Counting of events for P2chan1
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The simplest model is the free space loss which considers no obstacles between transmitter and receptor. (Parsons, 2000) However this is an ideal model that does not exist in real scenario because there are other losses in the wireless channel. Another option to describe a channel is by using statistical models which are based on probability density functions (pdf). Although they do not describe the behavior of the sent signal in a complete way, they give a good approximation of the conditions of the channel in a certain moment. (Nakagami, 1960; Abouraddy & Elnoubi, 2000) The main statistical channels and their corresponding pdf are:
Additive White Gaussian Noise, AWGN. This channel only includes the sum of the white noise that follows a normal or Gaussian density.
Where:
p(x), Probability density function.
μ,Mean.
σ,Standard deviation.
σ2,Variance.
Rice: represents a signal which is the result of the sum of the different multipath plus a dominant signal, known as the line of sight (LOS) between transmitter and receptor.
Where:
p(x),Probability density function.
σ2,Variance of the signal or mean power of the signal before the detection of the envelope.
A,Amplitude of the dominant signal.
I0(),Zero order modified Bessel function of the first kind.
The relation between the power of the dominant signal and the power of the multipath is represented in (3).
Where:
K, Rice factor.
σ2,Variance of the signal or mean power of the signal before the detection of the envelope.
A,Amplitude of the dominant signal.
As A value decreases, the function is closer to characterize a Rayleigh fading environment. Otherwise, if the A value increases, the function is used to model an AWGN channel.
Rayleigh: represents fast fading and describes the multipath phenomenon with no LOS between transmitter and receptor which can be caused by a non stationary user.
Where:
p(x), Probability density function.
σ2,Variance of the signal or mean power of the signal before the detection of the envelope.
Due to a wireless channel is a time variant channel, a better option to characterize a channel is Markov chains, which are a stochastic process with a limited number of states and whose transition between them is based on the probability of an event. States of Markov chains could be defined in agreement to channel conditions of an scenario, like it was done by E. Lutz who defined a two state channel model, one classified as good and the other one classified as bad depending on the conditions and therefore the attenuation level. Another important work is the one of B. Vucetic which characterizes the wireless channel of a certain area in Australia with a four state Markov chain by combining four different types of statistical channels.
Next sections explain in detail how to create a wireless channel model using Markov chains and its application in a communication system with a coder and modulator. To achieve this, it is also explained how to create a markovian chain using Matlab. The effects of this model are analyzed through BER curves. An analysis with a semimarkovian channel is explained in the last section and a comparative analysis is done between this model and that from Markov chains. Finally, conclusions about both subjects are given. All the analysis is also done with Matlab.
One type of stochastic process is Markov chains, named after Andrei Markov who studied the transitions between consonants and vowels in a poem at the beginning of the 20th century. In this process, a set is defined as {X(t), t = 0,1,2,...} whose number of elements is finite and denoted with real positive numbers. X(t) = i represents that the process is in state i at an instant of time t and take discrete values. It is said that there is a fixed probability pij that chain goes from a state i to a state j in the next time t. This process is represented in (5) and it is known as the Markov property.
Where,
X(tk),Current sample.
X(tk+1),Future sample.
X(t1),...,X(tk-1),Past samples.
xk, State of the sample in the moment k.
Markov property indicates that given the present state, the next state is conditionally independent of the past. This statement is illustrated in Figure 1 which shows that the system can change from one condition to another or continues in the same state.
There are three important elements in Markov chains:
Probability transition matrix P.
Transition diagram.
Steady-state vector π
The characteristics of each element will be given in next sections.
Markov Property
The switch between states is established in the probability transition matrix P. Each element of it represents the probability that switches or remains in the state. These switches are called transitions. P is a square matrix whose order is the same as the number of states. Equation (6) shows the structure of a probability transition matrix.
Each element of P must satisfy the next condition.
Where,
pij,Probability that current sample is in state i given the immediate precedent past time was in state j.
i,Transition state i.
j,Transition state j.
Condition of (7) is based on the argument that pij represents certain probability.
Another important characteristic of the probability transition matrix is that the sum of each row must be equal to one.
Where
pij,Probability that current sample is in state i given the immediate precedent past time was in state j.
i,Transition state i.
j,Transition state j.
An advantage of markovian models is that they describe in an efficient way the characteristics of the system and therefore they can be solved by mathematic methods. In communication systems, Markov chains characterize in a better way the channel because it represents the combination of some phenomena that affects the signal during its wireless transmission, having a better approach to a real channel.
A probability transition matrix can be also represented as a diagram called transition diagram. Each node ○ represents a state of the Markov chain indicated with a number inside; an arrow
Probability transition diagram for 2-state Markov chain
Probability transition diagram for 3-state Markov chain
Probability transition diagram for 4-state Markov chain
Another important element in Markov chains is the steady-state vector π, which represents the total appearing percentage of a state in a Markov chain. This vector can be computed by raising P to a large power. This is shown in (9).
Where,
P,Probability transition matrix.
π,Steady state probability vector
1,Column vector of ones: 1T = (1,1,…)
One property of the π vector is that the sum of its elements must be equal to one as it is shown in (10).
Where,
πi,Steady state probability for state i.
In this section you will find the steps and the code to create a Markov chain using Matlab for two and three states. This code will be useful to create a wireless channel model that, within a wireless communications system, will be simulated using Matlab in next section.
The simpler case in Markov chains is the one with two states. The first step for the creation of a chain is to establish a transition matrix that indicates the switch between states. The transition matrix and the steady state vector for a two state model are shown in (11) and (12).
