence, sequences were excluded if the E value of BLAST for the best match was larger than 0.05, or if the best matching sequence was more than two times longer than the E. coli sequence. If a reliably matching sequence was found in at least 73 species, the gene was retained as part of the high expression data set. Otherwise the gene was excluded for all species. This resulted in retention of the following 47 high expression genes whose sequences could be located in almost all species: L1–L7/L12, L9–L11, L13–L22, L24, L27, L28, L31, L35, S2–S20, EF–G, EF–Tu, EF–Ts. Finally, the two species Clostridium tetani E88 and Mycoplasma penetrans HF-2 were excluded because a reliably matching sequence could not be determined for more than 1/3 of the original 57 genes. Having determined the set of genes and species, the protein sequences were aligned for each gene using MUSCLE For ease of comparison with previous papers, we use the same set of 80 widely distributed bacterial species used by Sharp For purposes of comparison of high and low expression genes, the codon counts summed over the 47 aligned genes were counted as the high-expression data set, and the codon counts summed over all other genes in the genome were treated as the low-expression set. Although a small number of other genes may have expression levels comparable to the ribosomal proteins and elongation factors, these contribute very little to the total codon count in the rest of the genome, and this codon count is dominated by the large majority of genes whose expression level is much less than that of the ribosomal proteins.minf. Otherwise the site was counted as variable. We varied minf in the range 60–90%, and we used 80% for most of the results in this paper. The conserved codon counts are obtained from summing codons for the most frequent amino acid at the conserved sites. The variable codon counts are obtained by summing all codons at variable sites plus the codons for the less frequent amino acids at the conserved sites.For the purposes of comparison of conserved and variable sites, we identified the conserved sites within the alignments of the high expression genes in the following way. The most frequent amino acid at each site was determined from the alignment. There are very few sites for which the amino acid is 100% conserved in every species; therefore a strict definition of conserved sites is not possible. We counted a site as conserved if the fraction of species possessing the most frequent amino acid was at least equal to a specified value i in sets A and B are denoted i. The average codon frequencies in the combined sets areThe method given here is a general method for determining to what extent the codon frequencies in two data sets differ. We suppose that two sets of sequences (or two sets of sites within sequences) have been identified, which we will call A and B. For example, A and B could represent the high and low expression genes, or the conserved and variable sites, or any other two sets of codons. The number of occurrences of each codon Here the sum is over all codons except for stop codons and the single codons for Met and Trp. We then consider an alternative model in which codon frequencies are allowed to be different in the two groups. The ML estimators of the frequencies in the two groups are then given by 2 distribution with a number of degrees of freedom equal to the difference in the numbers of degrees of freedom of models 0 and 1. For each amino acid the number of degrees of freedom is one less than the number of synonymous codons. In the standard genetic code there are nine amino acids with two codons, one amino acid with three codons, five amino acids with four codons and three amino acids with six codons. Hence the number of degrees of freedom in the likelihood ratio test is 9×1+1×2+5×3+3×5 = 41. By calculating the p values from theχ2 distribution, the values of 2Δ can be used to determine whether codon frequencies are significantly different between sets A and B.A standard likelihood ratio test can be used to determine whether the alternative model is a significant improvement on the null model. If the null model is true, the quantity AN is the total number of codons in set A. The quantity Aδ is the improvement in the log likelihood per codon in set A obtained when the A set is treated separately rather than as part of the average. This is a measure of the strength of codon bias in the A set relative to the average. If we consider the specific case where set A is the high expression genes (H), then Hδ is a measure of the strength of selection for translational efficiency, whereas if set A is the conserved sites (C), then Cδ is a measure of the strength of selection for translational accuracy.The significance of this test depends on the total number of codons in each data set. Small differences in frequencies will show up as significant if the data sets are large. In order to compare the strength of codon bias in different cases with different data sets (e.g. different species) it is useful to defineδ is to compare the strength of translational selection in different sequences in a same organism. If we consider one single sequence with codon counts seqN, then the quantityAnother usage of δ and CAI will have high values for sequences whose codon usage matches that of the ribosomal proteins, thus they will be highly correlated. We compare values of δ and CAI later in the paper. Roth et al.P that uses