The monitoring of the cardiac output (CO) and other hemodynamic parameters, traditionally performed with the thermodilution method via a pulmonary artery catheter (PAC), is now increasingly done with the aid of less invasive and much easier to use devices. When used within the context of a hemodynamic optimization protocol, they can positively influence the outcome in both surgical and non-surgical patient populations. While these monitoring tools have simplified the hemodynamic calculations, they are subject to limitations and can lead to erroneous results if not used properly. In this article we will review the commercially available minimally invasive CO monitoring devices, explore their technical characteristics and describe the limitations that should be taken into consideration when clinical decisions are made. The need for the precise quantification of cardiac output (CO) in high-risk surgical patients, both in the operative room and the intensive care unit, is vital in modern medical practice. While up to 20 years ago CO had to be estimated from the PAC, nowadays new, less invasive techniques are available. When used together with perioperative protocols aiming at improving CO and oxygen delivery (DO2), their use is referred to as hemodynamic optimization or goal-directed therapy (GDT) .Much has changed since the introduction of the pulmonary artery catheter (PAC) by Swan and Ganz in 1970 for the measurement of CO using the thermodilution method. Although in the context of moderate and high-risk surgery the beneficial effect of the PAC combined with goal directed therapy (GDT) has been established in a recent meta-analysis , the invThe term ‘minimally invasive cardiac monitoring’ encompasses all the methods and devices that calculate the cardiac output without the need of inserting a PAC, ranging from methods almost non-invasive to marginally less invasive than the PAC. These include the pulse pressure analysis, the transpulmonary thermodilution, the indicator dilution, the esophageal Doppler, the thoracic electrical bioimpedance, the carbon dioxide rebreathing, and the echocardiography. Since each one of these devices utilizes a different method of estimating the cardiac output, the clinician should be aware of their distinct features, their limitations but also the sources of potential error that stem for their use.The pulse pressure analysis uses the arterial waveform, obtained either from an arterial catheter or a finger probe, in order to calculate the stroke volume (SV) and the systemic vascular resistance (SVR).Its principles first described by Erlanger and Hooker in 1904 , pulse pThis and the fact that the compliance is also age-related, prevented any straightforward correlation of the pressure to the volume . Only inOne should always keep in mind that the pulse pressure method relies heavily on an optimal arterial pressure tracing, making an under- or over-damped arterial waveform a potential source of errors in calculation. Moreover, the pulse pressure systems necessitate an arterial wave that is purely reflective of the forward SV. As a consequence, situations in which the arterial wave is distorted either by artifact or a physiologic phenomenon  will lead to inaccuracies . FinallyA variety of commercial systems that make use of the pulse pressure analysis method are available and they are divided in two groups, depending on the way that they are calibrated. Monitors that are ‘autocalibrated’ consist of the FloTrac/Vigileo, the Pulsioflex, the LidCO rapid, and the recently introduced Nexfin and esCCO monitors. On the other hand, there are devices that are externally calibrated: the PiCCOplus and the recently developed EV1000 use the transpulmonary thermodilution method, while the LidCO plus utilizes the lithium dilution technique for the same purpose. Moreover, apart from being useful tools in CO calculations, these monitors can also help predict the fluid responsiveness, as will be discussed later in this review article.Connected to a standard indwelling arterial catheter, the FloTrac sensor  uses an upgraded algorithm that derives the SV from the pulse pressure (PP) of the arterial waveform, after correcting for the compliance and the resistance of the arterial system.A similar pulse pressure analysis method is used by the ProAQT sensor which is incorporated in the Pulsioflex monitor . Utilizing an existing peripheral arterial catheter and analyzing the arterial waveform 250 times per second, a start value for CO trend monitoring is determined after the patient’s characteristics are inserted to the system. To increase accuracy, a CO value measured by another method (for example by echocardiography) can be entered and thus the system can be externally calibrated.As for the LidCO rapid system , it is based on the same algorithm as the LidCO plus monitor (which will be described later), but instead of thermodilution it relies on nomograms for the calculation of the CO.2I) is derived.One of the latest additions to the field of minimally invasive CO monitoring is the Nexfin monitor . Rather than a minimally invasive monitor, it is a completely non-invasive method of determining the patient’s hemodynamic parameters, as the need for an invasive arterial catheter is obviated. The monitor is connected to the patient by wrapping an inflatable cuff around the middle phalanx of the finger. The pulsating finger artery is ‘clamped’ to a constant volume by applying a varying counter pressure equivalent to the arterial pressure resulting in a pressure waveform. The finger arterial pressure is then reconstructed into brachial arterial pressure waveform using a transfer function and a level correction based on a vast clinical database. The resulting brachial pressure waveform serves as the basis for determining continuous CO. Real-time continuous CO and other hemodynamic parameters are derived by a novel pulse contour method (Nexfin CO-Trek®), which is based on the systolic pressure area and a physiological three-element Windkessel model individualized for each patient. Moreover, the presence of a co-oximeter enables the non-invasive calculation of hemoglobin, from which the oxygen delivery index . Also being a non-invasive monitor, it uses a new technology that derives the CO using the Pulse Wave Transit Time (PWTT), which is obtained by the pulse oximetry and the ECG signals of each cardiac cycle. The rationale behind this is that animal studies have shown a strong correlation between the SV and the PWTT. The only up-to-date validation study has demonstrated a clinically unacceptable performance of the device when compared to the CO values obtained with transthoracic echocardiography .The accuracy of the pulse pressure analysis method in estimating CO has been extensively investigated against CO calculations by the thermodilution method using the PAC. This holds true particularly for the FloTrac/Vigileo monitoring. In one of the most recent meta-analyses, Mayer et al.  showed iGiven its straightforward setup and use, it seems that the FloTrac/Vigileo is a useful tool correlating well with the gold standard of the thermodilution method with the PAC, in patients with a regular rhythm and stable respiratory pattern and mechanics, hospitalized in an environment with less abrupt hemodynamic changes as is the intensive therapy unit (ITU). While awaiting for further studies to assess this relationship, a more cautious approach should be adopted when it is used to assess the CO in patients that rely on substantial inotropic or vasopressor support or in environments and settings with rapid dynamic changes, as in the operating room (OR).Despite its relatively short presence in the market, the non-invasive Nexfin monitor has also been validated against the traditional methods of CO calculation, yielding positive results so far. Two different research groups demonstrated a reasonable correlation of CO values obtained by the Nexfin when they were compared with those calculated by transpulmonary thermodilution, both in the setting of cardiac surgery ,14. The The PiCCOplus monitor , which is based on the pulse pressure analysis to provide continuous real-time assessment of the CO, uses the transpulmonary thermodilution for intermittent calibration, being until recently the only device to incorporate this method in a commercial application. This method is based on the same principle as the traditional thermodilution but spares the need for a PAC insertion. The technique starts with the injection of a cold injectate in the superior vena cava (SVC) via a central venous catheter (CVC) which mixes with the ambient blood and travels through the right heart, the pulmonary vasculature and the left heart before reaching the aorta. A thermistor in the aorta or a major arterial branch measures the blood temperature and a thermodilution curve of temperature over time, similar to that from the PAC-based method but having a delayed peak temperature change, is plotted. The CO is measured by the thermodilution equation:B=blood temperature, TI=injectate temperature, and K=−computation constant  , which iSince a pulse contour method is used for continous CO display, the same limitations as in the FloTrac/Vigileo monitor apply for the PiCCOplus . Sources of potential errors that are specific for the transpulmonary thermodilution come from the fact that the PiCCOplus estimates the CO of the left heart whereas the PAC thermodilution that of the right side. These should be identical in ideal conditions, however a discrepancy is encountered in the presence of intracardiac and intrapulmonary shunts. Moreover, conditions related to indicator loss in the tissues  or recirculation will lead to a discrepancy of the calculated CO compared to the one derived by the PAC thermodilution, although these two phenomena may actually cancel each other .Regarding the reliability of the method, it appears that there is good correlation of the CO measurements obtained with the PiCCOplus compared to other methods. Two studies performed on pediatric animal models by the same scientific team showed a significant correlation when the transpulmonary thermodilution derived values were juxtaposed to those obtained with an ultrasound probe around the main pulmonary artery, both in normal cardiac anatomy and in the presence of a left-to-right shunt ,21.An older study confirms the good performance of the transpulmonary thermodilution even during substantial variations in vascular tone and hemodynamics . Taking The latest entry in the area of minimally invasive CO monitoring using the transpulmonary thermodilution comes from Edwards Lifesciences, which developed the EV1000/VolumeView monitor . Needing, as the PiCCOplus does, a specific to the set central arterial catheter and using a patented for the company algorithm, it also displays volumetric parameters as the EVLW and GEDV but also a new variable named the global ejection fraction (GEF). A recent clinical validation study proved the interchangeability of this new method to the PiCCOplus monitor, with VolumeView scoring better in the calculation of GEDV .