The input data for the Matlab code will be the probability transition matrix and the size of the output vector. Since this is a stochastic event, the first sample and the switch between stated will be obtained in a random way but always following the characteristics of P. It is also possible to have an initial distribution for the first sample. The precise steps to create the Matlab code are listed below.
Generate a random integer number between 1 and 2 (because of the two state markovian chain).
Generate a random natural number between 0 and 1.
If previous sample was 1 and the generated number in step b) is equal or less to p12, next sample of the chain is going to be 2; otherwise will be 1.
If previous sample was 2 and the generated number in step b) is equal or less to p21, next sample will switch to 1, otherwise will be 2.
Repeat steps b) to d) until complete the number of samples required. The generated series is the resultant Markov chain.
The Matlab code for these steps is shown next.
Another common case in Markov chains is the three-state case. The proceeding to create this type of chain in Matlab is similar to the two-state model. The input is the 3 x 3 size probability transition matrix, like the one shown in (13) and the output vector will be also the vector containing the Markov chain with the characteristics set by P.
The π vector for a three-state Markov chain is shown in (14).
The first step now will be to modify the probability transition matrix by computing the cumulative sum for each row because this will determine the transition between states. This step is show in (15).
Once P’3chan was computed, the proceeding to create the resulting Markov chain is the same as the two-state one. The steps are listed next.
Generate a random integer number between 1 and 3 (because now it is a three-state model). This will be the first sample of the chain, although an initial distribution can be established for this case.
Generate a random natural number between 0 and 1.
If previous sample was 1 and the generated number in step b) is less than p11, the next sample will be 1; if it is greater than p12’, next sample will be 3, otherwise will be 2.
If preceding sample was 2 and the generated number in step b) is less than p21, the next sample will be 1; if it is greater than p22’, next sample will be 3; if not, it will be 2.
If previous sample was 3 and the generated number in step b) is less than p31, next sample will be 1; if it is greater than p32’, next sample will be 3, otherwise will be 2.
Repeat steps b) – e) until complete the required size of the Markov chain.
The Matlab code for the previous steps is presented next.
To proof the created Markov chain follows a specific probability transition matrix is by counting the number of each one of possible transitions and dividing them by the sum of the total transitions for the corresponding state. To verify that the chain follows also the steady-state vector it is necessary to count the number of times each state appeared in the chain and divide each count by the total number of samples (size of the output vector).
Two and three-state Markov chains Matlab programs described above represent the wireless transmission channel that will be implemented in a communication system. This will be done by simulating a message is being sent through it, all with Matlab.
Another alternative to characterize a wireless channel is using Markov chains as it was said before. This model is a better option than statistic channels (AWGN, Rice, Rayleigh) because the former represent a statistical channel combination of the latter. To show the application of Markov chains in this area the next scenario is proposed.
“A wireless channel model must be created in such manner it characterizes the principal causes of attenuation, for instance: the obstacles between the transmitter and receiver, a mobile user or the influence of the line of sight (LOS).”
The statistic channels for the scenario area are defined as Rayleigh and Rice. The former characterize a mobile user and the latter the LOS between transmitter and receiver.
To simulate this scenario in Matlab, a communication system with a QPSK and rate 2/3 convolutional code is proposed. The block diagram of this system and the channel model are illustrated in Figure 3 and 4. Markov chains will be used as a base to create a wireless channel model and will represent the multiplicative fading, which is right after the transmitter, and will be switching between the possible channels according to the probability transition matrix, as it is shown in Figure 4. From now, this model will be called as a “markovian channel”.
To have a better understanding of this markovian model, several examples with different probability transition with its steady-state vector, calculated using (9), are proposed. The codes for the creation of a two and three state Markov chains are used to produce results. Interpretations are based on BER curves obtained by implementing the communication system and the markovian channel of figures below. Next sections explain with details the examples and its results.
As it was said before, this is the simplest model in Markov chains. According to the proposed scenario, the two statistical channels used for this case are:
Channel 1: Rice K = 14 dB. This channel represents the better conditions because of its strong LOS.
Channel 2: Rayleigh. This channel corresponds to a mobile user and multipath generated from the movement.
Now, three examples about two-state markovian channel model are proposed next.
Block diagram for a communication system with markovian channel
Block diagram of the markovian channel
Example 1. The next two Markov channels are proposed.
And their steady-state vectors are shown in (18) and (19).
Channel P2chan1 sets that channel 1 (Rice K = 14 dB) appears all the time, in other words, there is a strong LOS between transmitter and receiver, which can be referred as a rural environment where there are no tall buildings that blocks that line of sight. Conversely, channel P2chan2 establish that channel 2 (Rayleigh) will appear all the time, this channels can be seen as an urban environment where there are a lot of obstacles between transmitter and receiver that will cause the multipath or also it can represents an user who is moving from one point to another one. These two channels were simulated with the communication system of Figure 3 in Matlab and the BER curves obtained are shown in Figure 5.
Two state Markov cannel for Example 1
To verify the results of the markovian channel, BER curves of systems using exclusively each statistical channel were obtained too. It can be appreciated in Figure 5 that the resulting BER curve for P2chan1 is exactly the same as the one resulting from the simulation of the Rice K = 14 dB statistical channel. Likewise, BER curve generated from P2chan2 is exactly the same to the simulation where only Rayleigh statistical channel is implemented.
To proof the Markov channel follows the characteristics of (16) and (17), a counting of the transitions and the number of times both channels appeared is realized from the created Markov chain. The size of the simulated sent message was 100,000 bits, so the results of the count are given as percentages, which is equivalent to the probabilities of the transition matrixes. Those results are given in Table 1 and 2.
