**2. PD and the serotonergic system**

Tremor, rigidity, and bradykinesia, the classical motor symptoms of ideopathic PD, primarily result from loss of dopaminergic neurons in the SNc. However, neural degeneration also occurs in other sites of the brain, ranging from the brain stem to cortex, as the synaptic protein *α*-synuclein accumulates pathologically to form Lewy bodies (LB) or Lewy neurites. The clinical diagnosis of PD is based upon presence of the motor symptoms indicating dopamine deficiency (Chaudhuri et al., 2006; Jankovic, 2008). Postmortem analysis finds LB not only in remaining substantia nigra cells but in other specific brain regions where cells are lost (Gibb & Lees, 1988). Braak and colleagues (Braak et al., 2003) have proposed a scheme of six stages describing the development of ideopathic PD, characterized by the spatial extent of LB inclusions. Braak stage 1 involves LB inclusions in the region of the brain stem; neurodegeneration of the substantia nigra does not begin until stage 3. Braak's hypothesis concerning the progression of PD predicts that symptoms such as diminished olfactory sensitivity (Lim et al., 2009) or REM behavior disorder (Ahlskog, 2004) should precede the cardinal motor symptoms of the disease, a pattern observed in some but not all cases of PD (Linazasoro, 2007). Indeed, the retrospective nature of Braak's study obscures the actual course of progression (Halliday & McCann, 2010). In a longitudinal study, Halliday & McCann (2010) found that approximately half of ideopathic PD cases follow Braak's scheme. In all cases studied by Halliday and McCann, LB occurred not only in the substantia nigra but also in other brain areas including brain stem. Thus, extra-nigral aspects are always present in PD, and their significance can rival that of the cardinal motor symptoms (Chaudhuri et al., 2006).

Ahlskog (2004) reports that LB have been found in pontomedullary neurons of brains without substantia nigra pathology but that the reverse has not been observed. Among the nondopaminergic systems profoundly affected in PD is the serotonergic system. The extent of damage to the serotonergic system in PD is variable and is less severe than the loss of dopamine: Kish found that, while striatal dopamine concentrations decreased by more than 80%, serotonin markers decreased by less than 70% (Kish et al., 2008). It has not been clearly established to what extent this reduction in serotonin markers is due to raphe cell loss 2 Will-be-set-by-IN-TECH

has a model that represents (part of) the underlying physiology well, then *in silico* experiments are quick and inexpensive. The model provides a quantitative way of thinking about the phenomena being investigated and may suggest new hypotheses that can be checked by animal experiments. Thus, modeling, when combined with animal experiments and clinical trials, can shed some light on the complicated pharmacological, electrophysiological, and

In Section 2, we discuss the evidence for the role of 5-HT in PD and the side effects of levodopa therapy and in Section 3 we discuss possible mechanisms. In Section 4, we describe a mathematical model that we recently created to study homeostatic mechanisms in serotonergic signaling. In Section 5 we use the model, and a previous model of a DA terminal, to discuss the effects of gene polymorphisms, the stability of extracellular DA in the striatum in the face of cell death in the substantia nigra, and the mechanism of action of selective serotonin reuptake inhibitors. Finally, in Section 6 we outline how we plan to use existing models and new models to investigate the interactions between the 5-HT system and

Tremor, rigidity, and bradykinesia, the classical motor symptoms of ideopathic PD, primarily result from loss of dopaminergic neurons in the SNc. However, neural degeneration also occurs in other sites of the brain, ranging from the brain stem to cortex, as the synaptic protein *α*-synuclein accumulates pathologically to form Lewy bodies (LB) or Lewy neurites. The clinical diagnosis of PD is based upon presence of the motor symptoms indicating dopamine deficiency (Chaudhuri et al., 2006; Jankovic, 2008). Postmortem analysis finds LB not only in remaining substantia nigra cells but in other specific brain regions where cells are lost (Gibb & Lees, 1988). Braak and colleagues (Braak et al., 2003) have proposed a scheme of six stages describing the development of ideopathic PD, characterized by the spatial extent of LB inclusions. Braak stage 1 involves LB inclusions in the region of the brain stem; neurodegeneration of the substantia nigra does not begin until stage 3. Braak's hypothesis concerning the progression of PD predicts that symptoms such as diminished olfactory sensitivity (Lim et al., 2009) or REM behavior disorder (Ahlskog, 2004) should precede the cardinal motor symptoms of the disease, a pattern observed in some but not all cases of PD (Linazasoro, 2007). Indeed, the retrospective nature of Braak's study obscures the actual course of progression (Halliday & McCann, 2010). In a longitudinal study, Halliday & McCann (2010) found that approximately half of ideopathic PD cases follow Braak's scheme. In all cases studied by Halliday and McCann, LB occurred not only in the substantia nigra but also in other brain areas including brain stem. Thus, extra-nigral aspects are always present in PD, and their significance can rival that of the cardinal motor symptoms (Chaudhuri et al.,

Ahlskog (2004) reports that LB have been found in pontomedullary neurons of brains without substantia nigra pathology but that the reverse has not been observed. Among the nondopaminergic systems profoundly affected in PD is the serotonergic system. The extent of damage to the serotonergic system in PD is variable and is less severe than the loss of dopamine: Kish found that, while striatal dopamine concentrations decreased by more than 80%, serotonin markers decreased by less than 70% (Kish et al., 2008). It has not been clearly established to what extent this reduction in serotonin markers is due to raphe cell loss

behavioral issues in PD.

the DA system in PD.

2006).

**2. PD and the serotonergic system**

(Jellinger, 1991), serotonergic terminal loss in the striatum, or molecular regulatory changes (Kish et al., 2008).

In post-mortem analyses of brains from PD patients, Kish et al. (2008) found that serotonin and dopamine have substantially different patterns of loss within the striatum. Serotonin markers show greater loss in the caudate than in putamen, while the dopamine loss is greater in the putamen. Thus the striatal subdivision with the more severe dopamine loss (putamen) was less affected by loss of serotonin markers, possibly reflecting compensatory sprouting of 5-HT terminals (Maeda et al., 2003). Serotonergic responses to dopamine depletion may also be evident in changes in the electrical activity of serotonergic neurons. Zhang et al. (2007) reports that, in an animal model of PD, raphe neurons have altered firing rates and fire bursts more frequently. Under levodopa administration, DA may also be released in bursts from these serotonergic neurons.

One of the clearest and best-studied involvements of 5-HT in PD symptoms is in the motor symptoms, including tremor and especially levodopa induced dyskinesias (LID). Experiments have found that the serotonergic system plays an essential role in both symptoms. Brooks (2007) reports that in order to generate tremors with the characteristic PD frequency of 3-5 Hz in animal models it is necessary to lesion not just nigro-striatal dopaminergic projections but also the midbrain tegmentum, which contains serotonergic cell bodies in the median raphe, rubrospinal, and dentatothalamic tracts. He also notes that loss of midbrain serotonin 5-*HT*1*A* binding correlates with tremor severity in PD, unlike loss of striatal dopaminergic function. He speculates that this may explain why some parkinsonian tremors are relatively resistant to dopaminergic medications. 5-HT may not be equally involved in all motor symptoms of PD: it has been observed clinically that rigidity and bradykinesia are more responsive to dopaminergic drugs than is tremor (Fox et al., 2009).

Upon diagnosis of PD, patients can often use levodopa to effectively relieve symptoms for several years. However, more than 50% of patients develop motor complications in response to levodopa administration within 5 years (Olanow et al., 2000); after 10 years, the percentage is approximately 90% (Ahlskog & Muenter, 2001). These complications include a narrowing of the temporal window of efficacy (*i.e.*, the duration of benefit after a given dose of levodopa becomes progressively shorter until it approximates the plasma half-life of levodopa) (Olanow et al., 2006), sudden failures of efficacy known as "on-off fluctuations" (Nicholson & Brotchie, 2002) and, most troublesome, the appearance of involuntary movements (LID) (Carta et al., 2008; Nicholson & Brotchie, 2002).

#### **3. Possible mechanisms of serotonergic involvement in PD motor symptoms**

In order to understand the emergence of LID, it is useful to first review how levodopa may achieve therapeutic effect. The idea of administering levodopa is to provide dopamine replacement therapy. Dopamine itself is unable to pass the blood brain barrier, but its immediate precursor, levodopa, is able to reach the brain following peripheral administration when given in combination with a decarboxylase inhibitor to prevent metabolism while in the blood stream (Carta et al., 2008). The motor symptoms of PD typically emerge when a sufficient proportion of dopaminergic cells in SNc have been lost that dopaminergic terminals in the striatum are no longer able to maintain a high enough concentration of extracellular DA. Supplemental levodopa can be taken into the remaining dopaminergic terminals, converted to DA and stored in vesicles for synaptic release.

result in large swings in the extracellular concentration of DA. The resulting pulsatile stimulation of striatal DA receptors may be the proximate cause of abnormal movements (de la Fuente-Fernandez et al., 2001) and may induce post-synaptic changes. In animal models of PD, alterations have been identified in the *D*1 signaling pathway as well as in NMDA and AMPA receptor function and distribution (Bibbiani et al., 2005; Hallett et al., 2005; Robelet et al., 2004), and these changes have been linked to the induction and maintenance of abnormal movements (Gardoni et al., 2006; Hallett et al., 2005; Picconi et al., 2008; Santini et al., 2007). In fact, studies utilizing pumps to provide a fairly continuous dosing with levodopa or

Mathematical Models: Interactions Between Serotonin and Dopamine in Parkinson's Disease 409

Changes in gene expression also have been found following treatment with levodopa (Santini et al., 2007), and these may relate to the phenomenon of priming. Some PD patients can be treated with DA receptor agonists without developing dyskinesias. But eventually, as the disease progresses, they generally need to add levodopa in order to achieve relief from symptoms. The phenomenon of priming is that patients started on levodopa and then moved to DA agonists will exhibit dyskinesias even if placed on DA agonists without levodopa