+-sensitive electrode attached to the catheter that generates a voltage [The last of the calibrated CO monitors is the LidCOplus  that utilizes the lithium dilution technique. Based on the pulse power rather than the pulse pressure analysis via the PulseCO algorithm, which does not rely on the arterial waveform morphology, and needing only a peripheral arterial catheter, the LidCOplus technology uses the lithium dilution to intermittently calibrate the system. Specifically, boluses of 0.5-2 mL of lithium chloride are each time injected through a peripheral or central line and the lithium concentration is measured through aspiration of blood from the arterial catheter, using a Li voltage . Since t voltage .Apart from the expected lack of accuracy of the LidCOplus technology in a patient already on lithium treatment, the other interference that should be taken into account is the use of bolus doses of muscle relaxant drugs in the operative and intensive care setting. High peak doses of these drugs can cross-react with the lithium sensor as they incorporate a positively charged quaternary ammonia ion that can be detected by the sensor and thus lead to an overestimation of the CO. Muscle relaxant agents which are not compatible with the LidCOplus monitor are atracurium and rocuronium, whereas suxamethonium, vecuronium, and pancuronium can be used provided that a time interval of 15–30 minutes elapses between their bolus administration and the LidCOplus calibration.The consistency of the CO measurement with the LidCOplus technology compared to the traditionally established thermodilution method with the PAC, has been investigated in a number of validation studies. In one of the most recent studies by Mora et al. , the litThe Esophageal Doppler (ED) monitor, which is based on the Doppler effect in order to measure the velocity of blood flow, was first introduced in the 1970s as a non-invasive means to measure CO. The velocity is calculated from the following equation:d is the frequency shift, f0 is the frequency of the emitted ultrasound, and θ is the angle between the ultrasound beam and the direction of the blood flow. If the flow of blood in the descending aorta is known, this figure can be used to estimate the stroke volume and hence the cardiac output. The esophageal Doppler measures the velocity of blood in the descending aorta in centimeters per second (cm/s). In order to convert this figure into blood flow in milliliters per second (mL/s), the diameter of the aorta needs to be known. This is derived from published nomograms based on age, sex, weight, and height  or through direct ultrasound measurement . The ED also has the ability to measure the corrected flow time (FTc) as a measure of cardiac preload. The FTc is the duration of flow during systole corrected for a heart rate of 60 beats per minute. It is unclear as to whether the FTc or SV should be used to guide fluid therapy, but it appears that the ability to respond to a fluid challenge is best determined by FTc. Several studies have compared FTc with other indices such as pulmonary artery occlusion pressure and have found good agreement between the two [where v is the blood flow velocity, c is the speed of sound in tissue, f the two -32.There are some limitations to the usage of ED. First, the ED only measures descending aortic blood flow, which may not always be constant due aortic pathology or compression or due to abnormal upper to lower body blood flow distribution. Also, the aortic cross-sectional area is not constant, due to changes in pulse pressure, vascular tone, aortic compliance, volume status, or catecholamine use. Due to the fact that the radius of the aorta is squared in the final CO equation, even small changes in aortic area can significantly affect CO determinations . Moreoveversus anesthetist-directed fluid therapy in 108 patients undergoing elective colorectal resection. They found that despite both groups of patients receiving the same volume of intraoperative fluids, the group managed with the ED had a shorter hospital stay and lower morbidity rates than the control group. Interestingly, patients in the intervention group also had lower levels of interleukin-6, which suggested an attenuated inflammatory response to surgery, perhaps due to the improved organ perfusion. In a study by Wakeling et al. patients recovered gut function significantly faster and suffered significantly less gastrointestinal and overall morbidity [There have been studies that have compared ED measurements of CO with PAC-derived thermodilution CO. Dark and Singer performed a literature review regarding the validity of ED monitoring as a measure of CO in critically ill adults, concluding that the ED monitor has high validity in tracking changes in CO . In addiorbidity . These oorbidity .A completely non-invasive Doppler technology, the USCOM , is also available which uses Doppler technology to measure CO from a suprasternal Doppler probe. This technology has been studied in a few patient population groups (mostly stable ICU patients) and has shown reasonable correlation with PAC ,43.Variations in the electrical impedance of the thorax to an alternating current which occur synchronously with the cardiac cycle were observed nearly 40 years ago. The first use of this phenomenon to measure SV and CO was described by Nyboer , and KubElectrical bioimpedance involves the analysis of intrabeat variations in transthoracic voltage in response to the applied high frequency transthoracic current. Two commercial devices based on electrical bioimpedance use electrodes attached to an endotracheal tube  or the skin . Pulsatile changes in thoracic blood volume result in changes in electrical impedance. The rate of change of impedance during systole is measured and an estimate of the SV and the CO is derived from a mathematical equation.Sources of potential inaccuracies include motion artifacts, electrical interference, cardiac arrhythmias, heart and lung pathologies , and foreign bodies (as chest tubes). Clinical trials of TEB have been shown to be reliable in young healthy volunteers, but in septic or surgical patients, the results have been inconsistent -48.Recently, bioreactance , a modification of thoracic bioimpedance, has been introduced. Bioreactance refers to the electrical resistance, capacitive and inductive properties of blood and biological tissue that induce phase shifts between an applied electrical current and the resulting voltage signal. In contrast to bioimpedance, the bioreactance technique analyzes the frequency spectra variations of the delivered oscillating current. When blood flows out of the heart, phase shifts occur if alternating currents are applied across the patient’s chest. Such phase shifts are conceptually similar to a frequency modulation as used in radio transmission. The phase shifts are measured continuously and have been shown to relate almost linearly to blood flow in the aorta. This results in less interfering from the electrical noise, patient movement, respiratory effort, lead placement, and body mass index.In addition to cardiac output, mean bioreactance measurements are indicative of the total thoracic fluid content (TFC). TFC is affected by both intravascular and extravascular fluid in the chest cavity and although it does not correlate with pulmonary artery wedge pressure (PAWP), its changes are very reliable indicators of the changes in intravascular or extravascular fluid volume . In a stIt appears that the new generation of devices might be better than the first generation TEB machines, although there are still limitations regarding their accuracy in measuring CO during dynamic conditions.The partial carbon dioxide (CO2) rebreathing technique uses the Fick principle applied to the CO2 in order to estimate CO non-invasively. The NICO monitor  implements intermittent partial rebreathing through a specific disposable rebreathing loop. The monitor consists of a CO2 sensor, a disposable airflow sensor and a pulse oximeter. CO2 production (VCO2) is calculated from minute ventilation and its CO2 content, whereas the arterial CO2 content (CacO2) is estimated from end-tidal CO2, with adjustments for the slope of the CO2 dissociation curve and the degree of dead space ventilation. The partial rebreathing reduces CO2 elimination and increases end-tidal CO2. Measurements under normal and rebreathing conditions allow one to omit the venous CO2 content (CvCO2) measurement in the Fick equation, because CvCO2 does not change during this brief period of rebreathing .While the technique is easy to use, the correlation between the NICO and standard thermodilution has been shown to be adversely affected in spontaneously breathing patients, which limits the number of suitable candidates ,53. Partper se, the ClariTEE uses a monoplane transducer that enables the operator to acquire basic views of the heart  that, combined with a software tool, offer continuous calculations of the ventricular size and systolic performance. Moreover, echocardiography derived measurements of the stroke volume can help in the assessment of fluid responsiveness [Widely used in the cardiac operative and postoperative setting to demonstrate cardiac anatomy