Counting of events for P2chan1
Counting of events for P2chan2
As it can be observed, obtained results from counting are equal to the probability transition matrix of (16). This means that 100% of chances there was a transition from channel 1 to 1 and from channel 2 to 1. Channel 1 appeared 99.99% which says that at the first sample of the chain was channel 2 but immediately after switched to channel 1, that is why the third column of Table 1 is not the same to the steady-state vector of (18) but it is very close to it.
For the case of P2chan2, it is appreciated that channel 1 never appeared in the Markov chain, thus 100% of chances remained in channel 1, so data from the third column of Table 2 has the same characteristics of the steady state vector of (19).
Example 2. In contrast to Example 1, these two probability transition matrixes and its steady-state vectors are proposed.
The interpretation for the channel of P2chan3 is that 80% of chances, Rayleigh channel will be present in the Markov chain meaning that the user is moving (walking, running) and LOS conditions are poor. For channel P2chan4 probabilities are opposite than the other channel, in other words, there is a greater probability of having LOS than multipath, like in a rural area. Resulting BER curves for both channels are shown in Figure 8, where it shows that BER curves from markovian channels of (20) and (22) are very close to that curves resulting from simulating only the correspondent statistical channel but they are not the same, proving the combination of the channels according to the probability transition matrixes.
Two State Markov Channel for Example 2
Example 3. A probability transition matrix shown in (24) with its steady-state vector in (25) are presented as a new wireless channel model. In this channel model the user has LOS the most part of the time but in some instants experiments multipath. This seems a semi urban environment because it can exists some building that cause multipath but they are not that tall to block the line of sight. BER curve for this model is shown in Figure 9.
Two State Markov Channel for Example 3
To verify the channel model was well implemented the counting of switches and how many times a state appeared is presented next.
Counting of events for P2chan5
The count of transitions between states and the times each state (or probabilistic channel) appeared in the Markov chains indicate probability transition matrix shown in (25) was followed. This can be observed also in Figure 9 where the BER curve for the channel model presents an inclination to the curve obtained when only Rice channel is simulated but it is not identically to it.
A two-state channel model is not enough to characterize a wireless channel. To create a better model it is necessary to add more statistical channel. According to the proposed scenario at the beginning of the section, the the appropriate three statistical channels are:
Channel 1: Rice K = 14 dB, very strong LOS.
Channel 2: Rayleigh, multipath and moving user.
Channel 3: Rice K = 7 dB, not a strong LOS like channel 1.
As it was done for the two-state channel model, different probability transition matrixes with their steady state vectors are through BER curves to proof the correct implementation of the channel in a communication system of Figure 5.
Example 4. Three markovian channels are proposed.
Its steady-state vectors are shown next.
The goal of these models is to verify the correct implementation of the markovian channels into a communication system. Each one of them establishes that they must stay always in the same channel. Results are compared with BER curves when only statistical channels are simulated. Figure 10 shows each BER curve obtained from the Markov chains models of (26) – (28) are almost the same to the ones obtained when only the corresponding statistical channel is simulated.
Markovian channel of (26) can be compared to a rural area where LOS is very probable because there are no tall buildings. Channel model of (27) can be interpreted as an urban zone because the multipath and users are constantly moving. Markov channel of (28) indicates LOS but not as strong as channel 1, so it can be seen as a semi-urban area because there are not a lot of tall buildings to block the transmission.
Example 5. Another three markovian channel models are proposed where it is indicated that each channel must be present in the Markov chain 80% of times. Probability transition matrixes and steady-state vectors are shown in (32)-(37).
Three State Markov Channel for Example 4
Results are shown in Figure 11 where each BER curve are very close to the curve resulted from the simulation of only statistical channels (according to each case), confirming what is indicated in each steady-state vector.
Three state Markov cannel for Example 5
Example 6. Once the behavior of the markovian channel model created with Matlab, probability transition matrix of (38) is proposed for the scenario explained above. This model indicates that the probability of a type of LOS (Rician channel K = 14 dB or K = 7 dB) is less than the probability when the user is moving (Rayleigh channel). This model focus on a mobile user and when there is a LOS but it is not the best condition. The resulting curve presented in Figure 12 seems to follow a combination of the most probable statistical channel indicated in steady-state vector (but never equal to a particular channel), concluding that these model really represents a better characterization of the channel.
The effect of the combination of statistical channels is proved with the counting of events (Table 4). These data is very similar to the probability transition matrix of (38).
Counting of events for P3chan7
Three state Markov cannel for Example 6
The methodology applied to implement a markovian channel in a wireless communication system can be also used to create an n-state channel. Some authors have characterized channels up to four states. Let’s take the probability transition matrix proposed by B. Vucetic shown in (40) with these probabilistic channels:
Channel A: Rice K = 14 dB, strong LOS.
Channel B: Rayleigh, mobile user and multipath.
Channel C: Rice K = 7 dB, regular LOS.
Channel D: Rice K = 5 dB, a channel with more noise but not as bad conditions as Rayleigh, user without movement.
Computed steady-state vector of (41) was obtained by using property of (9).
Through steady-state vector, this model establishes that the biggest probability is found between channel B (mobile user) and channel C (Rice K = 7 dB, regular LOS). This can be interpreted as an urban zone scenario where users are constantly moving and there is less possibility of line of sight. BER curve of Figure 13 shows this trend and the behavior of the markovian chain is proved by counting the transitions and states. These last results are confirmed in Table 5.