weighting factors of the form b’s are the individual base frequencies. This formula is similar, but it is not suitable for our purposes because even the low expression genes do not have codon frequencies that are equal to the product of the three base frequencies. The purpose of our measure δ is to detect genes that have codon bias due to selection for translational efficiency, and for this purpose, the weighting factors in 2 test with one degree of freedom. This test was carried out on all U+C codon families in all genomes. The value of χ2 was significant at the 5% level in 80.4% of codon families across the range of genomes. In comparison, the difference between the conserved and variable sites is less marked, and was significant at the 5% level in 12% to 15% of codon families, depending on minf  and in conserved versus variable sites (CV comparison). The HL effect is very easy to detect in individual codon families. The simplest example is codon families with two codons ending in U and C (for example the UUU and UUC codons for Phe). The codon counts for the H and L set form a 2×2 table. The null hypothesis that the frequencies are equal in the two sets can be tested using a simple χfmin see . This deminf = 80%). The cumulative probability distributions of 2Δ are plotted in y axis shows the fraction of species that have a 2Δ value greater than or equal to the value on the x axis). The distribution for the null model (χ2 distribution with 41 degrees of freedom) is also shown. The distribution for the HL comparison . The measured 2Δ exceeds this for every single species, which confirms that there is strong selection on codon usage in high expression genes in bacteria.The likelihood ratio statistic 2Δ was calculated as in the methods section for each species for both HL and CV comparisons , is strongly correlated with the number of tRNA gene copies in the genome . However, Cδ are very much smaller than those of Hδ, and there is no correlation between Cδ and tRNA gene copy number. The scale of Hδ can be interpreted in terms of likelihood ratios. For a typical species with Hδ = 0.3, the likelihood improves by a factor of exp(0.3) = 1.35 per codon, when the difference between high and low expression genes is included in the statistical model. For a sequence of 100 codons, this is a factor of exp(0.3×100) = 1013, i.e. a large effect. However, for δ = 0.02, which corresponds to the smallest values observed in Hδ and the largest values observed in Cδ, the likelihood improves only by a factor of exp(0.02) = 1.02 per codon, or 7.4 for a sequence of 100 codons.Cδ  and it is not closely related to E. coli.With these points in mind, it is interesting to compare the distributions of CAI and E. coli the two measures are very strongly correlated. The spearman rank correlation coefficient ρ is 0.909 for reference set (large black points); while 0.969, for all other genes. This indicates that genes singled out by CAI would also be singled out by δ, and so the two measures are useful for the same purposes. For C. perfringens, the correlation is still clear, but less strong: ρ is just 0.672 for reference set (large black points); while 0.890, for all other genes. The separation between the reference set and the rest of the genes is greater with δ than with CAI, which suggests that δ is slightly improved as a measure. The scale of δ is also convenient because positive and negative values of δ indicate genes that are or are not adapted to rapid expression in the same way as ribosomal proteins. This same distinction can be used for any organism. For CAI, there is no obvious cutoff between high and low levels.For E. coli, the only exception is the Lys AAA codon, which is most frequent, but under slightly negative selection in high expression genes  where the mutation bias and selection pressure often favor different codons. Further advantages of δ are that it has a log-likelihood scale that is comparable across different organisms, and that it is associated with a simple statistical test for the significance of codon bias.This study was intended as a means to compare selection for translational speed and translational accuracy in the same sequences. For this reason we needed a test that works in the same way for the two quantities. The likelihood ratio method that we proposed is able to test the significance of the difference in frequencies between any two sets of codons, and also to measure the strength of the deviation in frequencies on a per-codon basis. It is suitable for comparison of different genomes with different GC contents and mutational biases, and for analysis of biases arising from different causes. In the final part of the paper, we considered the merits of CAI and 2 test on one codon family , growth rate and the number of copies of tRNAs and rRNAs can all be simply explained as results of the same selection pressure for translational speed and efficiency. However, it could also be argued that if selection for accuracy were acting as a result of toxicity of misfolded mistranslated proteins, then the effect would be strongest for highly expressed genes because these genes would produce more misfolded proteins It is clear that selection for speed will be strongest in those organisms that are adapted to fast growth because time saved in protein production directly effects the cell growth rate and hence its division time. The observed correlations between codon bias Click here for additional data file.