and identify pathology, the transesophageal echocardiography (TOE) has been impractical in assisting with continuous CO measurements outside the operative theater because of the size of the probe and the limitations that come with it. However, the recent development of a miniaturized 5 mm TOE probe  that can stay indwelled for up to 72 hours, has enabled hemodynamic management of the critically ill patients . Althougsiveness . ValidatThe assessment of intravascular volume status of an individual has been traditionally performed with static parameters, mainly filling pressures such as CVP and PAWP, which reflect the preload of the right and the left ventricles, respectively. It is now acknowledged that these values correlate poorly with the intravascular volume and the response to a fluid bolus , hence tAll the devices that use the pulse pressure analysis method for CO monitoring, also calculate those two parameters. Based on the effect of the cyclic variation of intrathoracic pressures with respiration on the preload of the left ventricle and using appropriate algorithms, the beat to beat variation of the SV and the pulse pressure (PP) is calculated. Specifically, positive pressure ventilation induces cyclic changes in vena cava blood flow, pulmonary artery flow, and aortic blood flow. During inspiration, vena cava blood flow decreases (venous return decreases) and, according to the Frank-Starling relationship, pulmonary artery flow decreases. Approximately three beats later this decrease in pulmonary artery flow is transmitted to the left ventricle inducing a decrease in SV and aortic PP. As a general rule, values of SVV >10% and PPV >13% are indicative of patients that will probably respond to the administration of fluids, while lower values indicate the opposite. The basic limitation is that the above calculations can only be applied to mechanically ventilated patients, as the correlation in spontaneously breathing individuals is weaker. Moreover, for optimal results the tidal volume (TV) should be >8 mL/Kg of body weight, the patient should be in sinus rhythm, and the chest must be closed   may help with the prediction of fluid responsiveness. The PVI is continuously calculated by the new non-invasive Masimo monitor , a device that resembles the traditional pulse oximeter. The monitor measures first the change during a respiratory cycle of the Perfusion Index (PI), which is the ratio of non-pulsatile to pulsatile blood flow through the peripheral capillary bed, and then calculates the PVI from the following formula:The greater the PVI value is, the more likely the patient will respond to fluid administration . As is tAll the above methods of quantifying the CO have the potential to reduce the morbidity and mortality of the patients if they are integrated into appropriate protocols that guide the therapeutic interventions. The use of CO measurements to guide fluid administration and inotropic therapy, optimizing this way the tissue perfusion and cellular oxygenation has been given the broad term goal-directed therapy (GDT). Its beneficial effects demonstrated as early as the late 1970s by the seminal work of Shoemaker and his team ,64, it iA whole array of minimally invasive devices and monitors that can reliably calculate trends in the CO without the need for a PAC are now available to the clinicians. Needing only peripheral or central arterial catheters or only a finger probe, as is the case in the Nexfin and Masimo monitors, they can give reliable measurements of CO and of dynamic indices such as the SVV and the PPV, provided that their limitations are taken into account.Additional tools in the area of minimal invasiveness are the OD, with its use strongly advocated by recent NICE guidelines, and the less widely used gas rebreathing and thoracic bioimpedance methods. Last, the introduction of a miniaturized TOE probe may revolutionize the management of ITU patients, providing real-time information on cardiac anatomy and function.The integration of these devices into therapeutic protocols enables the clinician to apply GDT and guide the inotropic support and fluid administration in a rational way, reducing this way the mortality and morbidity of the patients.AAA: Abdominal aortic aneurysm; BP: Blood pressure; CABG: Coronary artery bypass grafting; CI: Cardiac Index; CO: Cardiac output; CVC: Central venous catheter; CVP: Central venous pressure; DO2: Oxygen delivery; DO2I: Oxygen delivery index; ED: Esophageal Doppler; EPCI: Ejection phase contractility index; EVLW: Extravascular lung water; FTC: Corrected flow time; GDT: Goal-directed therapy; GEDV: Global end-diastolic volume; GEF: Global ejection fraction; HR: Heart rate; IABP: Intra-aortic Balloon Pump; ITBV: Intrathoracic blood volume; ITU: Intensive Therapy Unit; NICE: National Institute for Health and Clinical Ecxellence; OR: Operating room; PAC: Pulmonary artery catheter; PP: Pulse pressure; PAWP: Pulmonary artery wedge pressure; PWTT: Pulse wave transition time; PI: Perfusion index; PPV: Pulse pressure variation; PVI: Pleth Variability Index; PVPI: Pulmonary vascular permeability index; SV: Stroke volume; SVC: Superior vena cava; TEB: Thoracic electrical bioimpedance; TOE: Transesophageal echocardiography; TV: Tidal volume; VEPT: Volume of electrically participating tissues; VET: Ventricular ejection time.CC and LV declare no competing interests. MH has received lecture fees and expenses from Deltex Medical, Edwards Lifescienses, LidCO. MC has received honoraria, travel expenses, or unrestricted educational grants from LiDCO, Edwards Lifesciences, Deltex, Cheetah, Masimo, and Bmeye; he is part of the medical advisory board of Applied Physiology.CC has drafted the manuscript apart from the sections for the esophageal Doppler, the thoracic electrical bioimpedance, the bioreactance, and the gas rebreathing. LV has written the sections for the esophageal Doppler, the thoracic electrical bioimpedance, the bioreactance, and the gas rebreathing. MH has critically reviewed the manuscript. MC has conceived and critically reviewed the manuscript. All authors have read and approved the final version of the manuscript.


Although the symptoms of a transient ischemic attack (TIA) by definition resolve completely, the subsequent risk of cardiovascular complications is substantial. Urgent diagnosis and start of secondary prevention can reduce these risks. In light of the potential unfavourable prognosis, especially the first days after a TIA, we have developed and implemented a 24/7 TIA-service. Patients can be referred at any time and timing of analysis is determined by means of short-term risk assessment with a validated tool. Within half a day all investigations necessary to diagnose TIA and identify risk factors take place and secondary prevention at all levels is started immediately. This service is realized through integration of workflow of different specialities at multiple levels of care. Although patient service improves, the beneficial effects of a 24/7 TIA-service need to be established before further implementation is started. A preliminary analysis on the effects of continuous TIA-care and suggestions for the development of the necessary process and outcome indicators are provided. A transient ischemic attack (TIA) is defined as a focal neurological deficit of sudden onset attributable to ischemia of the brain or retina which resolves completely within 24 hours. Most TIAs last less than one hour. The 24-hour cut-off point is arbitrarily, but since 1975 no new definition of TIA has been universally accepted. When symptoms last more than 24 hours, a patient is diagnosed with a cerebral infarction (ischemic stroke) [Atherosclerosis is the main cause of TIAs. The major risk factors for the development of atherosclerosis and thus also for TIAs are hypertension, hypercholesterolemia, diabetes and smoking. Atherosclerosis can result in stenosis and ultimately occlusion of both large extracranial and small intracranial vessels. In large vessel atherosclerosis, such as in the internal carotid artery, thrombi can develop on the (post-)stenotic vessel surface, detach and be transported upstream until they occlude an artery and lead to cerebral ischemia. Thrombi can also develop in the heart as a result of atrial fibrillation or a prior myocardial infarction, which are other major causes of TIAs.Although the symptoms of a TIA, by definition, completely resolve, it is by no means a benign condition. The short and long-term risks of cardiovascular complications, such as cerebral and myocardial infarction are markedly increased after a TIA. In high-risk patients, the risk of subsequent cerebral infarction in the first two days after a TIA is 10% . Of all Of all patients with a cerebral infarction, 10% have had a TIA prior to the infarction . This il2 risk score  including diffusion weighted imaging can detect recent ischemia in a minority of TIA-patients . Other aThe aim of TIA treatment is prevention of new TIAs, cerebral infarction and myocardial infarction. In general it consists of antithrombotics, a lipid lowering and an antihypertensive drug. In case of a suspected cardiac origin of the TIA , anticoagulant therapy is started and the cardiologist is involved in further patient treatment. When significant stenosis of the cervical arteries is the probable cause of TIA, a vascular surgeon is consulted and, when deemed necessary, fast-track carotid endarterectomy is performed. All these treatments have been proven to reduce the risk of subsequent vascular events , 11.Within half a day all investigations necessary to diagnose TIA and identify possible risk factors take place. Results are immediately discussed with the patient, secondary prevention is started and appropriate referrals to other specialists are arranged. Finally, short-term follow-up at the outpatient department is planned. The programme consists of the following:Welcome and information about the program by acute day ward nurse;History taking and physical examination by neurologist;Length and weight measurements, determination of body mass index;Laboratory investigations consisting of kidney and liver