*2.5. Pyridoxine Deficiency Increases Lipid Peroxidation and Decreases Nrf2 and BDNF Expression*

In the PDD-fed sham group, malondialdehyde (MDA) levels in the hippocampus were higher (43.5%) compared to that in the CD-fed sham group. MDA levels in CD- and PDD-fed groups were dramatically increased three hours after ischemia to 368.0% and 395.0% of their respective sham gerbils and thereafter, MDA levels decreased with time after ischemia in both CD- and PDD-fed groups. Twenty-four hours after ischemia, MDA levels in CD- and PDD-fed groups showed 180.4% and 222.5% of their respective sham group. MDA levels were significantly higher in the PDD-fed group compared to that in the CD-fed group after ischemia, and this was not observed in the sham group (Figure 5A).

**Figure 5.** Measurement of malondialdehyde (MDA) levels (**A**) in the hippocampus and Western blot analysis of nuclear Nrf2 (**B**) and total mature brain-derived neurotrophic factor (BDNF) levels (**C**) in the CD- and PDD-fed gerbils of sham- and ischemia-operated groups (*n* = 6–7 per group; \* *p* < 0.05, significant difference between CD- and PDD-fed groups; # *p* < 0.05, significant difference between shamand ischemia-operated groups). All data are expressed as mean with standard deviation.

In the PDD-fed sham group, nuclear factor erythroid-2-related factor 2 (Nrf2) levels in nuclear fraction decreased compared to that in the CD-fed sham group, although statistical significance was not detected between groups. Twenty-four hours after ischemia, nuclear Nrf2 levels were slightly, but not significantly, increased in the CD-fed group, but they were maintained in the PDD-fed group. At this time point, nuclear Nrf2 showed significantly lower levels (71.6% of the CD-fed group) in the PDD-fed group (Figure 5B).

In the sham group, brain-derived neurotrophic factor (BDNF) levels in the PDD-fed gerbils were significantly decreased to 71.1% of CD-fed gerbils. Moreover, BDNF levels were significantly decreased in the hippocampus 24 h after ischemia/reperfusion in CD- and PDD-fed gerbils, and significantly lower levels (67.5% of CD-fed gerbils) of BDNF were found in the PDD-fed gerbils 24 h after ischemia (Figure 5C).

The two-way ANOVA test indicated that ischemia and PDD diets significantly changed MDA levels (df = 3, F = 3.807, *p* = 0.0193) in the hippocampus, while there were no interactive effects of ischemia and PDD diets on Nrf2 and BDNF expression in the hippocampus.

#### **3. Discussion**

Vitamin B6 is one of the essential vitamins that maintain the health of the nervous system in mammals, which should be taken in sufficient quantity from the food because it is not synthesized in mammals [25,26]. Deficiency of vitamin B6 causes cognitive function impairment, hippocampal neurogenesis reduction, cardiovascular disease, and Alzheimer's disease [20,27]. In the present study, we observed the effects of pyridoxine deficiency on cell death in the hippocampal CA1 region and on neuroblasts in the dentate gyrus after transient forebrain ischemia. We observed the changes in serum levels of PLP and homocysteine because vitamins B6, B12, and folic acid have been reported to be associated with the regulation of the methionine–homocysteine cycle [22]. PDD-fed gerbils showed a significant reduction in serum PLP levels in sham-operated animals as well as ischemic animals three and four days after ischemia. This result is consistent with our previous study that PDD-fed mice showed a significant reduction in serum and hippocampal PLP levels [20]. In contrast, pyridoxine deficiency significantly increased serum homocysteine levels in sham- and ischemia-operated animals and showed hyperhomocysteinemia, which is characterized by > 15 μmol/L homocysteine levels in the blood. Vitamin B6, B12, and folic acid are associated with homocysteine metabolism [18], and our previous study showed the presence of hyperhomocysteinemia in folic acid deficient gerbils, and

this condition increased the DNA damage in the hippocampus after ischemia [28]. Moreover, many studies demonstrated that hyperhomocysteinemia caused neuronal damage, cognitive impairments, and psychiatric diseases [29–33].