As a first step in using mathematics to help understand the serotonergic and dopaminergic systems, we have created mathematical models of a serotonin terminal (Best et al., 2010b) and a dopamine terminal (Best et al., 2009). Here we briefly describe the model for a serotonin terminal and in the next section give applications. The substrates in the model are indicated in Figure 1 by the pink boxes and the blue ellipses contain the acronyms of enzymes or transporters. Blood tryptophan is considered a (possibly time-varying) input to the model and there are differential equations for the other nine substrates. Each differential equation is just a quantitative expression of mass balance; i.e. the rate of change of the concentration of a substrate is simply the sum of the rates of the reactions by which it is made minus the sum of the rates of the reactions in which it is used. For example, the concentration of

where *V*TPH is the velocity of the TPH reaction and *V*AADC is the velocity of the AADC reaction. One must specify exactly how these velocities depend on the current values of

*Ki* )(*Kbh*4 + (*bh*4)) ·

The first term on the right is of Michaelis-Menten form and gives the dependence of the velocity on the concentrations of *trp* and *bh*4. The enzyme TPH shows substrate inhibition (Best et al., 2010a; Friedman et al., 1974; McKinney et al., 2005), which is the reason for the (*trp*)2 term in the denominator. The second term on the right expresses how the concentration of extracellular 5-HT influences the rate of synthesis via the autoreceptors. At normal e5-HT concentration (.768 nM) this factor equals one. As e5-HT goes up the factor can go as low as 0.5

*dt* = *V*TPH(*trp*, *bh*4,*e*5*ht*) − *V*AADC(5*htp*) (1)

1.5 − (*e*5*ht*)2

((.000768)2 + (*e*5*ht*)2)

. (2)

**4. Mathematical modeling of dopaminergic and serotonergic systems**

DA agonists have found fewer side effects (Nutt et al., 2000).

(Nicholson & Brotchie, 2002).

5-hydroxytryptophan, [5htp], satisfies:

various substrates. *V*TPH is given by:

*d*[5*htp*]

*V*TPH = *Vmax*(*trp*)(*bh*4) (*Ktrp* + (*trp*) + (*trp*)2

As the number of remaining dopaminergic cells continues to decrease, the levodopa may increasingly be taken up by other cell types including serotonergic neurons and glial cells. Serotonergic cells may play a special role here, as they also express the enzymes used in dopaminergic cells to convert levodopa to DA (amino acid aromatic decarboxylase, AADC) and to package DA into vesicles (vesicular monoamine transporter 2, MAT). Indeed, experiments have verified that serotonergic cells can store and release DA in vivo and in vitro (Nicholson & Brotchie, 2002). Evidence that serotonergic cells may be playing a role in LID comes from animal models of PD. (Tanaka et al., 1999) showed that, in levodopa treatment of a hemiparkinsonian rat, extracellular DA (eDA) decreased substantially when the serotonergic system was lesioned. Glial cells also contain AADC and so could contribute to the conversion of levodopa to DA; however, experiments by Kannari et al. (2000) in which he used reserpine to block vesicular packaging showed a great reduction of eDA, suggesting that most of the levodopa-derived DA is released by exocytosis of vesicles rather than by glia, at least at physiological levels of levodopa administration. Carta et al. (2007) have provided further evidence implicating serotonergic cells in LID in a rat model by showing that either toxic lesion of the serotonergic system or pharmacological impairment of the system with selective serotonin autoreceptor (5-*HT*1*A* and 5-*HT*1*B*) agonists resulted in a nearly complete elimination of LID.

The observation that LID becomes increasingly problematic as the disease progresses suggests that LID may result from the fact that DA released from serotonergic cells is not subject to the DA homeostatic mechanisms present in dopaminergic cells. Many approaches to eliminating LID therefore tend to focus instead on manipulating factors that regulate serotonergic cell activity, such as serotonergic autoreceptors that participate in serotonergic homeostatic mechanisms. Simply decreasing serotonergic cell activity by administering serotonin autoreceptor agonists has the drawback of also reducing the amount of dopamine released into the extracellular space, tending to worsen PD symptoms (Iravani et al., 2006). Carta et al. (2008) argue that it is reasonable to use 5-HT autoreceptor agonists especially because the DA intermixed with the 5-HT released by the serotonergic cell effectively lowers the binding of 5-HT to 5-HT autoreceptors and induces the cells to be over-active. A more detailed look at the serotonergic system, using mathematical models, may help suggest more nuanced approaches.

There are many types of serotonin receptors. 5-*HT*1*A* receptors are present on the cell body and dendrites of serotonergic neurons in the dorsal and median raphe; they function as autoreceptors and they decrease firing as extracellular 5-HT (e5-HT) goes up. 5-*HT*1*B* receptors are present on axon terminals in serotonin projection regions where they function as autoreceptors and decrease the release of serotonin as e5-HT goes up in the terminal region. Applying agonists only to 5-*HT*1*A* or only to 5-*HT*1*B* autoreceptors in a rat model of PD treated with levodopa can partially reduce LID (Bibbiani et al., 2001; Jackson et al., 2004). Carta et al. (2007) found that providing subthreshold doses of both 5-*HT*1*A* and 5-*HT*1*B* agonists (that is, doses that would have little or no effect alone) could completely eliminate LID. This is very strong evidence that the absence of the normal control mechanisms by the DA autoreceptors is connected to LID.

Post-synaptic mechanisms may play a role in LID. Given that serotonergic cells may be responsible for releasing much of the levodopa-derived DA in advanced PD and that these cells lack DA homeostatic mechanisms, the intermittent administration of levodopa may 4 Will-be-set-by-IN-TECH

As the number of remaining dopaminergic cells continues to decrease, the levodopa may increasingly be taken up by other cell types including serotonergic neurons and glial cells. Serotonergic cells may play a special role here, as they also express the enzymes used in dopaminergic cells to convert levodopa to DA (amino acid aromatic decarboxylase, AADC) and to package DA into vesicles (vesicular monoamine transporter 2, MAT). Indeed, experiments have verified that serotonergic cells can store and release DA in vivo and in vitro (Nicholson & Brotchie, 2002). Evidence that serotonergic cells may be playing a role in LID comes from animal models of PD. (Tanaka et al., 1999) showed that, in levodopa treatment of a hemiparkinsonian rat, extracellular DA (eDA) decreased substantially when the serotonergic system was lesioned. Glial cells also contain AADC and so could contribute to the conversion of levodopa to DA; however, experiments by Kannari et al. (2000) in which he used reserpine to block vesicular packaging showed a great reduction of eDA, suggesting that most of the levodopa-derived DA is released by exocytosis of vesicles rather than by glia, at least at physiological levels of levodopa administration. Carta et al. (2007) have provided further evidence implicating serotonergic cells in LID in a rat model by showing that either toxic lesion of the serotonergic system or pharmacological impairment of the system with selective serotonin autoreceptor (5-*HT*1*A* and 5-*HT*1*B*) agonists resulted in a nearly complete

The observation that LID becomes increasingly problematic as the disease progresses suggests that LID may result from the fact that DA released from serotonergic cells is not subject to the DA homeostatic mechanisms present in dopaminergic cells. Many approaches to eliminating LID therefore tend to focus instead on manipulating factors that regulate serotonergic cell activity, such as serotonergic autoreceptors that participate in serotonergic homeostatic mechanisms. Simply decreasing serotonergic cell activity by administering serotonin autoreceptor agonists has the drawback of also reducing the amount of dopamine released into the extracellular space, tending to worsen PD symptoms (Iravani et al., 2006). Carta et al. (2008) argue that it is reasonable to use 5-HT autoreceptor agonists especially because the DA intermixed with the 5-HT released by the serotonergic cell effectively lowers the binding of 5-HT to 5-HT autoreceptors and induces the cells to be over-active. A more detailed look at the serotonergic system, using mathematical models, may help suggest more

There are many types of serotonin receptors. 5-*HT*1*A* receptors are present on the cell body and dendrites of serotonergic neurons in the dorsal and median raphe; they function as autoreceptors and they decrease firing as extracellular 5-HT (e5-HT) goes up. 5-*HT*1*B* receptors are present on axon terminals in serotonin projection regions where they function as autoreceptors and decrease the release of serotonin as e5-HT goes up in the terminal region. Applying agonists only to 5-*HT*1*A* or only to 5-*HT*1*B* autoreceptors in a rat model of PD treated with levodopa can partially reduce LID (Bibbiani et al., 2001; Jackson et al., 2004). Carta et al. (2007) found that providing subthreshold doses of both 5-*HT*1*A* and 5-*HT*1*B* agonists (that is, doses that would have little or no effect alone) could completely eliminate LID. This is very strong evidence that the absence of the normal control mechanisms by the DA autoreceptors

Post-synaptic mechanisms may play a role in LID. Given that serotonergic cells may be responsible for releasing much of the levodopa-derived DA in advanced PD and that these cells lack DA homeostatic mechanisms, the intermittent administration of levodopa may

elimination of LID.

nuanced approaches.

is connected to LID.

result in large swings in the extracellular concentration of DA. The resulting pulsatile stimulation of striatal DA receptors may be the proximate cause of abnormal movements (de la Fuente-Fernandez et al., 2001) and may induce post-synaptic changes. In animal models of PD, alterations have been identified in the *D*1 signaling pathway as well as in NMDA and AMPA receptor function and distribution (Bibbiani et al., 2005; Hallett et al., 2005; Robelet et al., 2004), and these changes have been linked to the induction and maintenance of abnormal movements (Gardoni et al., 2006; Hallett et al., 2005; Picconi et al., 2008; Santini et al., 2007). In fact, studies utilizing pumps to provide a fairly continuous dosing with levodopa or DA agonists have found fewer side effects (Nutt et al., 2000).

Changes in gene expression also have been found following treatment with levodopa (Santini et al., 2007), and these may relate to the phenomenon of priming. Some PD patients can be treated with DA receptor agonists without developing dyskinesias. But eventually, as the disease progresses, they generally need to add levodopa in order to achieve relief from symptoms. The phenomenon of priming is that patients started on levodopa and then moved to DA agonists will exhibit dyskinesias even if placed on DA agonists without levodopa (Nicholson & Brotchie, 2002).