functions, full blood count and fasting glucose and cholesterol profile;Urine examination for proteinuria;Electrocardiography with special attention to atrial fibrillation, cardiac ischemia and left ventricular hypertrophy. In case of doubt, immediate consultation of a cardiologist is possible;Standardized repeated blood pressure measurements;Diagnostic imaging, either MRI or computed tomography (CT) of brain, cervical and intracranial arteries;In young patients (<50 years) additional investigations are done, since aetiology often differs from older patients.Neurologist discusses the results with the patient. Information is provided about the disease, its risk factors, secondary preventive medication and life style risk factors and advice what to do in case of recurrence. Finally a personalized follow-up is scheduled during which ample attention is given to compliance of medication, but also to lifestyle risk factors . Thereafter the patient returns home.Diagnostic imaging of the brain is preferentially performed with MRI, since this enables the possibility of detecting recent ischemia. Daily fixed slots at the radiology department are available. When there are contraindications for MRI or no slots are available any more, CT of the brain and cervical arteries is performed, with the aid of an iodine-containing contrast agent. When there are contraindications for the latter, duplex ultrasound of the cervical arteries is added to CT of the brain.A neurologist as well as a radiologist evaluates all diagnostic imaging. The radiologist makes an official report within minutes and actively reports unexpected or acute abnormalities to the responsible neurologist. Attention is especially focused on signs of recent or old ischemia, other structural abnormalities  as well as anatomy and stenosis of the cervical and cerebral vasculature.When the TIA-service takes places at the emergency department instead of the acute day ward, the protocol and sequence of investigations is essentially the same. However, for logistic reasons, there are a few minor differences:Determining fasting glucose and cholesterol values is frequently not possible, since patients have often already eaten when seen at the emergency department. These are postponed to the follow-up visit at the outpatient department;Diagnostic imaging of brain and cervical arteries always consists of CT including angiography with an iodine-containing contrast agent. The latter is substituted by duplex ultrasound when contraindications are present and in case of significant cervical artery stenosis additional MR angiography is planned for the next day.Through combining history and additional investigations, the final judgement of whether a TIA has occurred is made. When no TIA has taken place, further follow-up at the general neurology outpatient department is planned when deemed necessary. When the diagnosis of TIA is made, secondary prevention is started immediately. This rests on three cornerstones. The first is secondary prevention through medication, consisting of a combination of antithrombotics or anticoagulant therapy, depending on the suspected cause of the TIA. Furthermore a lipid-lowering drug is added when the value of fasting low-density-lipoprotein cholesterol is >2.5 mmol/l (96.7 mg/dl) and antihypertensive medication is started when blood pressure is >130/80 mmHg. The second cornerstone is carotid surgery when necessary and is proven beneficial to patients with an ipsilateral carotid artery stenosis >70%. In these cases the vascular surgeon is consulted immediately in order to accomplish surgery as soon as possible, but at least within 14 days after the TIA. The third cornerstone is evaluation of the lifestyle and assessing the motivation of a patient to for example stop smoking, increase exercise and change eating habits. This is organized in a structured way, through a multidisciplinary outpatient clinic organized by a specialized nurse. Based upon a hospital-wide protocol  lifestyle and cardiovascular risk factors are identified. Patient motivation is determined through a structured questionnaire and motivated patients are offered lifestyle interventions, provided by specialized nurses.The visit to the TIA-service ends with an extensive conversation between patient and neurologist, during which the concept of TIA is explained. Possible side effects of the medication and consequences for driving abilities are discussed. A self designed brochure containing all this information is given along with each patient. Finally, instructions are provided on how to act in case of recurrent symptoms.Patients are contacted by telephone two weeks after the initial visit by their vascular neurologist and are seen at the multidisciplinary outpatient clinic four weeks later. Afterwards, consultation is continued at regular intervals for different lengths of time, depending on the specific situation of a patient. The general practitioner is kept informed through letters and is actively involved in the treatment.A nationwide evaluation of TIA care in the Netherlands has not been performed until now. We therefore assessed the effect of the introduction of the 24/7 TIA-service by comparing different variables since the start of this service.The 24/7 TIA-service started during 2010 and data on patient’s and doctor’s delay became available right after the introduction of the 24/7 TIA facility. During the first full year of operation the total time from symptoms to diagnosis decreased by 30% from just over 10 days to 7 days. Unfortunately, most of these days were due to patient’s delay, whereas doctor’s delay was usually less than 48 hours on average.In order to accurately determine the effect of a 24/7 TIA-service on delay to analysis and start of secondary prevention, a longer evaluation period is needed. Nevertheless, the currently available data do seem to point towards a reduction in both doctor’s and patient’s delay. This can potentially prevent stroke and other cardiovascular events that are associated with a high risk in the first days and weeks after a TIA. This is of course the ultimate goal of an around-the-clock TIA-service. However, a nationwide analysis of patient data will be needed to perform an adequately powered study of the risk reducing effects of this care pathway.Although international studies have shown a beneficial effect of early diagnosis and treatment of TIAs with a reduced number of subsequent cerebral infarctions , 8, therIn the Netherlands, general practitioners (GPs) function as a gatekeeper to further specialized care. Patients experiencing a medical problem, consult their GP for advice and, if deemed necessary, are sent to a specialist for further analysis and treatment. Alternatively, patients suffering form an acute problem can turn to an emergency ward (ER), where they are primarily seen by an ER-doctor, who can decide to consult a specialist.This organisation of care has its benefits and limitations. With respect to a TIA, and the fact that this should be treated as a stroke, this situation is prone to doctor’s delay. Offering a 24/7-TIA service does not directly change the GP or ER-physician neurological evaluation interval. However, when a patient is finally referred to a neurologist for analysis of a possible TIA, any delay in this referral is completely ruled out.The main reason of delay between TIA symptoms and specialised analysis is patient’s delay. The most important way to reduce this delay is education about TIAs and their consequences. This is independent of the presence of a 24/7 TIA-service. However, some patients might be reluctant to immediately seek medical care after a TIA, because they know it will take days before they are eventually analysed and any intervention takes place. Knowing, for instance through media attention, that an around-the-clock dedicated TIA-service exists, where a patient is immediately fully examined and interventions can be started right away, could possibly help patients to decide to seek immediate medical attention. This is the category of patients that might benefit the most from an around-the-clock TIA-service.A theoretical beneficial effect on the number of strokes and myocardial infarctions has to be proven before our patient-friendly, but also more costly service is implemented in other centres. When proven, we should set out to determine the crucial steps in the process. In order to determine these steps the process of care around the diagnosis and treatment of TIAs in the Netherlands has to be evaluated. The primary end point would be the number of cerebral infarctions and myocardial infarcts occurring shortly after a TIA. In order to monitor the process a combination of outcome and process indicators has to be developed, making it possible to relate possible variations in outcome to changes in the process of care.The main outcome variable and quality indicator of the process of care around TIA is the incidence of cerebral infarction after a TIA. Both the EXPRESS-study  and the In the process of care around TIA there are many aspects that can serve as a process indicator. Although evaluation at the emergency department can take place at any time of day, the inherent commotion there can affect the duration of the visit. Waiting times before a neurologist sees a patient, before diagnostic imaging is performed or before results are discussed can increase substantially. These waiting times can function as process indicators. For the TIA-service at the acute day ward the same indicators can be used. The aim of the 24/7 TIA-service is to diagnose and treat as soon as possible. A valid indicator of the logistics of the process would be the proportion of patients analyzed within 24 hours. Ideally, this is more than 90%. For this purpose the exact times of the TIA, the subsequent visit to the general practitioner and referral are recorded at the 24/7 TIA-service.A neurology resident supervised by a vascular neurologist executes the 24/7 TIA-service. Care around a TIA patient is based on a clear protocol, increasing the level of expertise. This is the case not only for the neurology, but also for the radiology