To confirm whether pyridoxine deficiency facilitates neuronal death in the hippocampal CA1 region, we conducted immunohistochemical staining of NeuN, a marker for mature neurons, in the hippocampus three and four days after ischemia because neuronal death was detected in the CA1 region four days after ischemia. In the sham group, NeuN-positive neurons slightly decreased in the CA1 region, although there is no statistical significance between the CD- and PDD-fed gerbils. A study showed that hyperhomocysteinemia significantly increased neuronal death in the rat hippocampus [34]. In the present study, we observed that pyridoxine deficiency significantly reduced the number of NeuN-positive neurons in the medial side of the CA1 region, and this suggests that pyridoxine deficiency facilitates neuronal death in the CA1 region after ischemia. However, we did not observe any significant changes in the number of NeuN-positive nuclei four days after ischemia in CD- and PDD-fed gerbils because most of the neurons showed degeneration in the CA1 region. Pyridoxine deficiency also showed activation of astrocytes and microglia in the hippocampus of sham-operated gerbils, and microglial aggregation was found in the medial side of the stratum pyramidale three days after ischemia/reperfusion because of neuronal death in this region. These results suggest that pyridoxine deficiency facilitates glial activation in the hippocampal CA1 region of sham- and ischemia-operated gerbils three days after ischemia. Our study provides new insight into the relationship between pyridoxine deficiency and glial activation in the hippocampus. We could not elucidate the mechanisms of glial activation in the hippocampus of PDD-fed gerbils. One hypothesis is hyperhomocysteinemia induced by pyridoxine deficiency because treatment with homocysteine significantly increased reactive gliosis in astrocytes and microglia in rats [35], and excess homocysteine causes toxicity in the brain [36,37].

We examined the possible mechanisms of pyridoxine deficiency in the hippocampal neuronal death after ischemia based on oxidative stress due to the presence of antioxidant potentials in vitamin B6, which can quench hydroxyl radicals similar with vitamin C. In contrast, transient forebrain ischemia increases oxidative stress, including DNA damage and lipid peroxidation in the hippocampus [24,38–41]. In the present study, lipid peroxidation measured by MDA levels was significantly increased 3 h after ischemia in the CD-fed gerbils and thereafter decreased with time after ischemia. This result is consistent with previous studies that MDA products increased as an accumulation of aldehyde in various neurological disorders such as Alzheimer's disease, ischemia, and Parkinson's disease [24,40–45]. Additionally, MDA levels in this study were significantly higher in PDD-fed gerbils than in CD-fed ones 3, 12, and 24 h after ischemia, and not in the sham-operated group. This result suggests that PDD increases reactive aldehyde in the hippocampus, which aggravates neuronal death in the hippocampal CA1 region after transient forebrain ischemia. Changes in Nrf2 expression were also observed in the hippocampus because it is believed to be a key transcription factor in decreasing reactive oxygen species [46]. There have been reports that Nrf2 decreased ischemic damage by reducing oxidative stress [47], while Nrf2 deficient mice showed vulnerability to oxidative stress [48]. In the present study, lower Nrf2 expression levels were found in the PDD-fed gerbils than in the CD-fed gerbils 24 h after ischemia, and this result suggests that the reduction of Nrf2 may be associated with early neuronal damage after transient forebrain ischemia.

In this study, we also observed the effects of pyridoxine deficiency on regenerative potentials based on proliferating cells and neuroblasts in the dentate gyrus because we observed the reduction of neuroblasts in the mice hippocampus [20]. In gerbil brain, the proliferating cells and neuroblasts were reduced in the dentate gyrus of sham- and ischemia-operated animals, and this result suggests that pyridoxine deficiency reduces the regeneration potentials in ischemic brain. Additionally, we observed BDNF levels in the hippocampus because it modulates the hippocampal neurogenesis [49,50]. Pyridoxine deficiency and/or brain ischemia decreased BDNF levels in the hippocampus, and BDNF levels were lowest in PDD-fed ischemic gerbils. This result supports the immunohistochemical finding

for proliferating cells and neuroblasts in the dentate gyrus. Interestingly, Nrf2 is one of the essential elements to regulate the hippocampal neurogenesis [51] and homocysteine reduced cell differentiation in chicken embryonic brain [52]. However, neurogenesis in the dentate gyrus is unlikely to be related to regeneration; rather, migrating neuroblasts from SVZ may contribute to regeneration [53,54]. Moreover, the initial increase in neurogenesis in the dentate gyrus may be accompanied by its significant decrease at a later stage after ischemia [7] due to the limited pool of stem cells in this region [55].

In conclusion, pyridoxine deficiency facilitates neuronal death in the hippocampal CA1 region after transient forebrain ischemia by increasing homocysteine levels in the serum and lipid peroxidation in the brain, as well as reducing the Nrf2 levels in the hippocampus. Moreover, pyridoxine deficiency reduces the proliferating cells and neuroblasts, probably by reducing BDNF levels. This result suggests that pyridoxine is an essential element in fighting neuronal death and in increasing the regenerative potentials after ischemia.


**3. Polarization dependent metamaterial cover designs**

A considerable part of research at microwave frequencies is focused on isotropic metamaterial covers that are independent on polarization states. Polarization-dependent surfaces have recently found useful applications in changing the polarization state of the incident wave (Yang & Rahmat-samii, 2005; Veysi et al., 2010).