#### **4. Mathematical modeling of dopaminergic and serotonergic systems**

As a first step in using mathematics to help understand the serotonergic and dopaminergic systems, we have created mathematical models of a serotonin terminal (Best et al., 2010b) and a dopamine terminal (Best et al., 2009). Here we briefly describe the model for a serotonin terminal and in the next section give applications. The substrates in the model are indicated in Figure 1 by the pink boxes and the blue ellipses contain the acronyms of enzymes or transporters. Blood tryptophan is considered a (possibly time-varying) input to the model and there are differential equations for the other nine substrates. Each differential equation is just a quantitative expression of mass balance; i.e. the rate of change of the concentration of a substrate is simply the sum of the rates of the reactions by which it is made minus the sum of the rates of the reactions in which it is used. For example, the concentration of 5-hydroxytryptophan, [5htp], satisfies:

$$\frac{d[5htp]}{dt} = V\_{\rm TPH}(trp, bh4, e5ht) - V\_{\rm AADC}(5htp) \tag{1}$$

where *V*TPH is the velocity of the TPH reaction and *V*AADC is the velocity of the AADC reaction. One must specify exactly how these velocities depend on the current values of various substrates. *V*TPH is given by:

$$V\_{\rm TPH} = \frac{V\_{\rm max}(trp)(bh4)}{(K\_{trp} + (trp) + \frac{(trp)^2}{K\_l})(K\_{bh4} + (bh4))} \cdot \left(1.5 - \frac{(e5ht)^2}{((.000768)^2 + (e5ht)^2)}\right) . \tag{2}$$

The first term on the right is of Michaelis-Menten form and gives the dependence of the velocity on the concentrations of *trp* and *bh*4. The enzyme TPH shows substrate inhibition (Best et al., 2010a; Friedman et al., 1974; McKinney et al., 2005), which is the reason for the (*trp*)2 term in the denominator. The second term on the right expresses how the concentration of extracellular 5-HT influences the rate of synthesis via the autoreceptors. At normal e5-HT concentration (.768 nM) this factor equals one. As e5-HT goes up the factor can go as low as 0.5

Fig. 1. Steady state concentrations and fluxes in the 5-HT terminal model. The figure shows the reactions in the model. The pink rectangular boxes indicate substrates and blue ellipses contain the acronyms of enzymes or transporters; steady state values in the model are indicated. Concentrations (red) have units of *μ*M and rates (blue) have units of *μ*M/hr. Full names of the substrates are: bh2, dihydrobiopterin; bh4, tetrahydrobiopterin; trp, tryptophan; btrp, serum tryptophan; 5htp, 5-hydroxytryptophan; c5ht, cytosolic 5-HT; v5ht, vesicular 5-HT; e5ht; extracellular 5-HT; 5-hiaa, 5-hydroxyindoleacetic acid; *trp*−*pool*, the tryptophan pool. Names of enzymes and transporters are: Trpin, neutral amino acid transporter; DRR, dihydrobiopterin reductase; TPH, tryptophan hydroxylase; AADC, aromatic amino acid decarboxylase; MAT, vesicular monoamine transporter; SERT, 5-HT reuptake transporter; auto, 5-HT autoreceptors; MAO, monoamine oxidase; ALDH, aldehyde dehydrogenase. Removal means uptake by capillaries or glial cells or diffusion out of the system.

Mathematical Models: Interactions Between Serotonin and Dopamine in Parkinson's Disease 411

and as e5-HT goes down, the factor can go as high as 1.5. We chose *Km* and *Ki* values from the literature and chose the *Vmax* so that the normal velocity of the the TPH reaction is in the range given by experiments. The form of the second factor is more speculative. Though it is certain that increasing extracellular concentrations of 5-HT inhibit synthesis via the autoreceptors (Adell et al., 2002), there is relatively little information in the literature about the range of e5-HT concentrations over which the effect takes place and about the strength of the effect in the low nanomolar range. Here, as in other choices of parameters and functional forms, we base our choices as much as possible on the experimental literature. Full details of the model can be found in Best et al. (2010b).

The model can be used to show how the steady state values of concentrations and rates change if parameters, like serotonin transporter (SERT) density, or inputs, like serum tryptophan, change. One can also compute the time courses of the concentrations and rates on long time scales (hours) or very short time scales (msec) as the system responds to the release of 5-HT due to individual action potentials. However, the model has limitations. Various physiological processes known to be important are not included, for example the movement of vesicles or SERTs from the interior of the terminal to and from the synaptic membrane. The detailed biophysics of the autoreceptors is not included; instead the model has terms that represent the effect of e5-HT on TPH and on release from the vesicles. And finally, this is a model for a terminal and thus has limited value in studying network questions about the full serotonergic system.

It is important to keep in mind that there is no such thing as *the* serotonergic terminal. Important parameters vary considerably from one projection region to another. For example, SERT density (which corresponds roughly to the *Vmax* of *V*SERT) varies by about a factor of 5 (Bunin et al., 1998; Daws et al., 2005; Lin et al., 2004). And, functional polymorphisms for the TPH, SERT, and MAO genes are known to exist. Indeed, one of the strengths of the model is that it can be used to study the likely effects of such variations on the functional behavior of serotonergic terminals.


*6.2. Support Vector Machine—Recursive Feature Elimination*

The support vector machine (SVM) originated in the work of Boser, Guyon, and Vapnik [58] and Cortes and Vapnik [59]. The general idea of an SVM is to create a decision boundary (hyperplane) that maximizes the margin between itself and the closest observations (=data points) of each of the classes [54]. The points that are closest to the boundary and, thus, are on the margin are called "support vectors" [60]. It is noteworthy that the input variables, denoted *x*, are often mapped into a higher-dimensional feature space using a (nonlinear) mapping that can be denoted as *φ*(). Following the notation in [59,61], the decision function *f* for a data set *x* can be defined as

$$f(\mathbf{x}) = w\phi(\mathbf{x}) + b \tag{1}$$

where *w* are the weights for the optimal hyperplane (decision surface) that separates the classes with the largest margin, *φ*() is a function that transforms the input, and *b* is the bias value. The bias is the average over the marginal support vectors and can be calculated using the weights *w* [60]. The weights *w* for the optimal hyperplane are calculated as

$$w = \sum\_{i} y\_i a\_i \phi(\mathbf{x}\_i) \tag{2}$$

where *xi* is a support vector, *αi* is the weight for the support vector *xi* , and *yi* is the class label *e*{−1, 1} corresponding to the support vector [59,60]. The weights of the support vectors *α* are the parameters of an SVM, which are optimized using convex optimization [60]. For details on the optimization problem behind an SVM, please see [56,61].

The weight vector *w* for the hyperplane will be used in recursive feature elimination to determine the ranking of features. Recursive feature elimination using a support vector machine (SVM-RFE) was introduced by Guyon et al. [60]. It deploys a greedy backward elimination procedure where in each step an SVM is trained and the variable with the lowest squared weight *w* 2 is removed from the set of the remaining variables [48,60,62,63]. Thus, *w* 2 can be regarded as a ranking criterion for the variables [60]. It is noteworthy that in each step one or more variables can be removed [48,60]. Thus, SVM-RFE is inherently different from random forests: the former starts with a complete variable set and iteratively removes one (or multiple) variable(s) whereas the latter functions by iteratively selecting variables. The algorithm for SVM-RFE is depicted in Algorithm 2 (similar to [48,60]).

The logic behind this procedure is that *w* 2 estimates the effect of each variable on the objective function (sensitivity) with larger values indicating more important variables so that the resulting variable subset leads to the best class separation with the SVM classifier [48,60]. The number of variables to retain can either be user-specified (and the number of variables to remove would, thus, be all variables minus the number of variables to retain) [62,63] or the algorithm can be run until a single variable is left and the optimal subset can be selected using cross-validation as the subset leading to the highest validation accuracy. For this study, the variables are standardized using the weighted mean and weighted standard deviation, and the optimal variable subset is determined using cross-validation.

**Algorithm 2** Support vector machine—recursive feature elimination (SVM-RFE)

For *m* = 1 to *M* (number of features to remove)

	- 2.1. Obtain the weights *α* of the support vectors from the trained SVM
		- 2.2. Calculate the weight vector *w* of the optimal hyperplane *w* = ∑ *i αiyiφ*(*xi*)

3. Remove the variable associated with the smallest *w* 2 from the set of the remaining features *s*

End


**3. Treatment techniques**

#### **3.1. Treatment simulation**

variations, such as tumor shrinkage and other anatomical changes, plan adaptation is often

The chapter aims at illustrating the rationale and process in adaptive proton treatment of lung cancers, as well as the strategies and practical considerations in plan adaptation, with a focus

Depending on how proton beams are spread out laterally and in depth, there are mainly three proton delivery systems in clinical use: passive scattering proton therapy (PSPT), uniform scanning proton therapy (USPT), and pencil beam scanning (PBS). In PSPT, the proton beam is spread out laterally by a static scatterer (or double scatterers) located in the beam axis, and the beam modulation in depth is typically achieved by using a rotating range modulation wheel, which is composed of multiple steps of various thicknesses. Both USPT and PBS proton therapy use scanning magnets to sweep proton beams laterally and deliver the dose to a target volume layer by layer at various depths using proton beams of various energies. The main dif‐ ference between USPT and PBS is that proton beams are scanned continuously with a uniform intensity in a zigzag pattern at a fixed frequency for each energy layer in USPT, while deliv‐ ered with various beam intensities from one spot to another or continuously for each layer in PBS. PBS can be further divided into single field uniform dose (SFUD) delivery, which deliv‐ ers a uniform dose to the target for each field, and multiple field uniform dose (MFUD), which delivers a heterogeneous dose to the target for each field but achieves a homogeneous com‐ bined dose from all fields. MFUD is also called intensity modulated proton therapy (IMPT).