department, where specialized supervision is available. Due to the standardized structured approach patient volume is ever increasing with an attendant increase of expertise by the various health professionals. The personalized secondary prevention and possible life style modification is carried out under the responsibility of a specialized nurse. The secondary prevention is personalized in such a way that all risk factors and cardiovascular disease are discussed on a patient-by-patient basis during a multidisciplinary consultation between neurologist, cardiologist, vascular internist and vascular surgeon. This personal advice, both in terms of medication and life style can be executed in conjunction with both the first  and second line of care . In order to implement a 24/7 TIA-service, recent changes in work structure had to take place. The level of expertise can therefore serve as an index-specific indicator in the analysis of changes in the process of care.Given the complexity of the organization in an academic medical centre, realizing the 24/7 TIA-service took place rather smoothly. There is clear evidence that a round-the-clock mode of operation works, which provides a base of evidence on which to perform changes in the work structure. Furthermore, during weekly scientific meetings the relevant publications have been discussed with the neurologists and residents, questioning themselves whether this system should be implemented in our hospital. Because of the evidence-based medicine attitude, every neurologist was convinced that a 24/7 facility would increase the level of patient care. Moreover, the concept of a 24/7 TIA-service emphasises the urgency for medical attention, possibly increasing the sense of emergency in the general population.Implementing 24/7 TIA-services in the Netherlands should only be stimulated when there is clear evidence that such a procedure indeed leads to a better outcome, which is a reduction in the number of cerebral infarctions. The increased costs associated with this service can only be accounted for when it is shown to lead to a reduced disease burden. Not only the immediate higher costs of the service should be taken into account, but also the possible decrease in long-term costs, for instance due to less or shorter hospital admissions, less frequent acute interventions with emergency visits and transport, and reduction of the number of severely disabled patients with all associated costs. Such a cost-benefit analysis is still missing, since 24/7 TIA-services have not been implemented elsewhere in the Netherlands.Implementing 24/7 TIA-care throughout the Netherlands relies on cooperation of health care professionals at different levels. Neurologists, radiologists, cardiologists, internists and vascular surgeons will have to accommodate their working routine to fast and flexible analysis and treatment. Specific training on vascular neurology can be necessary. Nursing staff, radiologic laboratory staff and outpatient department personnel are all part of the chain of care around TIA patients. To optimize care at local as well as regional and national level money, personnel and infrastructure are needed.Patients should be aware of the signs and symptoms of a TIA in order to search medical attention in time. General practitioners will also have to be informed of the necessity and possibility of swift analysis and intervention, so that acute referrals actually take place.Implementing 24/7 TIA-care will put a strain on health care professionals at every level. Therefore it is of the utmost importance to unequivocally establish the benefit of such a service before continuing to a national implementation. In this there lies an important role for neurologists, patient associations and health insurance companies.24/7 TIA-service provides an improvement in both patient service and outcome. Implementation took place through the integration of workflow of different specialities and the design of new work modes aimed at flexibility and speeds. The motivation for these changes was the evidence available in literature that around-the-clock care for TIA patients works. It both improves the short-term outcome and possibly reduces the associated long-term costs.A preliminary analysis of the effect of this service on delay from TIA to start of secondary prevention shows a reduction in this delay. However, this is but a surrogate marker for the ultimate goal, namely a reduction in the incidence of cardiovascular events after a TIA. Such an effect of an around-the-clock TIA-service has to be established before implementation throughout the country takes place. Indicators, both process and index-specific are needed to relate a possible change in outcome to the changes in workflow. The combination of changes in patient care and workflow, implementation of a new mode of work and the design and monitoring of indicators necessitates the integration of care throughout every level in the chain of care, from patients and general practitioners to medical specialists and managers to ultimately health insurance companies and political decision makers.


The inference of gene regulatory network from expression data is an important area of research that provides insight to the inner workings of a biological system. The relevance-network-based approaches provide a simple and easily-scalable solution to the understanding of interaction between genes. Up until now, most works based on relevance network focus on the discovery of direct regulation using correlation coefficient or mutual information. However, some of the more complicated interactions such as interactive regulation and coregulation are not easily detected. In this work, we propose a relevance network model for gene regulatory network inference which employs both mutual information and conditional mutual information to determine the interactions between genes. For this purpose, we propose a conditional mutual information estimator based on adaptive partitioning which allows us to condition on both discrete and continuous random variables. We provide experimental results that demonstrate that the proposed regulatory network inference algorithm can provide better performance when the target network contains coregulated and interactively regulated genes. The prediction of the functions of genes and the elucidation of the gene regulatory mechanisms have been an important topic of genomic research. The advances in microarray technology over the past decade have provided a wealth of information by allowing us to observe the expression levels of thousands of genes at once. With the increasing availability of gene expression data, the development of tools that can more accurately predict gene-to-gene interactions and uncover more complex interactions between genes has become an intense area of research.Gene Clustering AlgorithmsSome of the first attempts at determining gene regulations are based on the gene expression clustering algorithms. These algorithms determine genes that are likely to be coregulated by grouping genes that exhibit similar gene expressions under the same conditions. Different clustering algorithms differ in the metric used to measure similarity between gene expressions, and how the metric is used to cluster into groups similarly expressed genes . In 2],,2], a hi5Graphical AlgorithmsWhile gene clustering algorithms allow us to discover genes that are coregulated, they do not reveal much of the underlying biological mechanism such as the regulatory pathways. In recent years, many models have been proposed attempting to understand how individual genes interact with each other to govern the diverse biological processes in the cell. In –10, gene11rix . In , the genule . In , gene reRelevance Network AlgorithmsAnother method that is related to graphical model is called relevance network. Relevance networks are based on the idea of "covariance graph" where a link exists between genes ependent . Differeependent , the corependent 17, mutua by . In , the proures. In , ARACNE  ), then . For a tWhile relevance-network-based methods such as ARACNE perform well when the interactions in the gene regulatory network are between pairs of genes, they are unable to completely discover interactions that are results of the joint regulation of the target gene by two or more genes. The XOR interactive regulation is one such interaction that can be recognized only by exploiting the conditional dependence between variables of interest. Using conditional mutual information (CMI), it is possible to detect the XOR and other nonlinear interactive regulation by two genes.Several recent works have attempted to incorporate information theoretic measures for more than two variables in regulatory network discovery. In , a CMI m21Here, we make use of both mutual information and conditional mutual information as measures of dependence between gene expressions. The main focus of this work is to discover the potential interactions between genes by adapting the relevance network model, which is also used in 18. The iThe remainder of the paper is organized as follows. In Section 2, we present the system model for regulatory network inference. In Section 3, we present the adaptive partitioning algorithms for estimating mutual information and conditional mutual information as well as our proposed network inference algorithm based on MI-CMI. In Section 4, we present experimental results. Section 5 concludes the paper.Suppose that the given set of genes In a network inference problem, our primary goal is to correctly identify the links representing direct regulation and reduce the false negative and false positive links. A false negative can be due to the incorrect estimation of the metric that measures the interaction between the expressions of two genes. When interactive regulation is introduced into the network, false negatives may occur for certain interactive regulations due to that no significant interaction is detected between the regulated gene and any one of the regulating genes, but rather the regulation is only detectable when the regulated gene and all of the regulating genes are