For a traditional metamaterial cover, the transmission phase remains the same regardless of the *x*- or *y*-polarization state of the incident plane wave. In contrast, the transmission phase of a PDMTM cover is a function of both frequency and polarization state. Hence, when a PDMTM cover is employed as a director, the polarization state of the transmitted wave is fully characterized by the transmission phase difference between the *x*- and *y*-polarizations and the polarization state of the incident wave. And thus a proper phase difference between *x*- and *y*-polarized waves leads to a desired change in the polarization state of the transmitted wave.

Directive circularly polarized antennas are widely used in satellite communication systems. To obtain directive circularly polarized antenna, various types of metamaterial antenna have been proposed in the literature (Iriarte et al., 2006; Diblanc et al., 2005; Arnaud et al., 2007). It was demonstrated in (Iriarte et al., 2006) that the directive circularly polarized antenna can be realized by metamaterial antenna with a circular feed. A major limitation of this method is inability to tune mechanically. In other words, the polarization state of the antenna is only determined by the feed mechanism.

Directive circularly polarized antenna can be also realized using either metallic wire polarizer (Diblanc et al., 2005) or meander line polarizer (Arnaud et al., 2007) stacked on the 284 Trends in Electromagnetism – From Fundamentals to Applications

Metamaterial antenna at f=5.6GHz Metamaterial antenna at f=5.7GHz Metamaterial antenna at f=5.8GHz

Conventional antenna

θ [degree]

(b)

A considerable part of research at microwave frequencies is focused on isotropic metamaterial covers that are independent on polarization states. Polarization-dependent surfaces have recently found useful applications in changing the polarization state of the

For a traditional metamaterial cover, the transmission phase remains the same regardless of the *x*- or *y*-polarization state of the incident plane wave. In contrast, the transmission phase of a PDMTM cover is a function of both frequency and polarization state. Hence, when a PDMTM cover is employed as a director, the polarization state of the transmitted wave is fully characterized by the transmission phase difference between the *x*- and *y*-polarizations and the polarization state of the incident wave. And thus a proper phase difference between *x*- and *y*-polarized waves leads to a desired change in the polarization state of the

Directive circularly polarized antennas are widely used in satellite communication systems. To obtain directive circularly polarized antenna, various types of metamaterial antenna have been proposed in the literature (Iriarte et al., 2006; Diblanc et al., 2005; Arnaud et al., 2007). It was demonstrated in (Iriarte et al., 2006) that the directive circularly polarized antenna can be realized by metamaterial antenna with a circular feed. A major limitation of this method is inability to tune mechanically. In other words, the polarization state of the antenna is only

Directive circularly polarized antenna can be also realized using either metallic wire polarizer (Diblanc et al., 2005) or meander line polarizer (Arnaud et al., 2007) stacked on the

Fig. 7. CST simulated radiation patterns at different frequencies over the operating

**3. Polarization dependent metamaterial cover designs**

incident wave (Yang & Rahmat-samii, 2005; Veysi et al., 2010).

bandwidth, (a) E-plane, and (b) H-plane.

transmitted wave.

determined by the feed mechanism.

Directivity [dB]

0

5

10

15

20

top of the one-layer metamaterial cover. In this section, instead of using meander line or metallic wire polarizer, the geometry of the metamaterial cover is changed to provide circular polarization. Consequently, the second layer (polarizer layer) can be replaced with another metamaterial cover layer, which in turn results in higher directivity.

Moreover, in contrast to the previous directive circularly polarized antennas (Iriarte et al., 2006; Diblanc et al., 2005; Arnaud et al., 2007), polarization state of the directive antennas using our proposed metamaterial cover can be mechanically changed regardless of the feed mechanism.

In this section, a useful guideline has been established as how to use the magnitude and phase of the transmission coefficient to identify the operational frequency band of the directive circularly polarized antennas based on polarization dependent metamaterial covers.

As revealed in the previous sections, when a plane wave normally impinges upon a metamaterial cover, the phase and magnitude of the transmitted wave change with frequency. In order to illustrate the polarization feature of the PDMTM cover, we assume that a left-hand circularly polarized (LHCP) wave, namely,

$$\overrightarrow{E^i} = \overrightarrow{a\_x}e^{-j\,kz} + \overrightarrow{j\,a\_y}e^{-j\,kz}$$

where *k* is the free-space wavenumber, is normally impinged upon a director placed in *X*-*Y* plane. The field transmitted through the director can be easily calculated from the following equation:

$$\overrightarrow{E^{\ddagger}} = e^{-j k x\_x} e^{j \theta\_x} \overleftarrow{(a x\_x} + j \overrightarrow{a}\_y e^{j (\theta\_y - \theta\_x)}) \tag{5}$$

The above field can be decomposed into two circularly polarized components

$$\overrightarrow{E^{i}} = e^{-j kz} e^{j \theta \mathbf{x}} \left[ \overrightarrow{e} \left( \frac{\mathbf{1} - e^{j(\theta y - \theta \mathbf{x})}}{\sqrt{2}} \right) + \overrightarrow{e} \left( \frac{\mathbf{1} + e^{j(\theta y - \theta \mathbf{x})}}{\sqrt{2}} \right) \right] \tag{6}$$