Since our main focus for this chapter is USPT, a detailed description of a USPT system at our center is described below. The proton therapy center is equipped with an IBA Cyclotron (IBA, Louvain‐la‐Neuve, Belgium), which accelerates proton beams to approximately 230 MeV before they are extracted to treatment rooms through a beam transportation system. The proton beam passes through an energy degrader, which can lower the energy when necessary, and an energy selection system (ESS) is then transported to a nozzle in the treatment room. After entering the nozzle, the proton beam will first pass through a first scatterer, which broadens the beam laterally to achieve the desired spot size at isocenter. The beam then passes through a range modulator wheel, which does not rotate continuously for uniform scanning beam delivery and mainly serves as an energy degrader. Together with the first scatterer, the modulator wheel lowers the proton energy to deliver a peak dose layer by layer in depth. The beam is scanned laterally with a constant frequency by two scanning magnets in a zigzag pattern to deliver a uniform dose for a near rectangular scanning area. It then passes through the main and backup ionization chambers that monitor the proton dose. At the end of the nozzle is a snout that holds an aperture and a compensator and can translate along the beam axis to achieve variable snout to isocenter positions. An aperture is used to collimate the beam to the treatment target later‐ ally, and a range compensator is used to conform the proton penetration to the distal boundary of the treatment target. More details on this system were described by Zheng *et al.* [5]. **Figure 1** shows a schematic diagram of the uniform scanning nozzle at our proton therapy center.

needed in proton therapy of lung cancer.

**2. Proton therapy system**

46 Radiotherapy

on the use of uniform scanning proton beams.

Patient immobilization and simulation for lung cancer patients under proton therapy are similar to those under photon therapy. However, since proton beams are very sensitive to setup uncertainty and patient motion, the reproducibility of immobilization and proper motion management are critical in proton therapy. At our center, patients typically lie supine, are immobilized with a vacuum bag, which is on top of an index fixed framing device (wing board), and with their arms up and hands holding the pegs on the wing board, as shown in **Figure 2**. The patient is scanned at 2.5 mm slice thickness. If contrast is used, one computerized tomography (CT) scan should be taken before the contrast is injected in addition to one after the injection. The CT data with intravenous contrast will be used primarily for target delineation, and the CT data set without contrast will be used for dose calculation.

Four dimensional (4D) computerized tomography (CT) scanning is typically used for lung cancer patients in proton therapy to evaluate patient motion. The motion can be monitored by a belt system or a Varian RPM system during the 4D CT scan. The magnitude of tumor motion is typically evaluated for each 4D CT scan and used to determine the strategies in motion management. Depending on facility and beam delivery system, a limit of motion magnitude is set, beyond which the patient will need additional motion management or be excluded from proton treatment. For example, at our center, we generally treat patients using USPT with a maximum motion of 10–15 mm, while at the MD Anderson Proton Therapy Center, 5 mm maximum motion was used for patients under PBS proton treatment [6]. While respira‐ tory gating or breath holding could reduce the tumor motion, currently, it is only used clini‐ cally in a very few proton centers due to challenges such as relatively low proton dose rate that leads to long treatment time for gated treatment, lack of connection between the respira‐ tory device and the proton beam delivery machine, and difficulty of holding breath for lung cancer patients.

**Figure 2.** Typical CT simulation and immobilization technique for lung cancer treatment using uniform scanning proton therapy.

#### **3.2. Treatment planning**

Treatment planning can be performed on the average CT based on the 4D CT scan, or at a cer‐ tain respiratory phase when gating or breast holding is used. At our center, we use the average CT and an Internal target volume (ITV) approach to account for motion effect during treatment, which is similar to what used at MD Anderson Cancer Center for lung treatment using pas‐ sive scattering proton beams [7]. The internal gross target volume (IGTV) is contoured on the maximum intensity pixel (MIP) images and expanded 7–10 mm to generate the clinical target volume (CTV), which is expanded further by 5 mm to obtain the planning target volume (PTV). The average CT will be used for treatment planning and dose calculation. The magnitude of motion will be evaluated by a physicist, and the treatment of lung patient with uniform scan‐ ning proton beams is often limited to those who have a motion magnitude of 10 mm or less. To be conservative, a smearing of 10 mm is used in compensator calculation for all lung cancer treatment planning. To ensure adequate coverage of the target at the presence of tumor motion, the stopping power ratio of IGTV is overridden with the average stopping power ratio of the tumor tissue, which is about 1.01 based on sampling of over 10 lung patients treated at our cen‐ ter. Each patient is treated with uniform scanning proton beams typically using 2–4 fields. The prescription is typically 74 Cobalt Gray‐equivalent (CGE) at 2 CGE per fraction for 37 fractions.

#### **3.3. Dosimetric advantages**

Proton beams provide a superior dose distribution for lung cancer treatment compared to photon beams. Chang *et al.* reported that PSPT significantly reduced dose to normal tissues and the integral dose to patients with non‐small cell lung cancer (NSCLC) compared to three‐ dimensional conformal radiation therapy (3D‐CRT) and intensity modulated radiation ther‐ apy (IMRT) [2]. Kadoya *et al.* reported that using proton beam significantly reduced Lung dose compared to stereotactic body radiation therapy (SBRT) for Stage I non‐small‐cell lung cancer [8]. The mean dose, V5, V10, V15, and V20 were 4.6 Gy, 13.2%, 11.4%, 10.1%, and 9.1% for pro‐ ton therapy compared to 7.8 Gy, 32%, 21.8%, 15.3%, and 11.4%, respectively, for SBRT with a prescribed dose for 66 Gy. In a similar study, Hoppe *et al.* reported that in addition to better dose sparing to the lung, PSPT delivered less dose (D0.1cm 3 and D5cm 3 ) to the heart, esophagus and bronchus compared to SBRT [9]. For locally advanced Stage III NSCLC patients, Wu *et al.* found that proton beam therapy was feasible and superior to three‐dimensional conformal radiotherapy for several dosimetric parameters such as the mean dose for lung, heart, and spinal cord [3]. Using IMPT, doses to normal tissues, such as the lung, spinal cord, heart, and esophagus, can be further reduced compared to passive scattering proton therapy and IMRT for extensive Stage IIIB NSCLC, as reported by Zhang *et al.* [10]. The dosimetric advantage of IMPT would allow further dose escalation from 74 to 84.4 Gy while keeping normal tissue sparing at a lower or similar lever. IMPT proved also advantageous in terms of lung sparing compared to both Tomotherapy and IMRT in a study by Stuschke *et al.* [11]. A brief summary of literature on plan comparison between proton and photon therapy discussed here is listed in **Table 1**.

When uniform scanning proton therapy is used, similar normal tissue sparing to passive scat‐ tering proton therapy can be achieved. **Figure 3** shows the dose comparison of USPT versus IMRT for a lung case. The patient was a 72‐year‐old female with severe chronic obstructive pulmonary disease (COPD) and Stage IIIA (cT1aN2MpG2) squamous cell carcinoma of the right upper lung.

Abbreviations: MDACC: M. D. Anderson Cancer Center; STPTC: Southern Tohoku Proton Therapy Center; UFTPI: University of Florida Proton Therapy Institute; NCCHE: National Cancer Center Hospital East; UHE: University Hospital Essen. Others see above.

Note: Reports from the literature.

**3.2. Treatment planning**

therapy.

48 Radiotherapy

**3.3. Dosimetric advantages**

Treatment planning can be performed on the average CT based on the 4D CT scan, or at a cer‐ tain respiratory phase when gating or breast holding is used. At our center, we use the average CT and an Internal target volume (ITV) approach to account for motion effect during treatment, which is similar to what used at MD Anderson Cancer Center for lung treatment using pas‐ sive scattering proton beams [7]. The internal gross target volume (IGTV) is contoured on the maximum intensity pixel (MIP) images and expanded 7–10 mm to generate the clinical target volume (CTV), which is expanded further by 5 mm to obtain the planning target volume (PTV). The average CT will be used for treatment planning and dose calculation. The magnitude of motion will be evaluated by a physicist, and the treatment of lung patient with uniform scan‐ ning proton beams is often limited to those who have a motion magnitude of 10 mm or less. To be conservative, a smearing of 10 mm is used in compensator calculation for all lung cancer treatment planning. To ensure adequate coverage of the target at the presence of tumor motion, the stopping power ratio of IGTV is overridden with the average stopping power ratio of the tumor tissue, which is about 1.01 based on sampling of over 10 lung patients treated at our cen‐ ter. Each patient is treated with uniform scanning proton beams typically using 2–4 fields. The prescription is typically 74 Cobalt Gray‐equivalent (CGE) at 2 CGE per fraction for 37 fractions.

**Figure 2.** Typical CT simulation and immobilization technique for lung cancer treatment using uniform scanning proton

Proton beams provide a superior dose distribution for lung cancer treatment compared to photon beams. Chang *et al.* reported that PSPT significantly reduced dose to normal tissues

**Table 1.** Comparison studies between proton and photon therapy for NSCLC patients.

**Figure 3.** Dose comparison of Uniform Scanning proton plan and IMRT plan. (a) Proton plan, (b) IMRT plan, and (c) DVH comparison (solid line—proton, dashed line—IMRT). The prescribed dose was 74 cobalt gray equivalent (CGE) at 2 CGE per fraction for 37 fractions.


**Compilers Are Highly Optimized; DSL Code Generators Just Do Their Work** For GPLs, compilers are highly optimized to particular needs, for example, runtime performance. In contrast, models are processed by code generators or interpreters (cf. Sect. 2.2). Both are generally not highly optimized. Hence, for particular types of software systems, for example, high-performance algorithms, a MBSE approach fails if it does not make use of sophisticated adaptation mechanisms. Such mechanisms allow to adapt either the code generator, interpreter, or the generated source code to perform optimization tasks or handle underspecification. However, even if adaption is possible, the adaption process may still be more expensive (in terms of, e.g., development time, maintainability, etc.) than writing efficient code from scratch.