considered together. For example, in Figure In the relevance network approach, two nodes are connected when they exhibit high degrees of interaction according to the chosen metric. Using metrics such as correlation coefficient and mutual information, high degrees of interaction between two genes typically indicate that one of the genes is directly or indirectly regulating the other gene, or the two genes are being coregulated by another gene. In relevance networks, indirect regulation and coregulated genes often are the cause of false positive links. ARACNE, as discussed in the previous section, removes indirect regulation by the application of DPI. However, ARACNE and other network inference algorithms based only on correlation coefficient or mutual information are unable to identify genes that are being coregulated, particularly if they are coregulated by the same mechanism. For example, in Figure The insufficiencies of using only mutual information or correlation coefficient as discussed above naturally lead us to the use of conditional mutual information as the metric of choice in our proposed regulatory network inference algorithm. For Figure From the above discussion, in the next section, we develop a relevance-network-based regulatory network inference algorithm that utilizes both mutual information and conditional mutual information to predict interactions between genes from the observed gene expression data. It is clear that we need efficient estimators that can accurately compute mutual information and conditional mutual information from data. Moreover, the conditional mutual information estimator should be able to support both discrete and continuous conditioning variables to allow for wider ranging uses.There are several mutual information estimators such as the Gaussian kernel estimator and the equipartition estimator  but eachLet us consider a pair of random variables For mutual information estimators that partition the samples according to equal length or equiprobable partition, many of the grids may turn out to be inefficient due to the distribution of the samples. For example, let posed in  that adaIn the adaptive partitioning scheme, the sample space Let us denote and their densitiesrespectively, where where asymptotically sufficient for We define a sequence of the partitioning of the sample space where ence. In , it is sGiven the pairs of samples that is, the frequency of the samples falling into the grid Furthermore, in  it is shThus, mutual information can be estimated by computing the relative sample frequency on appropriately placed rectangular grids.We now give the adaptive partitioning algorithm that constructs an asymptotic sufficient sequence of partitions for mutual information estimation.Algorithm 1 .(i) Initialization: Partition that is, (ii) Partitioning Denote If the sample distribution of the quadrants passes the uniform test, that is, (11) holds, (iii) Repeat step (ii) for all grids in (iv) Repeat steps (ii) and (iii) until (v) Using the partition Here, we give an example of how to adaptively partition a given set of sampled data. In this example, we sampled 100 times In Figure Works in various fields have utilized conditional mutual information to test for conditional independence. However, in most cases, they are often limited to conditioning on a discrete, often binary, random variable 32. When z-axis to allow the estimation of conditional mutual information when the conditioned random variable is continuous.This is done by simply dividing the samples into Let us consider a triplet of random variables Suppose that the space and its densitySimilar to (3), we can write Q denotes R denotes where We can rewrite z-axis partition Notice that this is simply a weighted sum for the restricted diversity as computed in (3) for samples grouped according to the and it can be estimated asFollowing the proof in 33,(19)We can see from (15) and (17) thatand the integralin the definition of We now present the algorithm for estimating the conditional mutual information with continuous conditioning variable.Algorithm 2 .(i) Initialization: partition that is, (ii) Partitioning Denote If the sample distribution passes the uniform test, that is, if (24) holds, the cuboid are added to (iii) Repeat step (ii) for all cuboids in (iv) Repeat steps (ii) and (iii) until (v) Using the partition Figures z-axis. The problem of estimating the conditional mutual information is thus broken down into estimating the mutual information for each group of samples, where the samples are grouped by which Compared to the estimation of conditional mutual information for discrete conditioning variable, we can see that instead of grouping samples into subsets where samples belonging in the same subset have the same values for the discrete-valued conditioning variable, here we group samples based on the adaptively determined partitioning of Note that the complexity of the Gaussian kernel estimator is known to be To infer a gene regulatory network that has various interactive regulations and coregulations, we propose a strategy of using both mutual information and conditional mutual information to reconstruct the regulatory network. In our proposed algorithm, we first use mutual information as metric to build regulatory network similarly to  to captuThe MI-CMI gene regulatory network inference algorithm is as follows.Algorithm 3 .(i) For a gene expression dataset containing (ii) Initialize the graph (iii) Detecting indirect regulation and coregulation: for any triplet of genes (a) Ifthis means that (b) Ifand larly to ,  is set(iv) Detecting interactive regulation: for any triplet of genes (a) If one or two of the CMI estimates is greater than (b) If all three of the CMI estimates are greater than In this section, we present simulation results to demonstrate the performance of the algorithms discussed in Section 3. We first illustrate the performance of Algorithm 2 for estimating the conditional mutual information of jointly Gaussian random variables. Next, we consider the performance of Algorithm 1 for estimating mutual information, by implementing the regulatory network inference algorithm in , but repTo assess the accuracy of Algorithms 1 and 2 for the estimation of gene regulatory networks, we consider estimating the pairwise and conditional mutual information of multivariate Gaussian distributions. In our simulation, we compare the MI and CMI estimates of Algorithms 1 and 2 with those of the b-spline estimators. A b-spline MI estimator is proposed in  which diposed in  to estimFor MI estimation, we generated bivariate Gaussian samples with correlation coefficients 0, 0.3, and 0.6. For each coefficient, we generated posed in . Each sawhere For CMI estimation, we generated samples trivariate Gaussian distributions with the following covariance matrices:For each Gaussian distribution, we generated where where As a comparison, we performed CMI estimation of covariance matrices 1 and 4 using b-spline estimator with 20 bins. In , it is sLooking more closely at CMI estimation, for small sample size and large CMI value, Algorithm 2 has a negative bias. As the sample size increases, the bias quickly reduces. On the other hand, when the true CMI value is small, Algorithm 2 tends to overestimate. It should be noted that estimating the CMI from a finite number of samples for a distribution with zero conditional correlation coefficient will typically result in a nonzero value. Nevertheless, the estimation results are still reasonably accurate, even for only 100 samples, so that conditional independence can be easily detected.Next, we implemented the algorithm described in  by replaIn Figure We now compare the performance of Algorithm 3, ARACNE, and BANJO for regulatory network inference in the presence of coregulated and interactively regulated genes. We again use the synthetic network modeling software NetBuilder to generate random networks. NetBuilder allows modeling of gene-to-gene interactions such as activation by transcription factor combination (AND and OR), repression (NOT), and other combinatory interactions. We generated 50 synthetic networks, each containing 15 to 25 nodes with 20 links. For each node, we generated 100 steady-state expression data samples. To compare the effects of interactive regulation and coregulation on the performance of the three algorithms, two sets of synthetic networks are constructed: one set contains 25 networks where 30% of the interactions involve interactive regulation and coregulation, the other set contains 25 networks where 60% of the interactions involve interactive regulation and coregulation. In Figures In Figure Figure We have proposed a new gene regulatory network inference algorithm that employs both mutual information and conditional information to discover possible direct and interactive regulations between genes, and to eliminate false links due to indirect regulations and coregulation. The mutual information and conditional mutual information are estimated from the expression data using an adaptive partitioning estimator. We have shown that the proposed network inference method outperforms BANJO and ARACNE when the underlying regulatory network contains coregulated or interactively regulated genes. In this work, we have focused on the discovery of the joint regulation of a gene by two other genes. It is possible to extend this work to joint regulation by multiple genes by modifying the proposed conditional mutual information estimator to a higher order. However, doing so would pose several computational problems. As the dimension of the CMI increases, increasing number of samples is needed to maintain the same level of accuracy. Also, as the dimension of the CMI increases, the number of sets of genes to be tested also increases, thus rendering this method impractical for brute force computation of all possible sets of genes. One possibility to reduce the amount of computations needed is to take into consideration the constraints placed on the possible connectivities from known biochemical reactions between the genes involved. This can be a future direction for research in this area.