Where

$$\overrightarrow{\mathcal{e}\_I} = \frac{(\overrightarrow{a\_{\overline{x}}} + j\overrightarrow{a\_{\overline{y}}})}{\sqrt{2}}, \text{ } \overrightarrow{\mathcal{e}\_{\overline{r}}} = \frac{(\overrightarrow{a\_{\overline{x}}} - j\overrightarrow{a\_{\overline{y}}})}{\sqrt{2}}$$

and *θx* and *θy* denote the transmission phases for the *x*- and *y*-polarized waves, respectively. For a traditional metamaterial cover (*θy*- *θx*=0), the transmitted wave is purely LHCP and thus the polarization does not change. In order to change the polarization state of the antenna, the PDMTM cover can be used as a director. At a certain frequency where phase difference is 180° and transmission is considerable, the transmitted wave is purely righthand circularly polarized (RHCP).

The left-hand circularly polarized incident wave can be also converted to the linearly polarized (LP) wave where the phase difference is 90° and the transmission is also considerable. One can follow the same procedure for the linearly polarized incident wave,

$$
\overrightarrow{E^i} = \overrightarrow{a\_x} \overrightarrow{e^{-jkz}} + \overrightarrow{a\_y} \overrightarrow{e^{-jkz}} \dots
$$

Theory and Applications of Metamaterial Covers 287

The axial ratio of the transmitted wave is plotted in Fig. 8. Also, Fig. 9 shows the transmission curve for both *x*- and *y*-polarized incident plane waves. The frequency band inside which the axial ratio of the RHCP transmitted wave is below 6dB and the magnitudes of the transmission coefficients for both the *x*- and *y*-polarized incident waves are more than

Another approach to realize PDMTM covers is to add space between the *x*- and *y*-directed strips of each layer (Veysi et al., 2011), as shown in Fig. 10. For a traditional metamaterial

For the nonplanar case discussed here the dimensions are chosen as follows: *L*=*W*=13.5mm, *P*=18.5mm, *h*=27.5mm, *hr1*=3.5mm, and *hr2*=7mm, where *hr1* denotes the relative height between the *x*- and *y*-directed strips of the first layer and *hr2* denotes the same height for the

Fig. 11 shows the magnitudes of the transmission coefficients for both *x*- and *y*-polarized waves. The axial ratio of the wave radiated from linearly polarized antenna is also plotted in Fig. 12. It can be seen from Figs. 11-12, that the operating frequency of the proposed structure is around 9.1GHz where the metamaterial cover has both the desired transmission

4 4.2 4.4 4.6 4.8 5 5.2 5.4 5.6 5.8 6

X: 4.764 Y: 1.279

 **Frequency(GHz)**

The FDTD simulated results presented in this section confirm the concepts of the proposed approach to control both the direction and the polarization of the transmitted wave. The

Fig. 8. Axial ratio of the transmitted plane wave from the rectangular hole metamaterial

cover, the *x*-directed strip is located on the same plane as the y-directed strip.

3dB RHCP 6dB RHCP

For a linearly polarized antenna, namely

90% ranges from 4.75GHz to 5GHz (5.12%).

second layer.

**3.2 Metamaterial cover with nonplanar strips**

phase difference and the remarkable transmission.

cover (Veysi et al., 2011).

 **Axial Ratio**

, *i jkz jkz E ae ae x y* − − = +

so that the transmitted field then becomes:

$$\begin{split} \overrightarrow{E^{i}} &= \overrightarrow{a\boldsymbol{\omega}} \, e^{-j(kz-\theta\boldsymbol{x})} + \overrightarrow{a\boldsymbol{y}} \, e^{-j(kz-\theta\boldsymbol{y})} = \\ &e^{-jkz} \, e^{j\theta\boldsymbol{x}} [\overrightarrow{e^{r}} (\frac{1+e^{j(\theta\boldsymbol{y}-\theta\boldsymbol{x}+\pi f/2)}}{\sqrt{2}}) + \overrightarrow{e} \, (\frac{1-e^{j(\theta\boldsymbol{y}-\theta\boldsymbol{x}+\pi f/2)}}{\sqrt{2}})] \end{split} \tag{7}$$

Consequently the radiation mechanism of the linearly polarized antenna with metamaterial cover is conceptually described by Eq. 7. For an isotropic metamaterial cover, the phase difference between two orthogonal polarizations is zero and thus the polarization state does not change.

An interesting feature of the PDMTM covers can be revealed by a closer investigation. When a PDMTM cover with 90° transmission phase difference is used as a director, the polarization state of the transmitted wave becomes LHCP. Moreover, when the phase difference is -90° the polarization state of the transmitted wave is RHCP. Consequently we can easily switch between LHCP and RHCP using a rotatory cover, which can be rotated smoothly with a 90° steps.