Counting of events for P3chan7
Four-state Markov channel
It has been proved until this point that the more statistical channels in a Markov chain wireless channel model, the better the channel will be characterized, however this must have a limit because maybe a large number of states in the chain could be exaggerated. Another analysis is suggested to demonstrate this hypothesis by proposing another markovian channels shown in Table 6. The common characteristic between all models is that Rayleigh channel (multipath, mobile user) has the biggest probability than a channel with some type of line of sight. The possible states are:
Channel 1: Rice = 14 dB, strong LOS.
Channel 2: Rayleigh, mobile user and multipath.
Channel 3: Rice K = 7 dB, regular LOS.
Channel 4: Rice K = 5 dB, the channel with more noise but “better” conditions than Rayleigh, user without movement.
Channel 5: AWGN, without any type of multiplicative fading. This is the channel with best conditions because it represents practically no losses.
Using the same methodology of all examples above, BER curve was computed and it is presented in Figure 14. It can be appreciated from graphic that the curve for two, three and four states are different between them; nevertheless five-state channel is very similar to four-state model although they are not exactly the same. This is very peculiar because there is nothing similar to the other cases. So the conclusion is that until four-state markovian channel model is enough to characterize a wireless channel because results are going to be very similar with more states. (Sánchez-Salas & Cuevas-Ruíz, 2007)
Markovian channels and steady-state vector for 1, 2, 3, 4 and 5 states
Comparison between n-states Markov channel model
Now let’s make the supposition that a process can be in any possible states (1,2,…,N) and each time goes to state i remains there for a certain random amount of time with media μi and then makes a transition to state j with probability pij. This practice is called semi-markovian process and it is very similar to Markov chains because switches between states follow the Markov property. However, the remaining time in a state is a random variable with some probability distribution. (Ross, 2007)
The probability transition matrix for a semi-markovian process is shown in (42).
The most relevant characteristic of the matrix above is that it has a zero diagonal matrix because it only considers transitions between states. The second important element in this kind of processes is the mean sojourn time wi in each state and it is represented as in (43).
The evolution of a semi-markovian process is explained through probability transition matrix P and sojourn time vector w in this way: the process begins in state i and remains there for a mean amount of time wi and then switches to state j with probability pij; after that remains in state j for another mean amount of time wj and can switch to state k with probability pjk or return to state i with probability pji and so on. The transition diagram for a two and three semi-markovian chain is shown in Figure 15 and 16.
Transition diagram for a 3-state semimarkovian process
Transition diagram for a 2-state semimarkovian process
If time follows an exponential probability density function, the process is called “continous-time Markov process”. When time in each state and transition is the same (time does not vary and generally is 1), then the process is called “discrete Markov chain”, consequently the analyzed models above are a particular case of semi-markovian process.
Semimarkovian process can be also applied to wireless channel modelling. The main difference between Markov chains and semimarkovian processes is that this last one includes the analysis of sojourn time in each state. In this way, the applications of the semi-markovian processes in a communication system centers in the analysis of the sojourn time in a particular condition. This can be useful to determine the performance of the designed communication system, the effectiveness of a fading mitigation technique in order to preserve optimal transmission conditions as long as possible, or to study some kind of fading that is only present in a certain hour or season, etc. An example is proposed to understand better the application.
Example 7. A three-state semimarkovian wireless channel model with probability transition matrix of (44) and mean sojourn time of (45) must be created. The remaining time follows an exponential probability density function. Analyze the model and give an interpretation of results for a wireless communication system like the one of Figure 5.
The statistical channels that form this model are:
Channel 1: Rice K = 14 dB, strong LOS.
Channel 2: Rayleigh, multipath and moving user.
Channel 3: Rice K = 7 dB, regular LOS.
Solution:
Markov chains Matlab code created in previous sections can be modified to create a semi-markovian process. The main change is that another random number is needed to determine the time in which the state will remain. The code is shown next.
Three state semimarkovian channel
However this image may not be very clear at first sight. Probability transition matrix and sojourn time vector gives a good description of the channel. Also the steady-state vector can be computed using equation (9), which is shown in (46).
From (45) and (46) it is observed that although channel 3 has not the largest probability, it does have the largest sojourn time of all of them. In other words, it is probable that channel with regular LOS is not experimented by the user so often but when it does, it remains there for much more time than any other channel. On the other hand, although the channel with multipath has the largest probability, it is not to be there for a large amount of time and it will switch to better conditions (strong or regular LOS). The behavior of these channels seems to characterize an environment in an urban zone where there are mobile users or there are many obstacles. In this type of situations it is necessary to compensate multipath by designing a link between transmitter and receiver with effective fading mitigation techniques.
To prove all what was said above, the counting of transitions and states for the simulated semi-Markov process was done.
Counting of events for P3semiM
The percentage of each transition is practically the same as the original transition matrix of (44), especially because there were no transitions to the same state in the semi-markovian process created. The percentages observed in the second row of Table 7 are the data of the steady state vector of (46). Finally, the same mean sojourn times was obtained as the one indicated in (45) proving the simulated process is correct.
The characterization of a wireless channel has become fundamental in the design of a communication system because of the rapid growing of telecommunications. The basic models are based on probability density functions although they represent real perturbations when a signal is sent through air, their characteristics are not enough because a real channel is composed by the combination of many statistical models.
A better choice to wireless channel modeling is Markov chains which are a type of stochastic processes and are based on the probability of an event given another past event. This type of model offers the combination of statistical channels. For this reason it is necessary to establish certain number of states for the probability transition matrix, which characterizes the channel. The larger the number of states (statistical channels) in the markovian chain, the better the channel is modeled but there is also a limit. The elements that model a Markov chains channel model are the probability transition matrix and steady-state vector.