A central aim of physics is to describe the dynamics of physical systems. Schrödinger's equation does this for isolated quantum systems. Describing the time evolution of a quantum system that interacts with its environment, in its most general form, has proved to be difficult because the dynamics is dependent on the state of the environment and the correlations with it. For discrete processes, such as quantum gates or chemical reactions, quantum process tomography provides the complete description of the dynamics, provided that the initial states of the system and the environment are independent of each other. However, many physical systems are correlated with the environment at the beginning of the experiment. Here, we give a prescription of quantum process tomography that yields the complete description of the dynamics of the system even when the initial correlations are present. Surprisingly, our method also gives quantitative expressions for the initial correlation. There is a rich history to the studies of decoherence of quantum systems due to the interactions with the surrounding degrees of freedom. When the dynamics of the system 202223242526272829313234Input states that span the space of The input states are sent through the process. The corresponding output states are determined by quantum state tomography. The knowledge of input states, the corresponding output states, and assuming linearity completely determines the process. The operational approach to quantum dynamics relies on the fact that quantum theory is a theory of preparations and measurements. The experimental method to determine a dynamical map corresponding to a quantum process is called P and output states as Q. The first step of QPT is state preparation. A preparation procedure takes an unknown state of Pm), in terms of matrix indices Pm)( = |πm)(〉〈πm)(|} be a set of pure states that linearly span the space of Let {πm)(|πn)(} that do not commute.A preparation map acting on αmn)( are the coefficients that determine ερm)|(.These preparations are can be thought of as a projection followed by a rotation. Action of any map on space of pm)( and pm), P(2), P(3), and P(4) are Before moving on a simple example may be useful. For one qubit, we may take the following projectors as a linearly independent basis:r″ and s″. Tracing over everything else we can find the initial state of pm)(, that is unit-trace, Hermitian and positive.Mathematically, r with s: Let us start with the trace of As with the case of general quantum operations, matrix µM are the Sudarshan-Kraus operators15The The properties shown above are precisely the conditions for a generic quantum operation to preserve trace, Hermiticity and positivity. Therefore


An actuator is required to change its speed andforce depending on the situation. Using multiple actuators forone driving axis is one of the possible solutions; however, thereis an associated problem of output power matching. This studyproposes a new active joint mechanism using multiple actuators. Because the actuator is made of a flexible bag, it does notinterfere with other actuators when it is depressurized. The proposedjoint achieved coordinated motion of multiple actuators. Thisreport also discusses a new actuator which has dual cylindricalstructure. The cylinders are composed of flexible bags withdifferent diameters. The joint torque is estimated based on thefollowing factors: empirical formula for the flexible actuatortorque, geometric relationship between the joint and the actuator,and the principle of virtual work. The prototype joint mechanismachieves coordinated motion of multiple actuators for one axis. With this motion, small inner actuator contributes high speedmotion, whereas large outer actuator generates high torque. Theperformance of the prototype joint is examined by speed andtorque measurements. The joint showed about 30% efficiencyat 2.0 Nm load torque under 0.15 MPa air input. For example, high speed is required to approach an object , 2. In cficiency . These mThis study proposes a new multiple actuator mechanism with a hydraulic skeleton. Hydraulic skeletons are found in living things such as earthworm and actinia. The hydraulic skeleton actuator in this study is made of flexible bags. Compared with former studies on flexible actuators –13, the Even a high-power actuator is flexible enough if depressurized, and it does not interfere with the other actuator motions. With the proposed mechanism, various arrangements of the actuators are possible compared to the mechanisms with general gearhead motors. The proposed mechanism has further advantages: ease of free rotation, light weight, and good antishock property because of actuator compliance.This paper discusses a prototype active joint mechanism with a new flexible actuator. The new actuator has dual cylindrical structure. The cylinders are made of flexible bags and have different diameters. The torque of the joint is estimated from the actuator torque and the geometrical relationship between the actuator and the joint. The coordinated motion of the inside and outside actuators is confirmed by a prototype joint mechanism. The torque, the power, and the efficiency are also measured to evaluate the performance of the joint.The dual structural actuator consists of two cylindrical flexible bags with different diameters. The stiffness of the actuator bag is controlled by the inner pressure. The inner pressure of each bag is controlled independently. The actuator generates the driving force by increasing the inner pressure of the bag, whereas the actuator is flexible under low input pressure. The actuator speed depends on the bag size because the maximum flow has an upper limit. The driving force of the actuator has positive relation to the width of the actuator as described in our previous paper . In otheThe schematic of the proposed joint mechanism is shown in τa is approximated by the following equation:ka is a constant of proportionality, p is the inner pressure, w is the width of the flexible bag, θ is the bending angle of the bag, and f(θ) is empirical formula, which is a polynomial of degree 5, while ki is constant for each θi [In our former study, the torque at the bending part of a flexible bag with a rectangular shape was investigated with both nonlinear finite element analysis and experiments . The acteach θi .The torque of the dual structural actuator is also estimated from . Accordiτj and τa are the torque of the joint and the actuator and Δθj and Δθa represent the small variations of their bending angles. This relationship is equivalent to the following formula:θj and θa is derived from the law of cosines as shown in τa is already approximated by . In contrast, with a heavy load torque (1.91 Nm), the power of the joint decreases near the large joint angle, whereas the instantaneous efficiency is extremely high. This result is caused by the inertia of the load and the compressibility of air. The result might change if the load is changeable or if the fluid is incompressible.The total efficiency becomes high at high torque range which is observed at power reduction as shown in This study newly proposes an active joint with dual structural actuator made of flexible bags. The inner and outer bags are in charge of quick motion and high torque. Coordinated motion of high speed approach and high torque motion are confirmed by the prototype joint. The maximum rotation speed of the joint was about 200 deg/s with the inner bag, while the maximum power of the outer actuator was 13 W under 1.9 Nm load torque. The actuator exhibits a hysteresis loop depending on the direction of motion. The efficiency of prototype joint is about 30%. Feedback control and practical application are our future works.