Based on above discussion, one can conclude that the metamaterial cover can be used as a changing polarization plane. The operational frequency band of an antenna with PDMTM cover is defined as the frequency region within which the magnitudes of the transmission coefficients for both *x*- and *y*-polarized waves are close to their maximum values and transmission phase difference takes the desired value.

This interesting feature has been realized by changing the unit cell geometry, such as cutting rectangular holes instead of square holes and changing the relative height difference between the *x*- and *y*-directed strips of each layer (Veysi et al., 2011).

## **3.1 Rectangular hole metamaterial cover**

The traditional metamaterial cover uses symmetric square holes so that its transmission phase for normal incidence remains the same regardless of the *x*- or *y*-polarization state of the incident plane wave. Therefore, the logical step is to replace the square holes by rectangular ones (Veysi et al., 2011).

First, the design parameters of the metamaterial cover are selected to have a reasonable transmission at a specified frequency. The effect of different design parameters of the metamaterial cover on the magnitude of the transmission coefficient can be found in (Huang et al., 2009).

After the successful design of the isotropic metamaterial cover, the width or/and length of the square holes are changed to obtain both the desired transmission phase difference and the maximum transmission within the specified frequency band. When the hole width is increased, the plasma frequencies shift down to the lower frequencies.

Thus, by adjusting the width and length of the rectangular hole, the polarization sense of the transmitted wave can be changed. An example design for these parameters is as follows:

 *h*= 24.5mm, *P*=20.5mm, *L*=17.5mm, *W*=16.5mm

For a linearly polarized antenna, namely

286 Trends in Electromagnetism – From Fundamentals to Applications

( 2) ( 2) 1 1 [ ( ) ( )] 2 2 *l*

θθπ

(7)

() ()

*jy x jy x jkz j x r*

− + − + −

θθπ

*e e*

Consequently the radiation mechanism of the linearly polarized antenna with metamaterial cover is conceptually described by Eq. 7. For an isotropic metamaterial cover, the phase difference between two orthogonal polarizations is zero and thus the polarization state does

An interesting feature of the PDMTM covers can be revealed by a closer investigation. When a PDMTM cover with 90° transmission phase difference is used as a director, the polarization state of the transmitted wave becomes LHCP. Moreover, when the phase difference is -90° the polarization state of the transmitted wave is RHCP. Consequently we can easily switch between LHCP and RHCP using a rotatory cover, which can be rotated

Based on above discussion, one can conclude that the metamaterial cover can be used as a changing polarization plane. The operational frequency band of an antenna with PDMTM cover is defined as the frequency region within which the magnitudes of the transmission coefficients for both *x*- and *y*-polarized waves are close to their maximum values and

This interesting feature has been realized by changing the unit cell geometry, such as cutting rectangular holes instead of square holes and changing the relative height difference

The traditional metamaterial cover uses symmetric square holes so that its transmission phase for normal incidence remains the same regardless of the *x*- or *y*-polarization state of the incident plane wave. Therefore, the logical step is to replace the square holes by

First, the design parameters of the metamaterial cover are selected to have a reasonable transmission at a specified frequency. The effect of different design parameters of the metamaterial cover on the magnitude of the transmission coefficient can be found in (Huang

After the successful design of the isotropic metamaterial cover, the width or/and length of the square holes are changed to obtain both the desired transmission phase difference and the maximum transmission within the specified frequency band. When the hole width is

Thus, by adjusting the width and length of the rectangular hole, the polarization sense of the transmitted wave can be changed. An example design for these parameters is as follows:

+ − +

 θ

*t j kz x j kz y x y*

−− −−

=+=

θ

*eee e*

*E ae ae*

θ

transmission phase difference takes the desired value.

**3.1 Rectangular hole metamaterial cover**

rectangular ones (Veysi et al., 2011).

et al., 2009).

between the *x*- and *y*-directed strips of each layer (Veysi et al., 2011).

increased, the plasma frequencies shift down to the lower frequencies.

 *h*= 24.5mm, *P*=20.5mm, *L*=17.5mm, *W*=16.5mm

so that the transmitted field then becomes:

not change.

smoothly with a 90° steps.

$$\overrightarrow{E^l} = \overrightarrow{a \times e}^{-j/k \cdot x} \overrightarrow{+a \cdot y} e^{-j/k \cdot x}$$

The axial ratio of the transmitted wave is plotted in Fig. 8. Also, Fig. 9 shows the transmission curve for both *x*- and *y*-polarized incident plane waves. The frequency band inside which the axial ratio of the RHCP transmitted wave is below 6dB and the magnitudes of the transmission coefficients for both the *x*- and *y*-polarized incident waves are more than 90% ranges from 4.75GHz to 5GHz (5.12%).