Markov chains are a special case of semi-markovian processes. The main difference between them is that in the latter there are no transitions to the same state and have another element: the sojourn vector. This vector represents the mean time of sojourn of a state. This type of model gives information about how long and in what exact moment stays in a particular state, therefore its application could be the analysis of time of a particular condition (LOS, multipath, shadows) or a cause of fading (rain, scintillation, snow). This model can be also useful to know the performance of the communication system or some fading mitigation technique.
Since the methodology exposed in this chapter is very flexible, explained models can be applied with other characteristics. Given the bases for a markovian and semi-markovian channel, the lector is invited to develop another application for wireless telecommunication channels.
Contrast media is a substance that is used to enhance the differentiation of tissues within the body in medical imaging. They are administered either intravenously, intraarterially, orally or into body cavities, majority being administered intravenously. Over the past few years there has been an increase in the number of radiographic examinations that use contrast media for better lesion characterization, more so in CT and MRI examinations [1] . Although contrast media has become progressively safer over time, especially with the use of low osmolar contrast media (LOCM), anaphylactic reactions still do occur. It is estimated that 0.6% of iodinated and 0.12% of gadolinium contrast cause anaphylactic reactions [2, 3, 4]. Reactions to contrast media range from mild reactions to life threatening severe reactions. Most acute reactions occur within 1 hour of contrast media administration, with majority occurring within the first 20 minutes. Therefore, it is important to be aware of these reactions, to monitor the patient closely in this period and to manage the reactions when they do occur [5].
\nThere are two main types of iodinated contrast comprising high osmolar (HOCM) or ionic contrast that dissociates in solution to form particles and low osmolar or non-ionic that does not dissociate in solution. Contrast media osmolality is determined by the number of particles formed in solution. Ionic contrast media dissociates into osmotically active ions in solution and therefore have a higher osmolality. Non-ionic agents do not dissociate to ions when dissolved in solution and hence have a lower osmolality. In recent years there has been a shift to using the LOCM because of associated fewer reactions therefore making contrast administration safer. Nevertheless, acute anaphylactic reactions can still occur unpredictably and therefore must be recognized and managed promptly. Some of the commonly used iodine-based contrast agents and their osmolality are listed in \nTable 1\n above.
\nTypes of contrast media | \n||||
---|---|---|---|---|
Contrast | \nTrade name | \nIonic/Non-ionic | \nIodine content | \nOsmolarity | \n
Diatrizoate | \nGastrografin | \nIonic | \n300mg/ml | \n1550 | \n
Ioxaglate | \nHexabrix | \nIonic | \n320mg/ml | \n580 | \n
Ultravist | \nIopromide | \nNon-ionic | \n300mg/ml | \n607 | \n
Optiray | \nIoversal | \nNon-ionic | \n300mg/ml | \n651 | \n
Isovue 370 | \nIopamidol | \nNon-ionic | \n370mg/ml | \n796 | \n
Omnipaque 300 | \nIohexol | \nNon-ionic | \n300mg/ml | \n672 | \n
Ioxilan 350 | \nOxilan | \nNon-ionic | \n350mg/ml | \n695 | \n
Iotrol 300 | \nIotrolan | \nNon-ionic | \n300mg/ml | \n310 | \n
Visipaque 320 | \nIodixanol | \nNon-ionic | \n320mg/ml | \n290 | \n
Types of iodine based contrast media and osmolarity.
Gadolinium based MRI contrast agents have been shown to be safe for intravenous administration, and actually a better safety profile than iodinated contrast for CT and other radiographic examinations. However acute reactions do occur and include urticaria, nausea and vomiting, and rarely anaphylaxis. In a study of 141,623 doses of MRI contrast administered Jae-woo et al. identified 0.079% immediate hypersensitivity reactions including urticaria, angioedema, bronchospasm and anaphylaxis and one fatality giving a mortality rate of 0.007% [6].
\nReactions can be categorized as mild, moderate and severe as well as immediate and delayed. Mild reactions are usually self-limiting and require just supportive treatment, whereas moderate to severe reactions require prompt treatment. Delayed reactions such as abdominal pains, joint pains, fever and chills, diarrhea, headache, rashes and dizziness may be seen within two weeks from the date of contrast administration. Renal toxicity is also a commonly encountered side effect of contrast reactions manifesting as impaired renal function within two weeks of contrast administration.
\n\n\nTable 2\n below shows the different types of reactions seen.
\nSeverity | \nReaction | \n
---|---|
Mild reactions | \nUrticaria | \n
Hives | \n|
Nausea | \n|
Vomiting | \n|
Moderate reactions | \nFacial oedema | \n
Severe vomiting | \n|
Bronchospasm | \n|
Laryngeal oedema | \n|
Severe reactions | \nPulmonary oedema | \n
Cardiac arrythmia | \n|
Cardiovascular collapse | \n|
Respiratory collapse | \n
Classification of contrast media reactions.
Anaphylactic reaction usually occurs within one hour of contrast administration, with majority occurring within the first 20 minutes. This is a life-threatening reaction and manifests with hypotension, bronchospasm/laryngeal oedema and circulatory collapse. Patient evaluation algorithm is as outlined in\nFigure 1\n above.
\nPatient evaluation algorithm.
Although contrast side effects are infrequent, the knowledge of their presentation, their relationship with pre existing conditions and their management is required to ensure optimal patient care [2, 7]. Non ionic agents are iso-osmolar or low osmolar in nature and have fewer adverse effects [8, 9].
\nMajority of contrast reactions occur unpredictably and severe reactions may occur even when there has been a previous uneventful examination.
\nRisk factors that increase the likelihood of occurrence of adverse reactions [10, 11, 12] include:
Previous history of allergy like reaction to contrast media.