Genetic algorithms are employed to optimize dimensionless temperature in nonlinear heat conduction problems. Three common geometries are selected for the analysis and the concept of minimum entropy generation is used to determine the optimum temperatures under the same constraints. The thermal conductivity is assumed to vary linearly with temperature while internal heat generation is assumed to be uniform. The dimensionless governing equations are obtained for each selected geometry and the dimensionless temperature distributions are obtained using MATLAB. It is observed that GA gives the minimum dimensionless temperature in each selected geometry. In many engineering and biological systems, conduction heat transfer plays a vital role. The basic information on conduction heat transfer can be found in any text book –3. Many Davalos and Rubinsky  incorporGenetic Algorithm is based on the Darwinian principle of evolution and it follows the principle of “survival of the fittest.” Genetic algorithms, proposed by Holland  and enhaGenetic algorithms have been successfully applied in the field of heat transfer since mid-1990s. Complex optimization involving nonlinear constraints can be easily solved using genetic algorithms. Optimization problems that cannot be solved because of the extremely massive computational requirements can be easily solved using genetic algorithms. Genetic algorithms are based on heuristic approach and searches for the best individuals. A generation consists of randomly generated population. The members of the population are tested for fitness. The most suitable candidates are allowed to reproduce the new generation. The next generation consists of the best individuals from the previous generation and their offspring. The chromosomes of each member are also mutated to generate a more suitable candidate in the next generation.The fitness function (the function to be minimized) is the entropy generation in all the cases. The simulation is developed in MATLAB. The fitness scores, returned by the fitness function, are ranked on the basis of their scores. The rank of the fittest individual is set to “1” and the next fittest is assigned a rank of “2” and so on. Rank fitness scaling removes the effect of raw scores. “Stochastic uniform” scaling function is used for selection of parents in the next generation. The parents are selected based on the rank as determined earlier. Stochastic uniform algorithm lays out a line in which each parent corresponds to a section of the line of length proportional to its expectation. The algorithm moves along the line in steps of equal size, one step for each parent. At each step, the algorithm allocates a parent from the section it lands on. The first step is a uniform random number less than the step size. Reproduction algorithm determines how the offspring are generated. The elite count is set to “2” which guarantees that a maximum of two individuals will survive in the next population. Crossover generates member of the new generation by combining genes from two individuals from the previous generation. The crossover process used is “scattered” which first creates a random binary vector. A “1” in the random binary vector is replaced by genes from the first parent and a “0” in the random binary vector is replaced by a gene from the second individual. Crossover fraction is a factor which determines how many individuals in the next generation will be generated by mixing genes from two different chromosomes. The crossover fraction has a value of 0.8. The remaining members of the generation will be generated by the mutation process. In the mutation process one or two genes are inverted in order to generate a better diversity in the population. The mutation function used in our experiment is “Gaussian.” Gaussian adds a random number to each individual; the random number is derived from a Gaussian distribution having zero mean and a standard deviation of 1. In all the experiments the size of the population in each generation was set to 10. Total generations were set to 10. The optimized values from the genetic algorithm for the three selected geometries are shown in L, a hollow cylinder of inside radius r1, outside radius r2, and length L or a hollow sphere of inside radius r1 and outside radius r2 with temperature dependent thermal conductivity k = k1[1 + β(T − T1)], where β(K−1) is a measure of the thermal conductivity variation with temperature and k1 is the thermal conductivity at temperature T1. Each geometry is experiencing a uniform volumetric heat generation at the rate T1 while the temperature on the right face or at the outer radius is T2, where T2 > T1. The dimensionless governing equations for a plane wall, hollow cylinder, and hollow sphere with temperature dependent thermal conductivity and uniform volumetric heat generation can be written asboundary conditionsConsider one-dimensional steady conduction in a plane wall of thickness θ(X) or θ(R) (depending upon the geometry) is obtained by utilizing “bvp4c”. A third order polynomial was approximated from the solution. The integral for the entropy generation rates in  are allowed to breed. The breeding process (in a broad sense) consists of crossover and mutation; the bad individuals are replaced by the best offspring. The genetic algorithm checks for the convergence. If the algorithm converges then it terminates otherwise it generates a new set of population [The optimization process is shown in pulation . In our x = {xt | t = 1,2,…., Nk}. “t” denotes the parameter space of the optimization problem. Nk is the maximum number of parameters to be considered in the optimization process. “xt” can be continuous or discrete, real or imaginary [xt into a symbolic representation “d” which is termed as a chromosome. Many genes combine to form a chromosome. The number of genes in a chromosome determines the quantization level of the parameters (used in optimization process). The chromosome “d” can be represented byNdl is the length of the chromosome. The encoding of a parameter value “xt” into “d” can be represented byxtmin and xtmax are the minimum and maximum values of the parameter xt. A generation Z consists of randomly generated population:R” is the maximum number of members in the population. The members of the population are tested for fitness. In our specific case the members are tested so that they lie within the bounds defined on the parameters. The filtered individuals are used to determine the cost (of the objective function). Production of new members in the next population consists of three major steps, namely, selection, crossover, and mutation. the most suitable candidates are selected as parents and are allowed to reproduce the new generation. The selectionoperation can be represented by ZSk = S(Zk) which produces a population of size “R.” Various selection schemes have been proposed such as ranking, roulette-wheel, and stochastic uniform methods [ty” chooses a random chromosome from Z and the operator “c” maps a pair of chromosomes z1 = {ej1 | j = 1,…, Ndl} and z2 = {ej2 | j = 1,…, Ndl} to another pair such that:ZMk = M(ZCk) and mathematically it can be represented asz = {ej | j = 1,…, Ndl}, m(z) = {ψ(zj) | j = 1,…, Ndl}, andGenetic algorithm is used for optimizing functions. Let the objective function to be minimized be denoted by maginary . The gen methods . The nexNdl is set to 10. Total generations were set to 10. The optimized values from the genetic algorithm for plane wall, hollow cylinder, and hollow sphere are shown in The fitness function (the function to be minimized) is the entropy generation rate in all the cases. The simulation is developed in MATLAB. The fitness scores returned by the fitness function are ranked on the basis of their scores. The rank of the fittest individual is set to “1” and the next fittest is assigned a rank of “2” and so on. Rank fitness scaling removes the effect of raw scores. “Stochastic uniform” scaling function is used for selection of parents in the next generation. The parents are selected based on the rank as determined earlier. Stochastic uniform algorithm lays out a line in which each parent corresponds to a section of the line of length proportional to its expectation. The algorithm moves along the line in steps of equal size, one step for each parent. At each step, the algorithm allocates a parent from the section it lands on. The first step is a uniform random number less than the step size. Reproduction algorithm determines how the offspring are generated. The elite count is set to “2” which guarantees that a maximum of two individuals will survive in the next population. The crossover process used is “scattered” which first creates a random binary vector. A “1” in the random binary vector is replaced by genes from the first parent and a “0” in the random binary vector is replaced by a gene from the second individual. Crossover fraction is a factor which determines how many individuals in the next generation will be generated by mixing genes from two different chromosomes. The crossover fraction has a value of 0.8. The remaining members of the generation will be generated by the mutation process. The mutation process generates a better diversity in the population. The mutation function used in our experiment is “Gaussian.” Gaussian adds a random number to each individual; the random number is derived from a Gaussian distribution having zero mean and a standard deviation of 1. In all the experiments the size of the population in each generation was set to 10, that is, The genetic optimization tool in the MATLAB environment was used to solve nonlinear heat conduction problem in three selected geometries. The most important task is to code the fitness function and to set all the constraints. The genetic algorithm calls the fitness function at each instant with random values of the parameters to be optimized. These random values are the members of the population. With each set of values, the boundary value problem is solved and the numerical solution is converted into a third degree polynomial. The polynomial is subsequently used (by invoking MUPAD from MATLAB) to determine the entropy generation rate. The entropy generation rate is determined for the complete population and the minimum value of the entropy generation rate is held and the remaining values are discarded.One case for each of the selected geometries that is, plane wall, hollow cylinder, and hollow sphere, is shown in Figures Genetic algorithms are successfully employed to optimize the dimensionless temperature in the selected geometries. The concept of minimum entropy generation was used to obtain the minimum dimensionless temperature. It is found that, for the same constraints, the minimum dimensionless temperature and hence the minimum entropy generation rates are obtained in case of plane wall.