#### **3.2 Metamaterial cover with nonplanar strips**

Another approach to realize PDMTM covers is to add space between the *x*- and *y*-directed strips of each layer (Veysi et al., 2011), as shown in Fig. 10. For a traditional metamaterial cover, the *x*-directed strip is located on the same plane as the y-directed strip.

For the nonplanar case discussed here the dimensions are chosen as follows: *L*=*W*=13.5mm, *P*=18.5mm, *h*=27.5mm, *hr1*=3.5mm, and *hr2*=7mm, where *hr1* denotes the relative height between the *x*- and *y*-directed strips of the first layer and *hr2* denotes the same height for the second layer.

Fig. 11 shows the magnitudes of the transmission coefficients for both *x*- and *y*-polarized waves. The axial ratio of the wave radiated from linearly polarized antenna is also plotted in Fig. 12. It can be seen from Figs. 11-12, that the operating frequency of the proposed structure is around 9.1GHz where the metamaterial cover has both the desired transmission phase difference and the remarkable transmission.

Fig. 8. Axial ratio of the transmitted plane wave from the rectangular hole metamaterial cover (Veysi et al., 2011).

The FDTD simulated results presented in this section confirm the concepts of the proposed approach to control both the direction and the polarization of the transmitted wave. The

Theory and Applications of Metamaterial Covers 289

X: 9.112 Y: 0.9951

X-pol Y-pol

3dB RHCP 6dB RHCP

4 5 6 7 8 9 10 11 12

 **Frequency(GHz)**

8 8.2 8.4 8.6 8.8 9 9.2 9.4 9.6 9.8

Metamaterial covers can be applied to conventional antenna to improve their performance. These include conventional metamaterial covers to increase both the impedance and directivity bandwidths of the proximity coupled microstrip patch antenna and polarization dependent metamaterial covers to change the polarization state of the antenna. Thin lattices of ungrounded metal plates can behave as a metamaterial cover and can be analyzed using a simple FDTD code. These surfaces have two important properties: (1) increasing of the transmission rate and (2) control of the direction and polarization of the transmission. Polarization dependent metamaterial covers can be realized by cutting rectangular holes instead of square holes and

Fig. 12. Axial ratio of the transmitted plane wave from the metamaterial cover with

changing the relative height difference between the *x*- and *y*-directed strips of each layer.

 **Frequency(GHz)**

X: 9.112 Y: 1.269

Fig. 11. FDTD simulated transmission of the metamaterial cover with offset strips (Veysi et

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

 **Axial Ratio**

nonplanar strips (Veysi et al., 2011).

**4. Conclusions**

al., 2011).

 **Transmission**

authors believe that the proposed cover can find many applications in the broad electromagnetic areas such as antenna engineering and optical sources.

However, a rigorous characterization should take into account the complex interactions between the antenna and the metamaterial cover, such as finite size of the ground plane and the antenna height. Consequently, it is indispensable to use full wave analysis method, such as the finite difference time domain (FDTD), in the antenna designs in order to obtain accurate results.

Fig. 9. FDTD simulated transmission of the rectangular hole metamaterial cover (Veysi et al., 2011).

Fig. 10. A unit cell of metamaterial cover with offset strips (Veysi et al., 2011).

288 Trends in Electromagnetism – From Fundamentals to Applications

authors believe that the proposed cover can find many applications in the broad

However, a rigorous characterization should take into account the complex interactions between the antenna and the metamaterial cover, such as finite size of the ground plane and the antenna height. Consequently, it is indispensable to use full wave analysis method, such as the finite difference time domain (FDTD), in the antenna designs in order to obtain

4 4.2 4.4 4.6 4.8 5 5.2 5.4 5.6 5.8 6

X-pol Y-pol

*P*

 **Frequency(GHz)**

Fig. 9. FDTD simulated transmission of the rectangular hole metamaterial cover (Veysi et al.,

Fig. 10. A unit cell of metamaterial cover with offset strips (Veysi et al., 2011).

*P*

electromagnetic areas such as antenna engineering and optical sources.

accurate results.

2011).

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

*hr*

 **Transmission**

Fig. 11. FDTD simulated transmission of the metamaterial cover with offset strips (Veysi et al., 2011).

Fig. 12. Axial ratio of the transmitted plane wave from the metamaterial cover with nonplanar strips (Veysi et al., 2011).

## **4. Conclusions**

Metamaterial covers can be applied to conventional antenna to improve their performance. These include conventional metamaterial covers to increase both the impedance and directivity bandwidths of the proximity coupled microstrip patch antenna and polarization dependent metamaterial covers to change the polarization state of the antenna. Thin lattices of ungrounded metal plates can behave as a metamaterial cover and can be analyzed using a simple FDTD code. These surfaces have two important properties: (1) increasing of the transmission rate and (2) control of the direction and polarization of the transmission. Polarization dependent metamaterial covers can be realized by cutting rectangular holes instead of square holes and changing the relative height difference between the *x*- and *y*-directed strips of each layer.