**Project Setting Has to Fit MBSE** A typical reason for MBSE project failure is rooted in the nature of the project itself. MBSE software projects are highly effective for software projects with repetitive and similar tasks. For example, imagine a software project that defines a REST interface for a particular domain model. In this project, the technology stack and the definition of a REST interface are clearly similar. Hence, suitable code generators can speed up development time by generating the REST interface from the domain model. However, for software projects without or with only little repetitive tasks—where every part of the source code is very individual—MBSE fails because it demands a code generator and a suitable DSL for each particular concern.

**Model Tooling Is Not That Elaborated as for Programming (IDEs)** The lack of tooling for model and code generator creation is a major challenge of MBSE. Even though there are language workbenches (cf. [15, 36]) that support generation or manual implementation of integrated development environments (IDEs) with syntax highlighting and auto completion, the resulting tools are not as supportive as well-established IDEs for GPLs. Furthermore, the tool support has to be maintained whenever the DSL evolves. A similar situation is also present in the development of code generators, where suitable adaptation concerns have to be addressed by additional infrastructures (cf. [21]).

**MBSE and Agility Do Not Yet Work Well Together** Agile software development has shown its effectiveness as a method to tackle complexity and ambiguity of software projects and to reduce the time to deliver software products. However, MBSE and agile software development methods are still not yet coalesced and demand for a combination of plan-driven and agile methods (cf. [27]). More importantly, the crucial role of model quality and tooling for creating, managing, and refactoring models is not yet resolved (cf. [8, 26]).

From the aforementioned pitfalls and failures of MBSE and from current research, the main questions to be answered are: *What kind of software systems can effectively be supported by MBSE? What needs to be improved to make MBSE suitable?* Clearly, software language engineering and code generator engineering needs to improve. This also holds for tooling supporting language reuse and composition as well as code generator and interpreter composition and creation. Hence, in the following, we present success stories of MBSE as well as the use cases' motivations and achievements with respect to MBSE. These examples are helpful to understand when MBSE is appropriate and why it is successful.

## **4 Where Model-Based Software Engineering Is Successful**

Example domains where MBSE has proven successful are cyber-physical systems (CPS) [2] and component-based software engineering (CBSE) [38]. In these contexts, MBSE has been adopted by means of architecture description languages (ADLs) [35]. ADLs are special modeling languages providing syntax to describe the structure of a system under development. Academia and industry produced over 120 ADLs [29] in context of different domains such as automotive [13], avionics [16], consumer electronics [53], or robotics [46]. In context of ADLs, code generators take models describing the structure of a system under development as input and produce a runtime infrastructure for executing the system. Such models typically abstract away component implementation details and focus on the system's structure, that is, the system's components and their interconnections. The implementation of each individual component thus typically has to be implemented by hand. Some ADLs additionally enable to describe component behavior implementations. Where this possibility is available, it is even possible to generate complete software systems. Examples for graphical and textual CBSE-related DSLs are integrated into the AutoFocus [3], MontiArc [6], and Simulink [47] frameworks.

Other example domains successfully employing MBSE that use model interpretation are the domains of software build automation and web development. Makefiles, for example, are executed by command line interpreters. Web browsers interpret HTML models as text layout definitions and interpret JavaScript programs, for instance, to execute a reaction in response to user interaction events.

The neuroscience domain has successfully produced the NestML, which is a DSL used by neuroscientists for creating neuron models in a precise and concrete syntax familiar to domain experts [40]. A code generator translates NestML models into C++ code that can be dynamically loaded into NEST [20], a simulator for networks of spiking point neurons. Before integrating NestML, domain experts created new neuron models for NEST by copy-and-paste from existing models. As neuroscientists are no programming experts, source code redundancy, suboptimal performance, improper documentation, and reduced maintainability are the consequences [40]. Investigations revealed cases where two different copy-and-paste models shared more than 90% of their contents [40]. The modeling language and its tools were well received by domain experts [40]. An evaluation revealing the increase in code reuse, performance, and documentation as well as the decrease in redundancy is currently not available.

MBSE has also been successfully applied in context of a customs information system to describe document verification rules and configuration files [18]. Such verification rules describe constraints that relate different fields of XML documents. A compiler translates verification rule models to Java byte code. A requirement on the verification rule DSL was that its models should be similar to rules expressed in natural language [18]. This indicates that verification rules are modeled by nontechnical users.

Another case study reports on successful application of MBSE in context of service robotics applications [1]. The goal is to achieve separation of concerns and to ease development of complex service robotics applications by applying models and code generators. Domain experts model the environment a robot operates in, robot and world abilities, as well as tasks and goals for the robot to achieve. The goal is to enable nontechnical domain experts to model the context of a service robotics application. From such models, generators produce scenariospecific source code. Robotics experts then complement the generated code with handcrafted implementations for the world and robot abilities at well-defined places. Thus, models capture the requirements of a particular instance in the service robotics domain (robot environment, robot/world abilities), and robotics experts complement the application with their robotics domain expertise. This ultimately reduces the costs for developing service robotics applications and enables separation of concerns.

JavaSM is a DSL that integrates state machines into Java to develop a commandand-control simulator [4]. The case study also relies on CBSE and product line architecture methodologies. The DSL is used for defining and refining state machines that specify component behavior. State machine-based implementations are frequently used in this case study. The motivation for developing the JavaSM is that state machine encodings in pure Java are extremely complex and thus hard to maintain and understand [4]. The achievement is a complexity reduction of component specifications: The case study's result is a more flexible way of implementing state machine-based simulators than is possible with pure Java implementations [4]. Hence, the case study is an example of where a DSL eases software development in a particular use case and hence increases productivity of developers.

Risla is a DSL for describing products developed in the financial engineering domain [52]. Financial engineering experts use Risla to model new products. The case study's motivation is to decrease the time needed for introducing new types of products and to ensure newly developed products are correctly implemented as intended [52]. The complexity of introducing a new product seems to be based on the case study's underlying software system, which is implemented in COBOL. The second motivation arises since it is only hardly, if even, possible to ensure a software engineer correctly implements the instructions given by a financial engineer. The goal is to employ models and code generators such that (1) new products can be added easily and (2) potential information loss during communication of domain experts and software engineers is avoided. This ultimately leads to a lower time to market for new products and eliminates a source for introducing incorrect behavior.

Other examples for well-known successful DSLs commonly used in (computer) science domains include, among many others, SQL for specifying database queries, LATEXfor writing documents, and MATLAB [33] for numerical computing and embedded systems. Other domains where DSLs have been used include artificial intelligence [34], graphics [14], model checking [23], operating systems [41], various protocols [7, 49], and video device drivers [50]. Most of these DSLs target at increasing productivity of software developers and ensuring program correctness.

## **5 Can We Draw Conclusions?**

While MBSE has its drawbacks and failures, it still keeps its promises in some domains and software projects. In particular, summarizing the reasons for successful MBSE, we obtain the following indicators:

4. If a system is grounded on a well-defined theory such as physics, chemistry, or biology, then scientists developing concrete models of their system under examination prefer to use models with syntax similar to the underlying mathematical theory. Such models are preferably used for simulation of real-world phenomena such as galaxies, climate, brain, chemical molecules, or physical particles.

In reverse conclusion, the overhead for initializing MBSE development processes often does not pay off compared to the benefits obtained from reusing models and generators in a modular way. This is the case, for instance, if a developing company is ensure whether an enhanced variant of an already existing software product needs to be delivered in a future project. This is often the case in purely software-based systems as, for example, enterprise information systems and software developed in web domains.

However, the use of models has still not yet been explored in all potentially possible domains. There are promising examples, such as nontechnical users writing Excel formulas without explicitly noticing they are actually programming. Supporting end users to program in a restricted and controlled fashion could be supported by appropriate modeling languages.

Like many other new and innovative technologies, MBSE has promised a lot and has not kept all of its promises. Fortunately, a lot of ideas and techniques from MBSE can be used for implicit modeling using GPLs. The encoding of state machines using the state design pattern [19] is such an example.

## **References**

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*3.1. Characterization of Synthesized Magnetite MNPs*

The X-ray powder diffraction patterns of the synthesized bare and PEG-coated MNPs are presented in Figure 3A,B, respectively. Characteristic peaks exhibited in the XRPD pattern are well-matched with the magnetite diffraction peaks and confirm the cubic inverse spinel structure of MNPs. The sharp diffraction of three characteristic peaks (220), (311) and (400) also indicate the spinel structure of magnetite [42]. The formation of pure cubic magnetite is confirmed by the value of the calculated lattice parameter "*a*" which has been determined to be 8.389 Å [43]. Using Scherrer's equation, the average crystallite size of bare and PEG-coated MNPs were calculated to be 25 nm and 19 nm, respectively. In addition, the decreased average crystallite size, another piece of evidence suggesting that PEG decreases the crystallinity of MNPs at a lower intensity and with broader diffraction peaks than PEG-coated MNPs.