Pseudoexfoliation syndrome (PEX) is a systemic disease involving the accumulation of pathological material deposits in the tissues of the anterior segment of the eye. The problem of modern ophthalmology is a quantitative assessment of the severity of PEX in the diagnosis and evaluation of the treatment progress in patients.M × N = 1280 × 960 pixels were obtained in jpg format using the slit lamp CSO 450-SL. The patients were aged 50–80 and were recruited from Poland. All patients who participated in the study provided written informed consent after explanation of the nature and possible consequences of the study. The image analysis method proposed by the authors contains the calculation of the direction field, setting a straight perpendicular line passing through each pixel of the edge of the pupil, the calculation of the intersection of straight lines in order to determine the central point of the pupil position, the detection of the contour of PEX and the outer border of the iris with the use of the polar coordinate system. All analyzed parameters were set automatically with one exception parameter chosen manually depending on the slit lamp type.For the purposes of this study, 52 images of the anterior segment of the eye with the resolution of A fully automatic measurement of PEX was carried out with the proposed method. Quantitative results enable to perform reproducible tests independently of the research centre. Owing to the image analysis method proposed by the authors, it is possible to obtain results in no more than 1 second on the Intel Core 2 Quad CPU 2.50 GHz with a measurement error below 3%. Other known methods of image analysis and processing that are compared in this paper give results with a greater error (4-35%) which depends on the degree of magnification  and are not fully automatic.The methods of image analysis and processing enable a quantitative, repeatable and automatic measurement of the severity and progress of PEX syndrome. They support medical diagnosis and automatic archiving of results. Pseudoexfoliation syndrome (PEX) is related to aging of the body. It is more common in people over 50 years of age, and in about 20% of the population above 60 years of age in the countries of northern Europe. PEX syndrome is a systemic disease and is recognized by an ophthalmologist during routine testing. Mydriasis and image analysis with a slit lamp enable to detect the nature and severity of PEX. This disease involves dysregulation of elastin synthesis and the formation of irregular elastic fibre aggregates, with a concomitant significant reduction of collagen fibres. Elastic changes are observed in the arterial and venous vessels and also around the sieve plates in the eye. Examples of images of the eye with PEX syndrome are shown in Figure The works on image analysis and processing of PEX images in ophthalmology are related to eye morphometric measurements performed in visible light. Morphometric analysis is presented in several works devoted to comparative analyses and in those associated with a selected region of the world. Quantitative parameters are presented in detail in the work of Seitz B. et al. from 1995 . 69 preoDue to the nature and shape of PEX syndrome -17, the M × N = 1280 × 960 pixels were obtained in jpg format using the slit lamp CSO 450-SL. The patients were aged 50–80 and they were all from Poland. All patients who participated in the study provided written informed consent after explanation of the nature and possible consequences of the study. In order to verify the sensitivity of the discussed method to the parameter changes, the images of the anterior segment of the eye were taken for 6-fold, 16-fold and 20-fold magnifications.For the purposes of this study, 52 images of the anterior segment of the eye with the resolution of The method of image analysis and processing was divided into three parts – Figure LRGB  derived from the slit lamp CSO 450-SL is subjected to median filtering using a mask he sized Mhe × Nhe = 3 × 3 pixels [LW obtained in this way is converted to gray levels LGRAY = 0.2989*LW + 0.5870*LW + 0.1140*LW [LGRAY is subjected to further image analysis  ,21. The LGRAY image convolution with the hs mask is calculated. The size of the mask hs is chosen once for a given type of the slit lamp. In the analysed case (slit lamps CSO 450-SL), it is Mhs × Nhs = 45 × 45. The mask hs is shown in Figure hs is rotated sequentially in the angular range θ∈[0, 180) by increments of 1°, 5°, or 10°. Small values of increments increase the computation time and accuracy, and vice versa, larger values reduce the accuracy and computation time. In each step of the rotation of hs mask, the weave with the LGRAY image is calculated and two matrices, namely Lm and Lθ, are formed. The first marix Lm contains the maximum pixel values obtained in each weave. The matrix Lθ, on the other hand, contains the angular values showing for what angle θ of rotation of the hs mask, it occured. On the basis of the matrices Lm and Lθ, it is possible to calculate the direction field shown in Figure θ + 90°, the intersection of straight lines is calculated. As a consequence, two matrices LT and Lr are formed. The first one ) contains information about the intersection of straight lines. The value of a given pixel in the matrix LT represents the number of intersections of the straight lines at this point ) contains information about the radius calculated from a given pixel to the intersection  of the maximum value in the matrix LT = max). The pupil diameter is a value read from the matrix Lr. This information is necessary to perform subsequent image analysis operations in the last step , conversion to polar coordinates is performed, which results in the image Lϕ , the image Lt was subjected to binarization, followed by the method of filling the holes. The resulting image Ls enables to detect the pupil edge position. Its position is further approximated by a polynomial  and the contour of the outer boundary of the iris KI(n) are determined using the method of the modified active contour [Kz(n), KP(n), KI(n)) are shown in the images Ls and Lt in Figure In order to calculate the severity of PEX syndrome, it is necessary to detect the contour of PEX and the outer border of the iris. With the value of the pupil radius ) Figure . The cha contour . The resWPEX enables to obtain reliable results only in the case of a fully visible contour KP(n). It is therefore necessary to check the following condition in each case:The defined value W1/0 = 0), the measurement is considered to be unreliable.When