Dictyostelium discoideum contains four genes coding for MADS-box transcription factors, two of these genes code for proteins that are more similar to SRF, and the other two code for proteins that are more similar to MEF2 animal factors.Transcription factors from the MADS-box family play a relevant role in cell differentiation and development and include the animal SRF (serum response factor) and MEF2 (myocyte enhancer factor 2) proteins. The social amoeba mef2A, is described in this article. This gene is expressed under the transcriptional control of two alternative promoters in growing cells, and its expression is induced during development in prespore cells. Mutant strains where the mef2A gene has been partially deleted were generated to study its biological function. The mutant strains showed reduced growth when feeding on bacteria and were able to develop and form fruiting bodies, but spore production was significantly reduced. A study of developmental markers showed that prespore cells differentiation was impaired in the mutant strains. When mutant and wild-type cells were set to develop in chimeras, mutant spores were underrepresented in the fruiting bodies. The mutant cells were also unable to form spores in vitro. In addition, mutant cells also showed a poor contribution to the formation of the tip-organizer and the upper region of slugs and culminant structures. In agreement with these observations, a comparison of the genes transcribed by mutant and wild-type strains during development indicated that prestalk gene expression was enhanced, while prespore gene expression decreased in the mef2A- strain.The biological function of one of the two genes that codes for MEF2-related proteins, a gene known as mef2A plays a role in cell differentiation in D. discoideum and modulates the expression of prespore and prestalk genes.Our data shows that  Exon regions are indicated in black capital letters while intron sequences are indicated in blue small letters. Consensus splicing sites are underlined. The sequence is numbered from the Adenine of the translation initiation codon, shown in bold characters. Transcription initiation sites, as determined by RACE, are indicated with red asterisks over the nucleotide sequence. The complete sequence of the third intron of the gene and the sequence of the large fourth exon, coding for the C-terminal region of the protein, are not shown but are schematically indicated on Figure 2.Comparative study of the amino acid sequences of the Click here for file


We discuss methods for fast spatiotemporal smoothing of calcium signals in dendritic trees, given single-trial, spatially localized imaging data obtained via multi-photon microscopy. By analyzing the dynamics of calcium binding to probe molecules and the effects of the imaging procedure, we show that calcium concentration can be estimated up to an affine transformation, i.e., an additive and multiplicative constant. To obtain a full spatiotemporal estimate, we model calcium dynamics within the cell using a functional approach. The evolution of calcium concentration is represented through a smaller set of hidden variables that incorporate fast transients due to backpropagating action potentials (bAPs), or other forms of stimulation. Because of the resulting state space structure, inference can be done in linear time using forward-backward maximum-a-posteriori methods. Non-negativity constraints on the calcium concentration can also be incorporated using a log-barrier method that does not affect the computational scaling. Moreover, by exploiting the neuronal tree structure we show that the cost of the algorithm is also linear in the size of the dendritic tree, making the approach applicable to arbitrarily large trees. We apply this algorithm to data obtained from hippocampal CA1 pyramidal cells with experimentally evoked bAPs, some of which were paired with excitatory postsynaptic potentials (EPSPs). The algorithm recovers the timing of the bAPs and provides an estimate of the induced calcium transient throughout the tree. The proposed methods could be used to further understand the interplay between bAPs and EPSPs in synaptic strength modification. More generally, this approach allows us to infer the concentration on intracellular calcium across the dendritic tree from noisy observations at a discrete set of points in space. Spatiotemporal dendritic imaging data, through fluorescent calcium indicators, opens an exciting window on computations performed by single neurons at a subcellular level. However, the analysis and interpretation of such data is challenging. The measurements are noisy, intermittent in space and/or time, and depend critically on the choice of the fluorescent indicator. Consequently, analysis is typically limited to a specific branch of the dendritic tree, neglects spatiotemporal correlations between neighboring compartments, and requires averaging over multiple trials. Here we derive a model for the spatiotemporal concentration of calcium bound probe molecules. Using state-space and optimization tools we derive a fast algorithm for estimating the most likely concentration based on the given measurements obtained from a single trial, and argue that it can provide an estimate of the fast transients of the underlying calcium concentration. In particular, our algorithm estimates the timing and amplitude of calcium transients due to backpropagating action potentials. It provides a flexible approach to inferring the structure of dendritic dynamics that are important in neural computation, but are inaccessible to direct measurement with current experimental techniques. The problem of understanding the mechanisms that govern the change in strength of a synapse remains a key problem in cellular neuroscience. Fluorescence microscopy provides a way to examine aspects of the structure and specifically the function of living cells that are inaccessible to direct electrical recording. The experimenter performs optical recordings after delivering fluorescent probe molecules that translate a biological or biochemical signal into an optical output  and excitatory post-synaptic potentials (EPSPs) that mediate synaptic changes through spike-timing dependent plasticity (STDP). However, the available experimental techniques still lead to noisy and spatiotemporally-subsampled observations of the true underlying calcium signals. Therefore we must use statistical methods to infer the details of the calcium transients from observed data. However, optimal spatiotemporal smoothing of the calcium profile on a dendritic tree given localized noisy measurements remains a difficult computational problem due to the high dimensionality (in terms of number of compartments) and complex structure of dendritic trees.In this paper we present a general methodology for fast spatio-temporal smoothing of calcium signals on dendritic trees, based on single-trial experiments. We take a functional approach according to which the evolution of calcium concentration on the whole tree is determined from a smaller set of hidden variables. These govern the temporal dynamics of the calcium bound probe molecules, at small but overlapping regions of the tree, and incorporate possible concentration “bumps” due to bAPs, EPSPs or external stimulation. These bumps in the hidden states are in general rapidly increasing and slowly decreasing, and model the corresponding spatially localized bumps in probe molecule concentration due to rapid calcium transients. The calcium measurements are then expressed as linear noisy measurements of the hidden variables. Our problem then reduces to the maximum a-posteriori space-time estimation of these hidden states. Using a standard state-space approach we formulate our problem as one of optimization that can be efficiently solved if the state-transition and measurement-noise distributions are log-concave in the hidden states. In this case the problem can be solved with a cost that scales linearly with Although related, the problem that we deal with in this paper is different from the one of extracting spikes from mesoscopic fluorescence recordings. In the latter, the data consists of images taken at a low rate from a population of neurons, and the goal is to extract a set of spike times. Several methods have been developed for this problem, such as template matching We will consider data obtained by measurements of probe fluorescence obtained with fast random-access multi-photon (RAMP) microscopy Measurements of the light intensity emitted by calcium sensitive dyes at discrete points in space and time can be used to infer the evolving concentration of calcium across the dendritic tree. Here we provide a description of an experimental situation suited for this approach, and show how it leads to a statistical model that can be used to estimate the calcium signal.in vitro, in acutely dissected hippocampal brain slices. A schematic of the stimulation protocol is shown in Although the statistical methods we present are general, we demonstrate them in the context of a particular experiment. It has been assumed that action potentials that backpropagate from the soma into the dendritic tree play an important role in learning Each evoked AP backpropagated into the dendritic tree. These bAPs resulted in a transient increase in intracellular calcium concentration, which has been previously shown to result from increased conductance through voltage-dependent calcium channels Recordings were performed using 3D RAMP microscopy, which uses acousto-optic deflectors (AODs) for high-speed recording within a volume of live brain tissue The concentration of calcium-bound probe molecules can be used as a proxy for the concentration of calcium in the system. A simplified reaction scheme describing calcium binding is shown in bound and free probe molecules respectively, at spatial location The light intensity emitted at location Assuming that probe molecules are conserved locally, i.e., The fast calcium signals in the tree, in our case, are due to a bAP that results in a transient increase in the concentration of bound probe molecules. High affinity calcium dyes, such as the Oregon Green BAPTA-1 (OGB-1) used here, bind calcium with a very fast onset and also have a much slower dissociation rate. Neglecting spatial correlations and diffusion terms, we can model the bound probe molecule dynamics asa priori. For instance, probe molecule concentrations are typically higher in the apical dendrite and near the soma, resulting in the higher luminosity of these regions. This variation may be due to nonuniform concentration of basal calcium across the cell. Also contributing may be limitations of the experimental setup, such as non-uniform laser illumination across the microscope's field of view or non-uniform volume of fluorophore excitation, due to thin processes that extend beyond the focal volume. Moreover, recording sites are sometimes placed slightly off a dendrite. To account for such variability in baseline fluorescence, we assume that such non-uniformities are primarily due to the experimental limitations which affect the number of probe molecules being excited. As a result, and based on the dynamics of calcium binding, we expect that during fast transients This baseline probe molecule concentration typically varies across the cell and is difficult to control relative change in bound probe molecules is reflective of the transients in calcium concentration. Hence, by Eq. (1), we need to estimate relative changes in light intensity at a given location, as a proxy for transients in calcium concentration. Dividing