Allergy to food or other drugs.
History of asthma.
Renal insufficiency.
Cardiac disease e.g. Congestive cardiac failure, angina.
Anxiety.
Infants and neonates.
Elderly, above the age of 60 years.
Hematological disorders: sickle cell anemia, polycythemia vera, multiple myeloma.
Use of drugs like beta blockers.
A detailed history should be obtained and pre medication administered prior to contrast use to reduce the risk of reaction occurrence.
\nAdverse reactions to contrast can be divided into organ specific and non organ specific or general reactions. They can also be classified into acute and delayed based on the timing after contrast administration.
\nAcute hypersensitivity reactions are those that develop within 1 hour of contrast administration and can classified into allergic-like and physiologic [13]. Allergic-like reactions are largely dose and concentration independent. They do not require prior sensitization or Ig-E and are thus called idiosyncratic /anaphylactoid reactions. They occur via direct mast cell stimulations or via activation of complement by immune complexes [14]. These are the most frequent type of adverse reactions and may have serious, occasionally fatal, complications.
\nPhysiologic reactions are those that are dose and concentration dependent are thus called non idiosyncratic reactions. They are due to direct chemotoxic or osmotoxic effects of the contrast media [15].
\nThese acute reactions can be further subclassified into into 3 categories based on severity-mild, moderate and severe [11]. Mild reactions are those that are self limiting. The mild allergic-like reactions include limited urticaria, pruritus, cutaneous edema, nasal congestion while the physiologic reactions include limited nausea and vomiting, transient flushing, headache, dizziness, anxiety and vasovagal reactions that resolve spontaneously [16]. Moderate reactions are those that are progressive and more pronounced and require medical management [17, 18]. The moderate allergic-like reactions include diffuse urticaria/pruritus, diffuse erythema with normal vital signs, facial edema, throat tightness, wheezing and bronchospasms. While the moderate physiological reactions include protracted vomiting, hypertensive urgency, vasovagal reactions that require treatment and respond to it [13]. Severe reactions are those that are potentially life threatening with impending death if not managed properly [2]. The severe allergic-like reactions include diffuse edema with dyspnea, diffuse erythema with hypotension, laryngeal edema with stridor, bronchospasms with hypoxia and anaphylactic shock. The severe physiologic reactions include vasovagal reactions resistant to treatment, convulsions, arrhythmia and hypertensive emergency [13]. The end result of severe allergic like and physiologic reactions is CPA which is a medical emergency and prompt and proper management using the BLS protocol and drugs including epinephrine, vasopressors, antihistamines and inhaled B-agonists is necessary to save lives.
\nContrast induced acute kidney injury and nephropathy can also occur following contrast administration [19]. Risk factors include co morbidities like diabetes mellitus, dehydration, cardiac disease, hypertension and multiple iodinated contrast media doses in less than 24 hours. Baseline serum creatinine +/− glomerular filtration rate should be availed before injection of contrast media in at risk patients [13]. Contrast media administration in such patients can be done with caution by: reduced dose of contrast media, hydration and use of iso-osmolar agents.
\nManagement of acute contrast begins with discontinuation of injection if not completed [13, 20]. General principals of BLS and ACLS should apply in case of cardiorespiratory arrest.
\nSummary of the management of contrast reactions is as outlined in\nTable 3\n below.
\nReaction | \nMonitoring | \nTreatment | \n
---|---|---|
\n | \n\n | \n |
Urticaria (skin rash) | \nInitial size with marking and follow | \nMild-Usually none; if symptomatic consider diphenhydramine, 25–50 mg orally Moderate/Severe-monitor vitals and obtain IV access. Consider diphenhydramine, 25–50 mg orally intramuscularly/ intravenously; epinephrine (1:1,000), 0.1–0.3 mL subcutaneously/intramuscularly | \n
Bronchospasm | \nOxygen saturation, pulse, Blood pressure (BP) | \nIn all forms of bronchospasms: preserve IV access, monitor vitals and oxygen saturation and give oxygen by mask 6-10 L/min Mild: Inhaled B-agonist- 2 puffs at 90mcg/puff and can be repeated up to 3 times. If response is not satisfactory, emergency response team should be contacted. Moderate Inhaled B-agonist- 2 puffs at 90mcg/puff and can be repeated up to 3 times Epinephrine (1:1000), 0.3 mL intramuscularly-this can be repeated every 5-15 minutes as needed up to 1 ml(1 mg)total; OR Epinephrine (1:10,000), 1 mL(0.1 mg) intravenously (slowly) if hypotensive; This can be repeated every few minutes as needed up to 10 ml(1 mg) total call the emergency medical team; call the emergency medical team Severe: Epinephrine (1:1000), 0.1–0.3 mL intramuscularly-this can be repeated every 5-15 minutes as needed up to 1 ml(1 mg)total; OR Epinephrine (1:10,000), 1 mL(0.1 mg) intravenously (slowly) if hypotensive; This can be repeated every few minutes as needed up to 10 ml(1 mg) total Call the emergency medical team and Inhaled B-agonist (may work synergistically). Call the emergency medical team | \n
Facial or laryngeal edema | \nOxygen saturation, pulse, BP | \nIn all forms of laryngeal edema: preserve IV access, monitor vitals and oxygen saturation and give oxygen by mask 6-10 L/min Call the emergency medical team if severe Epinephrine (1:1000), 0.3 mL intramuscularly-this can be repeated every 5-15 minutes as needed up to 1 ml(1 mg)total; OR Epinephrine (1:10,000), 1 mL(0.1 mg) intravenously (slowly) if hypotensive; This can be repeated every few minutes as needed up to 10 ml(1 mg) total call the emergency medical team | \n