## **5. References**

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Huang, C., Zhao, Z., Wang, W., & Luo, X. (2009). Dual Band Dual Polarization Directive

Iriarte, J. C., Ederra, I., Gonzalo, R., Gosh, A., Laurin, J., Caloz, C., Brand, Y., Gavrilovic, M.,

Ju, J., Kim, D., Lee, W. J., & Choi, J. I. (2009). Wideband High-Gain Antenna Using

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Yang, F. & Rahmat-Samii, Y. (2005). A low profile single dipole antenna radiating circularly polarized waves, *IEEE Trans. Antennas Propag*., Vol. 53, No. 9, pp. 3083–3086 Zhong, S.-S., Liu, G. & Qasim, G. (1994). Closed Form Expressions for Resonant Frequency

Zhu, F., Lin, Q., & Hu, J. (2005). A Directive Patch Antenna with a Metamaterial Cover,

Polarized Patch Antenna", *IEEE Trans. Antennas Propag*., pp. 2993-2996 Jafargholi A, Kamyab, M., Veysi, M. & Nikfal Azar, M. (2011), Microstrip gap proximity fed-

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times. The signal in voxel **x** can then be denoted as *S***x**(*b*, TE). Additional *b*0-images were acquired in the halfway-tilted (9◦) position (not shown). Remaining parameters were repetition time TR 3.5 s and voxel size 3 × 3 × 3 mm3.

#### *2.2 MRI Signal Processing*

The diffusion-*T*2 data were preprocessed to correct for subject motion, eddy current effects, Gibbs ringing and gradient non-linearities [31–33] for each subject and each head orientation. Spatial correspondence between the tilted and default head orientations was obtained in two ways: 1) by nonlinear registration [34] to the halfway-tilted (9◦) space, and 2) by a tractometry approach in native space.

The tractometry [29] approach in native space of each head orientation relied on the quantitative mapping of measures along reconstructed brain pathways. First, fibre orientation distribution functions (fODFs) [35, 36] were estimated at each voxel using multi-tissue multi-shell constrained spherical deconvolution (MSMT-CSD) [37]. For each coil position, peaks were extracted from the resulting fODFs and used as input to perform streamline tractography on the TE = 54 ms data. Bundles were automatically segmented [38], a representative core-streamline was computed [39], and the bundles were subsequently subdivided [40, 41] into n = 20 segments (*s*)

**Fig. 4** Extracted brain pathways of interest from subject 2. Bundles were segmented into 20 sections (0: ligth-blue, 20: dark-brown). CC: corpus callosum, UF: uncinate fasciculus, CST: cortiospinaltract, IFOF: inferior fronto-occipital fasciculus, ILF: inferior longitudinal fasciculus. Visualisation was performed using FiberNavigator [43]

(Fig. 4). Voxels with a single-fibre-population were identified [42] and assigned to *si* if their location was inside the segment and their orientation was within 30◦ of the orientation of the core-streamline in that segment. Note that only tract-segments with minimal fanning (assessed visually) were considered. *T*2 values were then profiled for each bundle independently by taking the mean and standard error of the mean within each tract segment.

#### *2.3 Estimation*

SNR estimates were obtained from the background of the images acquired at TE = 54 ms and *b* = 0 s/mm2 for both the (0◦) and (18◦) coil-orientations [44]. The voxelwise *T*2 was estimated from the *b*0-signals as *S*(0, TE) = *S*(0, 0)*e*−TE/*T*2 , using a nonlinear least-squares trust-region-reflective algorithm in Matlab.

Fibre orientation θ to the main magnetic field **B**0 was estimated for the voxels with single fibre population. With prior knowledge of θ orientation-dependent (anisotropic) and -independent (isotropic) components of *R*2 can be estimated as follows [20, 45]: *R*2(θ) = *R*2,isotropic + *R*2,anisotropic · sin4 θ.

#### **3 Results**

**Signal-to-noise ratio**. The estimated noise standard deviation was similar for the two coil-orientations. Figure 5a compares the signals in the default and the tilted position after registration to the common space; the signal (and thus SNR) between coilorientations varied within a similar range as the range seen between test-retest scans in the same orientation. Globally, the images are aligned but some local misalignments can still be observed.

**Voxel-wise** *T*2-**estimates**. Figure 5b highlights differences in estimated *T*2 for different coil-orientations. Globally, the difference in *T*2-values estimated from the data in default and tilted head orientations is larger than or equal to *T*2-values estimated from test-retest scans in default head orientation for subject 1 (Fig. 5b, left half). Local differences in *T*2 can be observed between the default and tilted position, as indicated by red arrows in the *T*2-maps in Fig. 5b, for example. The inverse *T*2-values in white matter mostly range between 9 s−1 and 21 s−1 for both subjects and head orientation.