The size and morphology of bare and PEG-coated mesoporous MNPs were observed by field-emission scanning electron microscope (FE-SEM), atomic force microscopy (AFM) and transmission electron microscopy (TEM), as shown in Figure 3A,B,G–J,K–L). Both bare and PEG-coated MNPs maintain a uniform spherical shape, some of them agglomerated due to magneto–dipole interactions between MNPs. While bare MNPs showed cluster structure with a very rough surface, the process of PEG coating revealed the flattened surface of mesoporous MNPs (Figure 3I,J). These findings have been confirmed by AFM imaging where the roughness of the MNPs surface has been increased by PEG coating, for almost 100%, from 5.58 ± 1.06 nm to 10.9 ± 2.1 nm, confirming the effective coverage of the bare MNPs by PEG [43]. The less agglomerated texture of the PEG-coated MNPs can be related to the effect of the PEG layer during the synthesis of MNPs. In addition, a size histogram of bare mesoporous MNPs obtained using SEM micrographs shows a broader size distribution than PEG-coated MNPs (*d*ave = 103.4 ± 0.7 nm and 101.0 ± 0.9 nm for bare and PEG-coated MNPs, respectively), indicating that polymer decreased the magnetic interaction among the particles and prevent their agglomeration. The cluster structure of mesoporous MNPs has been confirmed using AFM. The average size of bare MNPs and PEG-coated MNPs corresponds to results obtained by SEM, it was even 10% larger due to the convolution effect. However, in both 2D height images, it is shown that the cluster structure MNPs consists of smaller substructures, in the range of 15 to 35 nm, which roughly correspond to the dimension of the crystallite size obtained by X-ray powder diffraction. Hence, AFM revealed that only several nanometers increase in roughness is observed when PEG 4 kD is used, suggesting that the PEG layer is largely twisted the

magnetite surface, rather than stretch out linearly [44]. Furthermore, this PEG layer should decrease the magnetic interactions among the MNPs and prevents their agglomeration. The mean diameter of bare MNPs obtained by TEM is larger (143 ± 30 nm) than obtained by SEM (103.4 ± 0.7 nm), indicating a higher degree of polydispersity. However, the mean diameter of PEG-coated MNPs (96 ± 10 nm) corresponds the value obtained by SEM (101.0 ± 0.9 nm). Increasing the size of the PEG-coated MNPs can be attributed to the successful coating of PEG. As shown in Figure 3K,L, both MNPs maintain a typical spherical shape.

Nitrogen adsorption–desorption isotherms of bare MNPs confirmed their mesoporosity (see Figure 4). The surface area, pore size and total pore volume were calculated to be 20.5 m2g−1, 17.7 nm and 0. 09 cm3 g−1, respectively, strongly supporting the fact that the bare MNPs have mesoporous structure. The PEG coating of bare MNPs led to a slight decrease in surface area (19.3 m2 g−1) but an increase in pore size and total pore volume (24.6 nm1 and 0.11 cm3 g−1, respectively).

FTIR spectrum (Figure 5A) of bare magnetite MNPs shows bands at 585 and 395 cm−1 corresponding to the symmetric stretching vibration mode of the Fe-O bond. The absorption maxima at 3452 cm−1 and 1644 cm−1 suggest the presence of O-H linkages. In the pure PEG, the bands at 1341 and 1100 cm−1 belong to the C-O-C ether bond asymmetric and symmetric stretching vibrations. The band at 2890 cm−1 is attributed to -CH2- stretching vibration in PEG. In addition, absorption bands at 1283 and 1465 cm−1 attributed to the vibration of–CH2 and at 964 cm−1 corresponds to the CH out-of-plane vibration [18]. The hydroxyl groups were also confirmed at 3444 and 1631 cm−1. The presence of characteristic FTIR bands of PEG in PEG-coated MNPs spectrum confirmed the successful coating of PEG on the surface of magnetite MNPs. The PEG-coated MNPs spectrum shows a strong C-O-C ether stretch at 1110 and 1381 cm−1 [44]. In addition, the O-H linkages at the 1642 and 3445 cm−1 bands exhibited enhanced intensity which also indicates that PEG modified the surface of MNPs. The transmittance bands at 589 and 399 cm−1 confirm the symmetric stretching mode of the Fe-O bond. The results indicate that PEG is successfully functionalizing the surface of MNPs.

In order to confirm the superparamagnetic properties of synthesized bare and PEGcoated MNPs, measurements of the magnetization curve have been performed. The S-shaped hysteresis loops are a typical feature of superparamagnetic MNPs and obtained result is very similar to our previous work (77 emu g−1) on Fe3O4 MNPs [35]. The magnetization curve clearly shows that magnetization depends on the applied magnetic field, but not on the sign of the applied field. Magnetic characterization at 300 K indicates that the bare MNPs have saturation magnetization at the maximum field of 5 kOe value of 76.71 emu g−1, which is lower than obtained value for the bulk Fe3O4 (*M*s = 92 emu g−1) [42] or *M*s = 96.43 emu g−1 [19].

The observed decrease in the saturation magnetization could be explained either by the use of PEG for the surface modification process [43] that causes the softening of the magnetization or by the difference in particle size [45]. In addition, the saturation magnetization of PEG-coated MNPs at the maximum field of 5 kOe is 74.75 emu g−1, somewhat lower than bare MNPs (Figure 5B). However, the magnetization measurement of synthesized MNPs confirmed their superparamagnetic properties, thus confirming their further application in release studies under applied magnetic fields.


**1.1 Robust beamforming overview**

Beamforming is a ubiquitous task in array signal processing with applications, among others, in radar, sonar, acoustics, astronomy, seismology, communications, and medical imaging. Without loss of generality, we consider herein beamforming in array processing applications. The introduction to beamforming can be found in [1]-[9] and the references herein.

The traditional approach to the design of adaptive beamformers assumes that the desired signal components are not present in training data, and the robustness of beamformer is known to depend essentially on the availability of signal-free training data. However, in many important applications such as mobile communications, passive location, microphone array speech processing, medical imaging, and radio astronomy, the signal-free training data cells are unavailable. In such scenarios, the desired signal is always present in the training snapshots, and the adaptive beamforming methods become very sensitive to any violation of underlying assumptions on the environment, sources, or sensor array. In fact, the performances of the existing adaptive array algorithms are known to degrade substantially in the presence of even slight mismatches between the actual and presumed array responses to the desired signal [10]-[12]. Similar types of degradation can take place when the array response is known precisely but the training sample size is small, namely the mismatch between the actual and the estimated covariance matrix [13]-[15]. Therefore, robust approaches to adaptive beamforming appear to be of primary importance in these cases [16][17].

Many approaches have been proposed to improve the robustness of the adaptive beamformer during the past three decades. Indeed, the literatures on the robust adaptive beamformer are quite extensive. We provide a brief review as fellows. For more recent detailed critical reviews, see [18] and [19]-[25].

## **1.1.1 Robust approaches for signal direction mismatch**

For the specific case of the signal direction mismatch, there are several efficient methods have been developed. Representative examples of such techniques are the linearly constrained minimum variance (LCMV) beamformer [26], which is also denoted as the linearly constrained minimum power (LCMP) beamformer in other references [27] and this chapter, signal blocking-based algorithms [10][28], and Bayesian beamformer [29]. Although

Robust Beamforming and DOA Estimation 89

method to compute the optimal weight vector, and the second-order cone (SOC) programming-based approach is used to solve the original problem. Ayman Elnashar et al make use of the diagonal loading technique to implement the robust beamformer [24], but the optimal value of diagonal loading level is not solved exactly, alternatively, the diagonal loading technique is integrated into the adaptive update schemes by means of optimum variable loading technique. R. G. Lorenz and S. P. Boyd also solve the similar beamformer by the Lagrange multiplier techniques [23], but they express the weight vector and the array manifold as the direct sum of the corresponding real and imaginary components. Almir Mutapcic et al show that worst-case robust beamforming with multiplicative uncertainty in the weights can be cast as a tractable convex optimization problem [37], but they can't give the solving method, In fact, the proposed robust beamformer with uncertain weights can be

S. Shahbazpanahi et al consider the general-rank signal model, and the robust beamformer is proposed for the distributed sources [21], therein, an elegant closed-form solution is given, but its performance improvement depends on the constraint parameter severely, and

Jian Li et al propose a Capon beamforming approach with the norm inequality constraint (NIC) to improve the robustness against array steering vector errors and noise [22], although the exact solution is given, and optimal loading level can be computed via the proposed method, but by analysis and simulation, its efficiency is not as good as expectation. Since the constraint parameter determines its robustness, but how to select the constraint parameter is

Quadratic inequality constraints (QIC) on the weight vector of LCMP beamformer can improve robustness to pointing errors and random perturbations in sensor parameter [27]. The weights that minimize the output power subject to linear constraints and an inequality constraint on the norm of the weight vector have the same form as that of the optimum LCMP beamformer with diagonal loading of the data covariance matrix. But the optimal loading level cannot be directly expressed as a function of the constraint in a closed form, and cannot be solved exactly. Hence, its application is restricted by the optimal weight vector finding. So that some numerically algorithms are proposed to implement the QICLCMP, such as Least Mean Squares (LMS) or Recursive Least Squares (RLS) [27], but the

This chapter is organized as follows [38]. First, the norm inequality constraint Capon beamformer (NICCB) is introduced and analyzed particularly. Second, the choice of the norm constraint parameter and the selecting bound is discussed. Third, the norm equality constraint Capon beamformer (NECCB) is proposed and is solved effectively. Finally, the

The Capon beamformer can experience significant performance degradation when there is a mismatch between the presumed and actual characteristics of the source or array. The goal of NICCB is to impose an additional inequality constraint on the Euclidean norm of **w** for

**1.1.4 Weight norm constraint approaches for general mismatch**

converted to that in [19] equivalently.

application effect isn't good as the expectation.

simulation analyses and the conclusion are given.

**1.2 Capon beamformer under norm inequality constraint (NICCB)**

is not up to optimal.

not discussed.

all these methods provide excellent robustness against the signal direction mismatch, they are not robust against other types of mismatches caused by poor array calibration, unknown sensor mutual coupling, near-far wavefront mismodeling, signal wavefront distortions, source spreading, and coherent/incoherent local scattering, as well as other effects [17].

Chun-Yang Chen and P.P.Vaidyanathan consider a simplified uncertainty set which contains only the steering vectors with a desired uncertainty range of direction of arrival (DOA) [25], although the closed-form solution is given, and the diagonal loading level can be computed by the iteration method systematically, but how to determine the DOA uncertainty range is the critical problem.


*4.5.1. Camptodactyly*

Camptodactyly is the irreversible flexion of one or both interphalangeal joints at the level of one or more fingers, being most frequently a congenital condition.