Hypotension(systolic BP <90 mmHg) and tachycardia (>100 bpm) | \nOxygen saturation, pulse, BP | \nPreserve IV access, Elevate legs 60°; oxygen, 6–10 L/min; rapid intravenous fluids(1 liter of 0.9% normal saline or lactated Ringer’s); epinephrine (1:10,000), 1 mL(0.1 mg) intravenously (slowly); This can be repeated every few minutes as needed up to 10 ml(1 mg) total OR Epinephrine (1:1000), 0.3 mL intramuscularly-this can be repeated every 5-15 minutes as needed up to 1 ml(1 mg)total call the emergency medical team | \n
Hypotension(systolic BP <90 mmHg) and bradycardia (<60 bpm) | \nOxygen saturation, pulse, BP | \nElevate legs 60°; oxygen, 6–10 L/min; rapid intravenous fluids(1 liter of 0.9% normal saline or lactated Ringer’s) If mild, no further treatment is necessary If patient remains symptomatic despite the above measures: Atropine, 0.6–1 mg intravenously (slowly); repeat to total of 2–3 mg (0.04 mg/kg) if needed; call the emergency medical team | \n
Cardiac arrhythmia | \nOxygen saturation, pulse, BP, ECG | \nFollow ACLS protocols; call the emergency medical team | \n
Hypertensive crisis (diastolic BP >120 mmHg; systolic BP >200 mmHg) | \nOxygen saturation, pulse, BP, ECG | \nNitroglycerine, 0.4 mg sublingually; can repeat every 5-10 minutes OR Labetalol intravenously 20 mg, administer slowly over 2 minutes. The dose can be doubled every 10 minutes. OR Lasix intravenously 20-40 mg,slowly over 2 minutes. Phentolamine, 5 mg intravenously for pheochromocytoma; Call the emergency medical team | \n
Seizures | \nOxygen saturation, pulse, BP, ECG | \nObserve and protect the patient Secure airway; oxygen, 6–10 L/min; Preserve IV access and give diazepam, 5 mg intramuscularly/intravenously OR midazolam, 0.5–1 mg intravenously OR phenytoin infusion, 15–18 mg/kg at 50 mg/min; call the emergency medical team | \n
Hypoglycemia | \nOxygen saturation, pulse, BP | \nIf patient is able to swallow orally give half a cup of fruit juice or 15 g of glucose Is the patient is unable to swallow safely, obtain IV access and give 50% dextrose, 1 ampule-25gms over 2 minutes OR 100 ml/hr. of 5% dextrose. Is patient is unable to swallow and IV access is not available give intramuscular glucagon 1 mg. | \n
Pulmonary edema | \nOxygen saturation, pulse, BP, ECG | \nPreserve IV access, Secure airway; oxygen, 6–10 L/min; Elevate head of the bed furosemide, 20–40 mg intravenously (slowly over 2 minutes); morphine, 1–3 mg intravenously; call the emergency medical team | \n
Management of contrast reactions.
Premedication of patients who have a higher risk of acute allergic like reactions should be considered to reduce the chance of reaction occurrence [18]. For elective premedication oral prednisolone and diphenhydramine are used. For emergency premedication I.V methyl prednisolone sodium succinate or dexamethasone sodium sulfate. I.V diphenhydramine can be used instead of steroids in emergency cases [13].
\nIntravenous corticosteroids play a role in preventing short term recurrence of an allergic like reactions. They may also be administered to patients having severe allergic like manifestations prior to transport to an emergency unit. They are however not useful in the acute treatment of any reaction.
\nThe hospital administration in liaison with the heads of the radiology department and the radiology contrast committee should set up and publish an institutional policy and procedure manual on contrast media administration.
\nThe purpose of this manual is:
To ensure that administration of contrast media is done according to the protocols set up by the hospital and imaging department.
To ensure that in case of adverse reactions to contrast media, appropriate steps are taken to manage them.
To ensure that patients at risk of contrast media reactions or with prior history of such reactions receive appropriate premedication and are imaged using suitable protocols.
To ensure that patients due to receive intravenous contrast media have appropriate laboratory tests done and reviewed by the radiologist to determine their suitability for the procedure.
Guidelines for administration on intravenous contrast:
Administration of intravenous contrast should be done by a trained radiology technician / nurse under the supervision of the radiologist and these staff should be competent in recognizing and managing an adverse reaction if it occurs.
Standard operating procedures on the administration of intravenous contrast media should be set up and made available to the radiology clinical staff for reference when needed.
The Radiologist should review all the imaging requests that require administration of intravenous contrast, to determine the protocol to be used which will depend on the patient’s condition and clinical indication for the study.
The radiology technician and nurse attending to the patient must take a detailed history on the current clinical condition, current medications, history of allergy, asthma and prior adverse reactions to drugs and contrast media.
If the patient is found to have risk factors or contraindications to administration of contrast media, then the radiologist will determine the protocol to be followed and premedication to be administrated if required.
Protocols on the recognition and management of adverse reactions to contrast media should be set up and made available to all radiology clinical staff. These protocols ought to be illustrated in flow charts and placed in the various imaging sections in which intravenous contrast media is administered to facilitate proper management of these emergencies.
Close liaison between the radiology department, the emergency response team and intensive care unit must be present to ensure that the radiology department will get adequate support in case of an emergency.
All imaging sections in the radiology department must be equipped with the emergency equipment and medication required to monitor and manage a patient in cardiopulmonary arrest and more specifically a patient undergoing a severe reaction to contrast media.