the pupil contour coincides with the set contour of PEX (hs (for a given type of the slit lamp). However, the quality of the obtained image of the PEX contour has the greatest impact on the results. In many cases the image analysis had to be conducted despite the high level of noise. The image noise was usually caused by disturbances of the measurement path , small inclusions, dust, etc. The observed image disturbances were characterized as Gaussian noise. Therefore, a verification of the results obtained according to the artificial noise added to the image LRGB was conducted. The artificial noise was the Gaussian noise with zero mean value and the variance σ2 ranged from 0 to 0.05 at 0.001. The Figure WPEX value dependent on the increase of the noise level (variance σ2) on the input image LRGB. Additionally the Figure WPEX value was noticed when the variance value exceeded 0.035 . In this presented case the reason for measurement errors was incorrectly determined contour KP(n) – Figure KI(n) contour determination (marked red). The reason is a sufficient contrast between the iris and the sclera and thus little influence of noise on the obtained results.The proposed method and algorithm was used for analysis of 52 images. Representative examples of obtained results and image processing parts were presented on Figures The comparison among other known methods with the proposed methods is presented in the next part.WPEX determined automatically by three methods with the value WPEXE determined by a specialist physician. Denoting the subsequent values WPEX as WPEXM, where M - method number, an error for each method was calculated:The discussed measurement method of PEX syndrome was compared with two other methods. The results were referred to the contours marked by a specialist physician. As a result, a comparison was made of the value The comparison of the quality of the results was performed based on the following methods:WPEX1) – image pre-processing is the same as for the described case . Proper analysis concerning determination of the contours of PEX, the pupil and the iris is based on the active contour method proposed by Wu H. et al. in [Method 1  – image pre-processing only involves conversion of an ego colour image into a grayscale image. Proper analysis is related to binarization which is necessary to pre-determine the position of the pupil. The resulting binary image is used as a mask on which the contour is determined using Canny method [Method 2 (y method . The resWPEX3) – described in this paper.Method 3 ,– information for the physician concerning the quality of the measurement ,– single image analysis time in under 1 second on the computer Intel Core 2 Quad CPU Q9300 @ 2.GHz RAM 8GB.The practical usefulness of this method has been confirmed by specialist physicians. It is used in many branches of ophthalmology supporting medical diagnostics or enabling clinical trials. It is now being implemented in the Department of Ophthalmology in District Railway Hospital in Katowice, Poland.Further papers of the authors will focus on the analysis of the correlation between other ocular parameters such as intraocular pressure or visual field and the severity of the pseudoexfoliation syndrome.PEX: Pseudoexfoliation.The authors declare that they have no competing interests.RK and ZW suggested the algorithm for image analysis and processing, implemented it and analysed the images. AN, EW performed the acquisition of the 52 images and consulted the obtained results. All authors have read and approved the final manuscript.


The coordination of cell division and cell expansion are critical to normal development of tissues. In plants, cell wall mechanics and the there from arising cell shapes and mechanical stresses can regulate cell division and cell expansion and thereby tissue growth and morphology. Limited by experimental accessibility it remains unknown how cell division and expansion cooperatively affect tissue growth dynamics. Employing a cell-based two dimensional tissue simulation we investigate the regulatory role of a range of cell division rules on tissue growth dynamics and in particular on the spatial heterogeneity of growth. We find that random cell divisions only add noise to the growth and therefore increase growth heterogeneity, while cell divisions following the shortest new wall or along the direction of maximal mechanical stress reduce growth heterogeneity by actively enhancing the regulation of growth by mechanical stresses. Thus, we find that, beyond tissue geometry and topology, cell divisions affect the dynamics of growth, and that their signature is embedded in the statistics of tissue growth. Plant cells are constrained by cellulosic walls and glued to their neighbors by a pectic lamella, therefore, the regulation of growth has to be achieved without cell migration or cell removal. This makes the orientation of cell divisions and the direction of cell expansion critical for normal development Smith, . While iin vitro plant tissue cultures  in the central zone of the shoot apical meristem, where mechanical stress is predicted to be isotropic. If desired the impact of curvature can be incorporated in the simulation by adding the appropriate global stress field, assuming that relative values of cell turgor driven stress and organ shape driven global stress can be estimated.In the following we detail the ingredients of the model.2.1i) is driven by the growth of an individual, anisotropic target ellipse represented by a matrix iM =  defined as the second moment of area of its v vertices with position x, y.To model tissue growth we employ a generalized vertex model simulation as introduced in Uyttewaal et al. . A tissuka = kyk+1x − k+1ykx. Positions and shapes of cells are determined from the condition of mechanical equilibrium balancing the quest of individual cells to attain their target ellipses. This is achieved by minimizing the total energy of a tissue encompassing i ∈  cells.with iM and target ellipse iP represents the tension in cell walls. The minimization of the total energy with respect to cell vertex positions determines not only cell position and shape within the tissue but also the local stress tensor iS exerted by surrounding cells on cell i. The definition of stress on a cell i follows from . Therefore, the target ellipse changes in time asGrowth is described by the time-evolution of th rate γ ± σ exhiη stands for the strength of the stress feedback and quantifies the capacity of cortical microtubules to reorient according to stress, and the speed at which this