Considering the presence of this sign in multiple chromosomal anomalies, some authors con-

The Neonate with Minor Dysmorphisms http://dx.doi.org/10.5772/intechopen.71902 523

Usually, the treatment is not necessary. If necessary - because of emotional stress due to esthetic reasons or the impairment of the fine hand movements - the treatment is surgical [69]. For surgery, preoperative radiographs of the pollex are performed, establishing the size of the graft and the degree of angulation necessary to restore the normal function of the distal phalange.

It is one of the most common congenital abnormalities of upper limbs, seen in all ethnicities, and it refers to the presence of additional fingers, being usually bilateral [70]. Most often, polydactyly affects the upper and lower limbs synchronously. Supernumerary fingers do not

The classification of this condition is based on the location of the additional fingers, the poly-

Polydactyly may appear isolated, de novo, sometimes autosomal dominant inherited or may be associated with syndromes [73, 74] such as Bardet-Biedl Syndrome, Carpenter Syndrome, Elis-Van Creveld Syndrome, Fanconi Syndrome, Greig Syndrome, Holt-Oram Syndrome, Meckel-Gruber

sider it a "soft sign", if detected in an antenatal ultrasound scan.

If the clinodactyly is isolated, it has an excellent prognosis.

usually have adequate muscle connections [71, 72].

• Mesoaxial/central (duplication of fingers II, III, IV),

*4.5.3. Polydactyly*

dactyly being:

• Mixed.

• Postaxial (duplicated finger V),

**Figure 11.** Clinodactily of the fifth finger.

• Preaxial (duplicated thumb),

It can be diagnosed antenatally [63–65] "in utero" or postnatally, being a clinically obvious deformity, which subsequently requires imaging investigations. An abnormal insertion of lumbrical and flexor digitorum tendons of the hand is often noted.

Camptodactyly may occur sporadically, de novo or by autosomal dominant inheritance.

It may be an isolated clinical manifestation or clinical expression in syndromes such as Trisomy 18 and 13, Freeman Sheldon Syndrome, Pena Shokeir Syndrome, CACP Syndrome (Camptodactyly, Arthropathy, Coxa vara, Pericarditis), arthrogryposis [63, 65–67].

#### *4.5.2. Clinodactyly*

Clinodactyly is a congenital malformation consisting of the lateral deflection of the fingers by affecting the first interphalangeal joint, which interests any finger, especially the pollex and the auricular fingers (the fifth finger), (**Figure 11**).

Clinodactyly is a descriptive term, which refers to a radial angulation at a common interphalangeal joint in radio-ulnar or palmar planes, and can often be a normal anatomical variant.

The incidence varies, ranging between 1 and 18%, as it is most frequently under-reported.

Clinodactyly may be a very common isolated clinical manifestation in the context of a family history [68] - with autosomal recessive inheritance, but it may also occur in several syndromes, in association with other locomotor abnormalities or in other organs and systems.

Clinodactyly is seen in over 60% of children with Down syndrome [63], Klinefelter syndrome, trisomy 18, Turner syndrome, Cornelia de Lange Syndrome, Feingold Syndrome, Roberts Syndrome, Russell-Silver Syndrome or Fanconi Syndrome. It may also be a clinical manifestation associated with other abnormalities such as macrodystrophia lipomatosa and brachydactyly type A3.

**Figure 11.** Clinodactily of the fifth finger.

Considering the presence of this sign in multiple chromosomal anomalies, some authors consider it a "soft sign", if detected in an antenatal ultrasound scan.

If the clinodactyly is isolated, it has an excellent prognosis.

Usually, the treatment is not necessary. If necessary - because of emotional stress due to esthetic reasons or the impairment of the fine hand movements - the treatment is surgical [69]. For surgery, preoperative radiographs of the pollex are performed, establishing the size of the graft and the degree of angulation necessary to restore the normal function of the distal phalange.

### *4.5.3.  The number of nevi is influenced both genetically - the family history is very important - and from the sun exposure

Congenital pigmentary nevi over 20 cm in diameter have an increased risk of malignancy.

The management of pigmentary nevi depends on the type of nevus and the degree of uncertainty of the diagnosis. Benign ones require nothing else than monitoring after the neonatal period [60, 61], while those with special characteristics - asymmetry, uneven, irregular margins, color variations, diameter > 6 mm - very rare cases, require biopsy with histopathology,

Camptodactyly is the irreversible flexion of one or both interphalangeal joints at the level of

It can be diagnosed antenatally [63–65] "in utero" or postnatally, being a clinically obvious deformity, which subsequently requires imaging investigations. An abnormal insertion of

It may be an isolated clinical manifestation or clinical expression in syndromes such as Trisomy 18 and 13, Freeman Sheldon Syndrome, Pena Shokeir Syndrome, CACP Syndrome (Camptodactyly,

Clinodactyly is a congenital malformation consisting of the lateral deflection of the fingers by affecting the first interphalangeal joint, which interests any finger, especially the pollex and

Clinodactyly is a descriptive term, which refers to a radial angulation at a common interphalangeal joint in radio-ulnar or palmar planes, and can often be a normal anatomical variant. The incidence varies, ranging between 1 and 18%, as it is most frequently under-reported.

Clinodactyly may be a very common isolated clinical manifestation in the context of a family history [68] - with autosomal recessive inheritance, but it may also occur in several syndromes,

Clinodactyly is seen in over 60% of children with Down syndrome [63], Klinefelter syndrome, trisomy 18, Turner syndrome, Cornelia de Lange Syndrome, Feingold Syndrome, Roberts Syndrome, Russell-Silver Syndrome or Fanconi Syndrome. It may also be a clinical manifestation associated with other abnormalities such as macrodystrophia lipomatosa and brachydactyly type A3.

in association with other locomotor abnormalities or in other organs and systems.

Camptodactyly may occur sporadically, de novo or by autosomal dominant inheritance.

Pigmentary nevi are commonly diagnosed clinically or using the dermatoscope.

immunohistochemistry and electron microscopy [57, 62].

one or more fingers, being most frequently a congenital condition.

lumbrical and flexor digitorum tendons of the hand is often noted.

Arthropathy, Coxa vara, Pericarditis), arthrogryposis [63, 65–67].

the auricular fingers (the fifth finger), (**Figure 11**).

of the infant [59].

522 Congenital Anomalies - From the Embryo to the Neonate

**4.5. Minor hand anomalies**

*4.5.1. Camptodactyly*

*4.5.2. Clinodactyly*

It is one of the most common congenital abnormalities of upper limbs, seen in all ethnicities, and it refers to the presence of additional fingers, being usually bilateral [70]. Most often, polydactyly affects the upper and lower limbs synchronously. Supernumerary fingers do not usually have adequate muscle connections [71, 72].

The classification of this condition is based on the location of the additional fingers, the polydactyly being:

Polydactyly may appear isolated, de novo, sometimes autosomal dominant inherited or may be associated with syndromes [73, 74] such as Bardet-Biedl Syndrome, Carpenter Syndrome, Elis-Van Creveld Syndrome, Fanconi Syndrome, Greig Syndrome, Holt-Oram Syndrome, Meckel-Gruber Syndrome, Pallister-Hall Syndrome, Smith-Lemil-Opitz Syndrome, Trisomy 13, Trisomy 18, Short Rib Polydactyly Syndrome Type I (Saldino-Noonan Type) (Majewski type), Trisomy 21, Townes-Brocks Syndrome.

*4.6.2. Dysplastic nails*

palpebral fissures.

(**Figures 12** and **13**).

**Figure 12.** Phalanx anomalies.

tyly, macrostomia, macroglossia.

formation, agenesis of corpus callosum.

*4.6.3. Phalanx anomalies: digital deformities*

tions such as:

Insufficient development of nails [82] may occur in isolation or in many genetic malforma-

The Neonate with Minor Dysmorphisms http://dx.doi.org/10.5772/intechopen.71902 525

• Simpson-Golabi-Behmel Syndrome (Bulldog Syndrome). The most common etiology of this syndrome is the mutations in the GPC3 gene to chromosome X [83]. Nail hypoplasia is accompanied by other clinical manifestations such as macrosomia, hypertelorism, polydac-

• Fetal Alcohol Syndrome [84]. Prenatal exposure to alcohol causes numerous fetal malformations, including nail dysplasia accompanied by: microcephaly, facial hirsutism, short

• Fryns Syndrome. This syndrome is a genetic disorder inherited in an autosomal recessive manner, in which dysplastic nails occur along with other minor and major malformations such as diaphragmatic hernia, hirsutism, distal phalangeal hypoplasia, Dandy-Walker mal-

The small bones and soft tissues of the feet can be affected by systemic disorders, and frequently, the findings are quite unique and virtually help diagnose some genetic or metabolic disorders [85]. Sometimes the changes in the structural bones of the feet, metacarpals and metatarsals, or the phalangeal units are so astonishing that they ensure the diagnosis of peculiar and rare syndromes. There are many disorders – some genetic, some neoplastic, some inflammatory – which sometimes produce extraordinary changes in the patient's feet. In some cases, phalanx abnormalities occur as a result of the sucking of the finger by the fetus, causing elongation and hypertrophy

Usually, polydactyly is diagnosed antenatally, but if it is postnatally discovered, it requires paraclinical investigations in order to be included in one of the genetic syndromes, except for cases of family history. The investigations are performed using imaging techniques (MRI, CT scan, ultrasound examination), followed by genetic consultation in case of association with other malformations. The most commonly associated malformations are syndactyly, hypoplasia or aplasia of long bones, hydrocephalus, microcephaly, spina bifida, ventricular septal defect, atrial septal defect, esophageal atresia, duodenal atresia, anal imperfection, abdominal wall defects, renal agenesis, polycystic kidney disease, hydronephrosis, diaphragmatic hernia, anophthalmia, cheilopalatoschisis.

In the case of isolated polydactyly, no treatment is required. If this anomaly affects the mobility and gross/fine movements of the fingers/hands, the treatment is always surgical.