\nMajority of the emergency equipment and medication are part of the standard crash cart/ emergency trolley; therefore, it is upon the administration of the radiology department to decide whether a dedicated contrast reaction kit is necessary. This will depend on the size of the imaging department, patient numbers and budget allocations.
\nThe basic equipment required to monitor patients experiencing an adverse reaction to contrast media include:
Devices for hemodynamic Monitoring-Pulse and blood pressure monitors.
Devices for respiratory monitoring – Pulse oximeter.
Body temperature monitor – Thermometer or adhesive pads with thermoelectric transducer.
Blood glucose monitor.
Stethoscope.
Equipment and supplies for managing patients in an acute adverse reaction include:
Oxygen supply from a wall unit or oxygen cylinder.
Devices to supply the supplemental oxygen e.g. nasal cannula, simple face mask, face mask with oxygen reservoirs (non-rebreather mask). The latter is preferred as it is able to deliver a large dose of approximately 95–100% oxygen at a flow rate of 10-15 ml/min. Another device is a bag mask device which uses positive pressure ventilation with a face mask or advanced airway to administer a high concentration of oxygen to the patient. These devices must be available in adult and pediatric sizes.
Suction device used to clear the airway of secretions to enable the patient to breath. A patent airway is required for effective cardiopulmonary resuscitation in case of cardiopulmonary arrest in the case of severe contrast media reactions. The suction device may be wall mounted or mobile an I used in conjunction with suction tubing/ catheters.
Basic medication required in case of a contrast media reactions include:
Epinephrine
Emergency trolley / crash carts in hospital setting are usually equipped in 1 mg in 10 ml of epinephrine for intravenous administration (1:10000).
Epinephrine 1 mg in 1 ml vial is used for intramuscular injection.
Epinephrine autoinjectors in pediatric, and adult doses can also be used if available.
Oral and intravenous antihistamines.
Inhaled or nebulized B2 agonists.
Normal saline intravenous fluid in 500 ml and 1 liter bags/ bottles.
Atropine 1 mg in 10 ml for intravenous administration.
Additional medication and supplies include:
Emergency drugs – these include the standards emergency medications which are part of standard crash cart/ emergency trolley.
Supplies that form part of the standard emergency trolley like various sizes of intravenous cannulas, needles, syringes and intravenous giving sets.
Advanced cardiovascular life support equipment including:
Advanced airway adjuncts e.g. endotracheal tube.
Suction catheters.
Automated external defibrillator.
In view that cardiopulmonary arrest and adverse reactions to contrast media in the radiology department are rare, it is imperative that periodic stock checks are done to ensure the equipment and medications stocked for the management of these emergencies are within the recommended validity period.
\nWhen faced with a severe reaction to contrast media in which the patient’s condition warrants implementation of basic life support and advanced cardiac life support protocols, it is imperative that the hospital emergency response team be alerted to assist in initiation of these lifesaving protocols.
\nModern radiology departments are fitted with an emergency bell that alerts the emergency response team to respond to an emergency in each imaging section. All radiology staff must be made aware of the location of these bells to activate them when needed.
\nIn the event that such a system is not in place, the phone number of an internal/ external emergency response unit should be clearly posted in each imaging section.
\nDespite the rare occurrence of contrast media reactions, they may carry substantial morbidity and mortality and thus require immediate intervention by the attending staff. These staff must therefore be equipped with the knowledge and skills to initiate effective cardiopulmonary resuscitation in order to manage these emergencies as they await the arrival of the emergency response team.
\nAll clinical staff should receive life support training upon employment and thereafter attend at least three yearly refresher course as recommended by the American heart association.
\nContinuous medical education on contrast media reactions and their management should be held frequently to ensure these vital knowledge and skills are up to date.
\nAdvanced radiology life support ™ is a course that uses concepts from basic life support and advanced cardiac life support to radiology clinical staff on recognizing and managing life threatening emergencies occurring in the imaging department.
\nThis training covers:
Types of contrast media used in imaging.
Recognition of the signs and symptoms of contrast media reactions.
Risk factors of contrast induced nephropathy and approach to administration of contrast media in renal insufficiency.
Safety of Gadolinium based contrast agents and nephrogenic systemic fibrosis.
Airway management in emergencies.
Safe management of sedated patients in the imaging department.
Advanced radiology life support ™ has been successful in United states of America and Canada in training of radiologists, radiology technicians and nurses in the management of contrast media reactions and cardiopulmonary arrest in the radiology department. Accreditation is by the Mayo clinic of medicine and Science.
\nThis training is available online in form interactive videos, therefore imaging departments should allocate a budget for purchase of this training for each of its clinical staff members.
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\\n\\nOur books contain scientific content written by two Nobel Prize winners, two Breakthrough Prize winners and 73 authors who are in the top 1% Most Cited.
\\n\\nWith regular submission for coverage in the single most important database, the Book Citation Index in the Web of Science™ Core Collection (BKCI), and no rejected submissions to date, over 43% of all Open Access books indexed in the BKCI are IntechOpen published books.
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\\n\\nYOUR WORK, YOUR COPYRIGHT
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\\n\\nCan collaboration be inspired by a publishing format? At IntechOpen, the answer is yes. The way the research is published, the way it is accessed, it’s all part of our mission to help academics make a greater impact by giving readers free access to all published work.
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\\n\\nPUBLISHING PROCESS STEPS
\\n\\nSee a complete overview of all publishing process steps and descriptions here.
\\n\\nCURRENT PROJECTS
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\n\nQUALITY CONTENT
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\n\nCURRENT PROJECTS
\n\nTo view current Open Access book projects that are Open for Submissions visit us here.
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