Eq. (3) by Based on the above discussion, we make an important conclusion: The The signal, Using Eq. (4) for the dynamics of relative bound probe molecules in the presence of incoming calcium spikes, we have thatMore generally, the timing of the APs may not be known or not the same for all the locations in the tree and must be inferred from the bound probe molecule trace. This is a challenging problem in itself To address the issue of spatial correlations, we model the relative concentration of bound probe molecules at location As the spline basis functions are typically defined on a line, here we use a suitable generalization to trees. Splines are defined on subdomains of the tree defined by the cell shape. This tree therefore needs to be partitioned. We chose to define the partition using the topological distance from the soma, i.e., the distance from the soma along the tree. Thus all points that lie within a given distance from the center of a spline function belong to the same subdomain. Picking this distance is important because a very large/small value can lead to significant under/over-fitting of the data. In the Results section where we apply our algorithm to experimental data, we propose a data-driven method for determining this parameter.We discretize the cell into We assume the same temporal dynamics as in Eq. (2), but now for the weight variables not assumed to be a sum of delta functions with unknown weights occurring at known times. Moreover, as we will see below, the inference will be done at once for the whole tree and not individually and independently for each location. Thus, this statistical approach is more general since the algorithm is capable of finding spike times, and more biologically accurate, since it allows for spatial correlations for nearby compartments.There are two essential differences between the model described here by Eqs. (8)–(12) and the motivating model described in Eq. (7): estimation of spike times, and incorporation of spatial correlations. In the present model the input, We use a Bayesian approach, and start by specifying a prior distribution on Now taking into account the dynamics of probe molecules (see Eqs. (1),(4) and (5)), the emitted light intensity can be written asWe have access to After discretizing time, Eqs. (8) and Eq. (14), correspond to the state-space modelWe emphasize again that Eq. (14) provides a biophysically inspired statistical model. As earlier, we aim to approximate a signal proportional to the bound calcium concentration across the dendritic tree. Note that certain parameters in the model such as the time constant We would like to compute the maximum a-posteriori (MAP) estimate of the relative spatiotemporal concentration of calcium-bound probe molecules Additionally, since the calcium concentration is nonnegative, we have to ensure that all the activation variables, as well as the bumps In the Supporting Information we describe the technical details of a fast method for the solution of Eq. (17). Briefly, we construct a log-barrier method for the incorporation of the non-negativity constraints We discuss a particular example of choices for the prior and noise likelihoods that are realistic and also ensure log-concavity. As a first example, we consider the case where the The prior on A reasonable intuitive choice for the bump prior would be a marked point process Putting everything together we seek the MAP estimateWe demonstrate our approach using data generated by numerically simulating calcium transients on a dendritic tree, and then continue with the analysis of experimental data.We apply the developed methodology on a reconstructed dendritic tree from a rat CA1 pyramidal cell. The tree was discretized in http://www.stat.columbia.edu/~eftychios/Home/Calcium_Smoothing.htmlSample code to generate We also tested the effect of the minimum topological distance between imaged positions. We used the same setup as above, but imaged the signal at 100 locations at every time step. Additionally, at each repetition we imposed a minimal topological distance between the imaged locations. Since the units are arbitrary here the exact results are not reported. However, for small values of the minimal distance the error grows slowly with the minimal separation between the imaged locations. Large errors are observed when the minimal distance between imaged locations becomes comparable or larger than the distance between centers of the interpolating spline functions. In the next section we present an adaptive method of determining the smoothing spline basis based on the locations of the measured locations.The algorithm was tested on calcium imaging data from a CA1 pyramidal neuron obtained with a fast three dimensional optical scanner. The details of the scanner are given in For each pair of imaging data we estimated one set of model parameters, so that the results of the imaging algorithm on the two different protocols could be compared. The measured data was normalized using the Our model has several parameters that have to be estimated before we apply our smoothing algorithm. These are the baseline probe molecules concentration, the time constant of calcium unbinding and the noise statistics. Below we describe simple heuristic methods to estimate the model parameters. In practice more sophisticated and powerful methods can be developed such as Monte Carlo estimation methods  The baseline fluorophore concentration Next, the decay constant of the recorded signal, The state transition (amplitude) prior was considered to be an exponential distribution, as discussed in the Methods section. There a marked point process with rate Finally, the noise likelihood at each measurement location was assumed to be independent and Gaussian with zero mean, and variance estimated directly from the measurement traces. To find the noise statistics we subtracted the filtered traces http://www.stat.columbia.edu/~eftychios/Home/Calcium_Smoothing.html.see e.g. . In the The first row (A) of In some cases, there are also a few spikes detected outside the A possible solution to prevent such spikes would be to set the spike rate outside the excitation window to a very low value. However this led to overfitting in the amplitude of the spikes in the interval From As an additional test of the robustness of our results we examined how removing measurements from selected locations affects the inferred traces. In The results shown in Finally, we examined the effect of the temporal sampling rate, by applying our algorithm to a subsampled version of the data. In We finally applied our algorithm to simulated data in a dendritic tree receiving multiple synaptic input from both excitatory and inhibitory presynaptic neurons.  given single-trial, spatially localized, noisy imaging measurements. We showed that our algorithm can infer the timing of bAPs and provide estimates about the amplitude of the transients that they initiate. Although the optical measurements come from a small subset of the neuron's compartments the algorithm estimates the full spatiotemporal calcium profile. Moreover, it runs with complexity that scales linearly both with the length of the experiment and the size of the tree, and as a result it can be used in arbitrarily long experiments and large dendritic trees. Our full spatiotemporal smoothing algorithm therefore enables the study of selective propagation of bAPs into specific dendrites, and of the effects of calcium as a coincidence indicator between bAPs and EPSPs. Although the focus of this study was the study of the interactions between bAPs and known EPSP stimulation, we also tested the generality of our algorithm by applying it to a conductance based neuron driven by random (unobserved) synaptic inputs. More generally, our algorithm opens up the possibility of single-trial analysis of spatiotemporal calcium dynamics imaged on large dendritic trees, and could therefore potentially lead to a better understanding of these complex dynamics.To obtain a relatively simple model and an efficient inference algorithm, we had to make a number of assumptions. For example, we employed a functional approach by assuming that the relative bound probe molecule concentration can be spatially approximated by a sum of smooth spline functions on the tree. This is reasonable since calcium diffuses locally through the dendritic tree. We assumed that the baseline fluorescence is constant before and after the spike stimulation. While this is true in general, we observed that in some locations , the baseline can change significantly after the excitation, leading to the inferred spikes outside the excitation window, as discussed in the Results. The model also relies on the assumption that the bound probe molecules do not saturate during repetitive excitation, and that the rate of calcium unbinding remains constant. Analysis shows that the amplitude of the transients in general decreases as more spikes are applied. This has been reported in many studies e.g. . HoweverApart from constructing a spatial basis for the relative bound probe molecules, we also tried the same approach on the un-normalized, raw bound probe molecule measurements. However, we noticed that in this case the required dimension Our model, so far, assumes only temporal dependencies on the hidden activation states The prior on the transient amplitude used in our model was very simple. It reflected only the knowledge of the interval over which the bAPs were initiated and their rate, but not the exact timing of the bAPs and other qualitative characteristics of the evoked transients. A more sophisticated prior can be chosen that exploits several characteristics of the bAPs. For example, the exact knowledge of the bAP timings can be incorporated to a greater extent by manipulating the time varying spike rate so that it becomes high in the time windows when we expect spikes, and low elsewhere. Moreover, at the dendrites, the amplitude of spikes usually decreases with the distance from the soma. In our approach “we let the data speak”, i.e., we determine the prior of the spike amplitude from the recordings as we discussed in the Results section. However, we can further impose a decreasing amplitude constraint as a regularizer to further promote this behavior, to better deal with the case where individual dendrites are very sparsely imaged. In matrix-vector notation this can be written as One natural question is whether the full spatiotemporal profile of calcium concentration can also be estimated. Our model promotes the inference of sparse events; this sparse regularization is necessary to avoid overfitting artifacts given our undersampled measurements. These sparse events, in turn, are interpreted as indicators of calcium concentration transients which are assumed to be instantaneous. As a result, due to these simplifications the detailed calcium dynamics cannot easily be inferred from our algorithm at its current form; see the Methods section for further discussion. Additional constraints on the model  could improve this estimation, but this remains a direction for future work.A final interesting question concerns the design of an optimal path for measuring at different locations across the tree. In our dataset the set of imaged sites was chosen by the experimenter and held fixed for each imaging session. Such an approach is suboptimal since it leaves many sites unrecorded and also neglects the spatial correlations along the tree. A heuristic method was presented in Text S1Description of the log-barrier method for the fast solution of our MAP estimation problem. (PDF)Click here for additional data file.