**2. Monitoring and induction of general anesthesia**

Timing to get the patient ready to receive the new organ is crucial because the ischemia of the donor heart should be as short as possible to avoid the ischemia-reperfusion injury.

besylate (0.15–0.2 mg/kg for induction and 1–2 mcg/kg/min for continuous iv infusion during surgery) is a good alternative since it is metabolized by ester hydrolysis and Hofmann reaction, so the duration of block is not affected by renal or hepatic function. During induction of general anesthesia, severe hypotension can occur, so that a fluid iv bolus ad availability of rapid onset vasoconstrictors as metaraminol, phenylephrine, noradrenaline should be ensured. Cardioplegia is not administered in the recipient during heart transplantation, so that the risk of related hemodilution is less than routine cardiac surgery. On pump, sevoflurane or iv 2% propofol infusion (4 mg/kg/h) are the options for maintenance of general anesthesia. Monitoring the depth of anesthesia with bispectral index (BIS) should be routinely adopted in order to decrease the risk of awareness. Once having put the patient asleep, central lines must be placed (queen central venous pressure [CVP] line and 8 Fr line for the pulmonary artery catheter [PAC]). The ideal site for puncture (blind or ultrasound-guided) is the left internal jugular vein (IJV), since the right one can be reserved for eventual postoperative biopsy (necessary to evaluate the level of graft rejection). When this is not possible (presence of ICD on the left side), we can adopt the right subclavian vein. Sometimes, when the preoperative renal function is really compromised, we can already place into the femoral or subclavian vein a catheter for continuous renal filtration afterwards. The PA catheter is flown through the 8 Fr line up to the right atrium, and then, once the new heart is placed, it will be advanced by the cardiac surgeon up to the superior right pulmonary artery. Vigilance calibration will be done

Anesthesia and Intensive Care Management for Cardiac Transplantation

http://dx.doi.org/10.5772/intechopen.79837

137

If the graft is not carried out into the organ care system (OCS), the ischemic time is crucial and the risk of ischemic/reperfusion injury is proportionally high, with possible dramatic increase of blood lactate levels and decrease of the graft global function. This is the reason why we must ensure adequate glycemia control, urine output, and, in general, an optimal tissue

means to keep MAPs about 60–80 mmHg and Hb levels at least about 8–9 mg/dL. When the aorta is unclamped, VF can occur (50% of patients). A shock delivery (10–30 J) followed by lidocaine bolus (when VF is refractory to electrical therapy) will take to resolution of the arrhythmia and return to sinus rhythm. In case of sinus bradycardia, temporary epicardial pacing will ensure adequate heart rate (100–110 bpm). Due to limited muscular mass, the ability of the right ventricle (RV) to increase contractility is limited and a temporary pacing at about 110 bpm will increase RV output and will overpace possible arrhythmias. Surgeons will also place a left atrial catheter for continuous measurement of the left atrial pressure (LAP) as an indicator of the left ventricle performance and stiffness. This value, together with CVP, PAPs, MAPs, and SvO2, will influence the posttransplantation hemodynamic management. Throughout this period, it will be mandatory to ensure adequate MAPs and diastolic pressure to allow adequate coronary perfusion, while maintaining medium-low preload pressures (CVP < 12 mmHg, LAP/PCWP < 12 mmHg). The biventricular assessment with transesopha-

), which

perfusion during CPB. This means to guarantee an adequate oxygen delivery (DO2

Pharmacological tools for CPB weaning will include the following [**Tables 3** and **4**]:

immediately before weaning from the CPB.

geal echocardiography should be done simultaneously.

**3. CPB and weaning**

Everyone in the theater should wear sterile surgical gown, hat, mask, and sterile gloves for any procedure on the patient especially because he will go under immune deficiency. Once the patient is in the theater, he will be connected to multiparametric monitor, with the 12 lead ECG and oximetry probe. Two peripheral venous lines are placed (generally 18G for iv sedation and 14G for rapid fluid infusion), and an arterial catheter, generally 20G, is placed into the radial or humeral artery. When the patient is very unstable, an arterial catheter is placed in the left femoral artery, to estimate central to peripheral arterial pressure gradients. Placement of an arterial line can be very difficult in patients with previous implantation of LVADs as bridge to transplant, due to the absence of arterial pulse. In such situations, ultrasound guidance can be very helpful (see **Table 2**).

Induction of general anesthesia usually starts just with the final acceptance of the donor organ. Drugs used for general anesthesia should impact the less possible on hemodynamics. A rapid sequence induction is preferred since recipients are always very stressed and sometimes not present with an empty stomach [6].

Midazolam (10–15 mg) or etomidate (20 mg) are preferred to propofol for hypnosis, due to the less impact on hemodynamics. Opioids like fentanyl or sufentanil are preferred for the same reason ("stress-free anesthesia"), with an induction dose of 0.2–0.4 mcg/kg for sufentanil and 2–4 mcg/kg for fentanyl. Continuous infusion analgesia remifentanil is preferable for the less impact on renal function since it is metabolized by plasmatic esterase. This is particularly important in patients with low cardiac output and preexisting renal failure. Remifentanil will be turned off and replaced by morphine or tramadol (30 mg/die and 300 mg/die, respectively), before moving to the intensive care unit. Mean term muscle relaxant rocuronium (1 mg/kg) is usually the first choice for rapid sequence induction. Sometimes short-term cisatracurium

**Table 2.** Standard monitoring.

besylate (0.15–0.2 mg/kg for induction and 1–2 mcg/kg/min for continuous iv infusion during surgery) is a good alternative since it is metabolized by ester hydrolysis and Hofmann reaction, so the duration of block is not affected by renal or hepatic function. During induction of general anesthesia, severe hypotension can occur, so that a fluid iv bolus ad availability of rapid onset vasoconstrictors as metaraminol, phenylephrine, noradrenaline should be ensured. Cardioplegia is not administered in the recipient during heart transplantation, so that the risk of related hemodilution is less than routine cardiac surgery. On pump, sevoflurane or iv 2% propofol infusion (4 mg/kg/h) are the options for maintenance of general anesthesia. Monitoring the depth of anesthesia with bispectral index (BIS) should be routinely adopted in order to decrease the risk of awareness. Once having put the patient asleep, central lines must be placed (queen central venous pressure [CVP] line and 8 Fr line for the pulmonary artery catheter [PAC]). The ideal site for puncture (blind or ultrasound-guided) is the left internal jugular vein (IJV), since the right one can be reserved for eventual postoperative biopsy (necessary to evaluate the level of graft rejection). When this is not possible (presence of ICD on the left side), we can adopt the right subclavian vein. Sometimes, when the preoperative renal function is really compromised, we can already place into the femoral or subclavian vein a catheter for continuous renal filtration afterwards. The PA catheter is flown through the 8 Fr line up to the right atrium, and then, once the new heart is placed, it will be advanced by the cardiac surgeon up to the superior right pulmonary artery. Vigilance calibration will be done immediately before weaning from the CPB.


**5. Immobilization techniques in biosensors**

To create a biosensor, biological elements must be immobilized on the transducer's surface. Depending on the component of biorecognition, the physical-chemical environment, the transducer, and the features of the analyte, two well-known ways are physical and chemical immobilization strategies. One of the most crucial steps in sensor preparation is enzyme immobilization, which guarantees that the biomolecules can retain their biological activity, structure, and usefulness [2].

#### **5.1 Chemical immobilization**

This technique involves creating powerful chemical interactions between the functional groups of the biorecognition element and the transducer surface, such as covalent binding or covalent connection. Chemical immobilization techniques, on the basis of chemical bonding type, are divided into two groups: (a) direct covalent binding and (b) covalent cross-linking [2].

#### *5.1.1 Direct covalent bonding*

The biorecognition component is directly covalently bonded, a technique frequently used to immobilize enzymes, to either the electrode or transducer surface, the inert matrix of the membrane, or both. The production of the functional polymer and covalent immobilization are the two approachable steps. Excellent environmental resilience, less leakage of the biorecognition element (enzyme), and strong bond formation between the biorecognition element (enzyme) and matrix are benefits of direct covalent binding. The inability to replenish the

formed matrix after use and the use of harsh chemicals are two downsides of this method [2].

#### *5.1.2 Covalent cross-linking*

Cross-linking is a technique where biorecognition elements and inactive proteins create intermolecular covalent cross-linkages, such as enzymes. It uses multifunctional chemicals as linkers to connect enzyme molecules in threedimensional (3D) aggregates to the transducer surface. The optimal conditions for cross-linking include pH, temperature, and ionic strength. It offers advantages like faster reaction times, stronger adhesion, and higher enzyme catalytic activity. However, partial protein denaturation limits cross-linking immobilization and results in covalent cross-links between protein molecules rather than between the protein and matrix [2].

### **5.2 Physical immobilization**

This method relies on affixing enzymes to the transducer's surface without using chemical bonds. These immobilizations consist of (a) entrapment and (b) adsorption.

### *5.2.1 Entrapment*

This method involves using 3D matrices to physically entrap biorecognition components through covalent or noncovalent bonds. Enzymes are added to a monomer solution, polymerized by a chemical reaction, or modified experimental conditions. Biorecognition components are connected to organic or inorganic materials in a 3D network. Organic materials include polydimethylsiloxane, photopolymer, gelatin, alginate, cellulose, and acetate phthalate, while inorganic materials include activated carbon and porous ceramic materials. Sol-gel methods, microencapsulation, and electropolymerization are used for this process [2].

#### *<IP_ADDRESS> Sol-gel method*

At low temperatures, the sol-gel method is a method used to capture enzymes. Metal alkoxides are hydrolyzed and condensed to produce a nanoporous material that contains bioelements in a three-dimensional matrix. It is more easily synthesized, thermally and chemically stable, and capable of encapsulating large concentrations of biomolecules under mild immobilizing conditions [2].

## *<IP_ADDRESS> Microencapsulation*

A semipermeable membrane is enclosed by biorecognition components (such as enzymes) by using the microencapsulation technique. The two processes that are preferred are the polymerization of a monomer at the interface of two immiscible substances and the phase separation of enzyme microdroplets in water-immiscible liquid phases. As a result, the polymeric membrane's internal enzyme is obscured [2].