re-orientation occurs. As extension to incorporate anisotropic growth one can also interpret the basal growth rate as a tensor instead of a scalar and thereby enforce for example preferred growth along one direction of space.2.2To study the regulatory role of different cell division modes we restrict ourselves to the case of roughly symmetric cell divisions by considering only cell divisions planes pivoted at the cell’s center of mass. Hence, cell division modes only differ in the cell division plane’s direction within a cell. The five cell division modes are sketched in Figure A(0). Upon cell division along axis i = 1, 2, according to the following rules, which ensure that, in the coordinate system spanned by the division axis Cells divide once they have reached a threshold area 2.3−2, as this ensures convexly shaped cells. Choosing the parameter γ amounts to setting the simulation time step and must therefore be chosen small enough to allow equilibration of the tissue after each growth step. In each simulation run the tissue is initialized as an isotropic hexagonal tissue consisting of three cells with their The simulation is implemented in a custom written C++ program. Simulation parameters are chosen as α = 0.02, β = 7.0, χ = 1.0, γ = 0.01, η ∈ , and σ ∈ , specifically values of σ = 0.5 and σ = 0.85 have been used for low and high intrinsic noise levels. Simulation results are independent of the precise choice of the tissue energy model parameters α, β, and χ as long as the relative order of magnitude between the line tension parameter α and the “elastic” parameters β, χ is kept at 102.4A main tissue characteristic is its local growth variability,G, of an individual cell i relative to the mean of its own growth rate and its nearest neighbor’s growth rate G itself is defined as the difference of the actual form matrix after a growth and subsequent energy minimization step normalized by the actual cell form,which denotes the normalized variability in growth, measured by the growth tensor iS instead. Furthermore, the stress anisotropy is calculated as the absolute difference between the largest and smallest eigenvalue of the stress tensor normalized by their sum. The tissue’s geometric and topological properties are assessed with the cell area, the number of edges per cell, a shape factor defined as area over perimeter squared, and as a measure of the positive opening angle between edges the squared opening angle at a vertex. Further, we measure the amount of stress released due to a cell division and subsequent energy minimization as,As further tissue characteristics we consider the local stress variability, which is defined according to the same formula as the growth variability evaluating a cell’s stress tensor i> denotes the sum over cell i and its nearest neighbors and S stand for the stress before and after cell division, respectively.where <3We started by investigating the impact of the five cell division modes (moment of area, stress, previous plane, random, and equal area, as defined in Figure 3.1On the very local level the direction of a cell division plane instantaneously affects the stress distribution within the tissue. In the dividing cell itself the new cell wall increases stress following division, as the new wall like any cell wall in the tissue bears tension. But this cell wall also affects the mismatch between target and actual cell form of the dividing cell and, hence, opens room for neighbors to reduce their mismatch as well. Thus including the neighborhood, stress is most often released on average in the group of cells comprising the dividing cell and its nearest neighbors, as shown in Figure 3.2On the global scale of the whole tissue the differences in cell division modes also affect tissue mechanics, and overall geometry and topology. Table 3.3Taken together the release of stress on the local scale and the tissue wide characteristics already suggest different impacts on growth dynamics for the two modes of division according to moment of area or to stress, compared to the two random modes of division. The case of a division plane oriented perpendicular to the previous division plane seems to be a chimera, releasing least stress on the one hand but giving rise to tissue properties that resemble those for the two other deterministic division modes, which release most stress. This chimeric behavior is indeed reflected qualitatively in the snapshots of Figure 4Plant tissues have two ways to regulate their growth, on the one hand by coordinating cell expansion and on the other hand by directing the orientation of cell division planes. Both pathways seem to be regulated by mechanical stresses within the tissue. Cell expansion is asymmetric, reduced in the direction of maximal stress due to a mechanical feedback on cell wall strengthening mediated by cortical microtubules. The orientation of cell division planes often agrees with the direction of the cell’s shortest midplane (Besson and Dumais, It has been shown that the mechanical feedback on cell expansion can provide a mean to reduce or amplify growth heterogeneities in tissues (Uyttewaal et al., From our observations the level of noise within a cell division rule arises to be the determining factor of how much regulation this rule can provide, see summary in Figure ton1 (Traas et al., pok1;pok2 (Müller et al., While the case of random cell divisions might appear a bit extreme in the context of development, the choice of the cell division mode might nevertheless be regulated, even when restricted to the rules that depend on an interaction with the tissue. Cell division along a cell’s shortest midplane, which we implemented according to the direction of maximum principal second moment of area, has been found to be in agreement with large scale tissue statistics (Sahlin and Jönsson, In summary we show that the orientation of cell division does not only contribute to tissue geometry and topology but also to the dynamics of tissue growth. Cell division planes that are oriented along the cell’s shortest midplane or the direction of stress actively contribute to the tissue growth dynamics by releasing stress and thus reducing stress variability and growth variability within a tissue. While geometric and topological tissue characteristics are limited to discern between different modes of cell division, measuring quantities such as growth variability provides handles to distinguish cell division modes and beyond learn about the regulation of growth via the orientation of cell division.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.