**Fig. 5 a** *b* = 0 s/mm2 image for the default (0◦) and tilted (18◦) orientation registered to the halfway-tilted (9◦) space, and their difference (tilted—default). σˆ is the estimated standard deviation in the background of the image. **b** Estimated *T*2 for the default (0◦) and tilted (18◦) orientation registered to the halfway-tilted (9◦) space, and their difference. Red arrows indicate regions of visible difference

**Fig. 6** Relaxation rate 1/*T*2 as a function of the fibre-orientation θ with the main magnetic field, in the default (left) and tilted (right) position. Each point represents a single-fibre-population voxel and is colour-coded according to its orientation (red, blue, and green correspond to the left-right, superior-inferior and anterior-posterior axis, respectively). The black line represents a model-fit of 1/*T*2 as a function of θ as described in previous literature and references therein [13, 19, 20]

**GlobalWM isotropic and anisotropic** *T*2-**stimates**. The total isotropic (orientationindependent) component of relaxation rate of *R*2 = 1/*T*2 in WM was estimated at 13.7 ± 0.2 s−1 and 13.6 ± 0.2 s−1, in default and tilted head orientations, respectively, for one of the subjects (Fig. 6). For the same subject the total WM anisotropic components of the inverse *T*2 were 1.6 ± 0.25 s−1 and 1.7 ± 0.25 s−1, for default and tilted head positions, respectively. The range of *T*2-values in white matter and their total isotropic and anisotropic components are consistent with previously reported values in [20, 45].

**Tractometry analysis**. Figures 7, 8 and 9 show the along-tract profiles of the estimated *T*2 (top plot) and angle w.r.t. **B0** (bottom plot) for different tracts. Globally, the angular profiles show comparable characteristics between subjects in the default and tilted position. For Subject 1, the angular profiles remain similar in the default and default-retest acquisition, except for the inferior parts of the corticospinal tract (CST).

Profiling of *T*2 in the CST, which runs along the *z*-axis (i.e., inferosuperior), reveals a significant increase in *T*2, for example in segment 16 which experiences a change in orientation w.r.t. **B0** from ∼35◦ in the default position to ∼55◦ in the tilted position (Fig. 7). This is in the regime where the derivative of the relaxation rate 1/*T*2 as a function of angle is the largest (Fig. 6). The uncinate fasciculus (UF) shows a noisier pattern, likely because the number of single-fibre voxels per segment is generally lower (∼5−10 in the UF compared to ∼15−20 in the CST).

**Fig. 7** Tractometry results (mean and standard error) for the corticospinal tract (CST, top plots) and the uncinate fasciculus (UF, bottom plots). *T*2-values and fibre orientation to **B**0 are plotted against segment numbers for each fibre tract and subject. Colour bar indicates tract-segment location, corresponding to the colour-encoding on the visualised tracts. Note that only tract-segments with minimal fanning (assessed visually) were considered

In the inferior longitudinal fasciculus (ILF) (Fig. 8) a global decrease in angle w.r.t. **B0** from default to tilted position leads to an overall, yet subtle, increase in *T*2. In the inferior fronto-occipital fasciculus (IFOF) the pattern is less clear.

In the callosal midbody the angle w.r.t. **B**0 remains relatively unchanged and so does *T*2.

#### **4 Discussion**

In this work we have incorporated a tiltable coil in *T*2-diffusion-correlation experiment to modulate the white matter fibre orientation with respect to the main magnetic field **B**0.

**Fig. 8** Tractometry results (mean and standard error) for the inferior fronto-occipital fasciculus (IFOF, top plots) and the inferior longitudinal fasciculus (ILF, bottom plots). *T*2-values and fibre orientation to **B**0 are plotted against segment numbers for each fibre tract and subject. Colour bar indicates tract-segment location, corresponding to the colour-encoding on the visualised tracts. Note that only tract-segments with minimal fanning (assessed visually) were considered

We observed changes in the *T*2-tract-profile after the participants' heads were re-oriented in the scanner, with up to ∼10 ms difference in *T*2-values between the default and the tilted head orientation. The test-retest *T*2-tract profiles in the default head position are more similar to each-other than to the tract profiles in the tilted head position, as for example evident from the results for the CST and IFOF. These initial results suggest variation of *T*2 as a function of fibre orientation to **B**0 and that tilting the participant's head by 18◦ can reveal those variations.

**Fig. 9** Tractometry results for the genu of the corpus callosum (CC2). *T*2-values and fibre orientation to **B**0 are plotted against segment numbers for each subject. Colour bar corresponds to tract-segment location, and this is colour-encoded on the tracts themselves. Note that only tractsegments with minimal fanning (assessed visually) were considered

#### *4.1 Incorporating Tiltable Coil in T***2***-diffusion correlation experiments*

**Robustness of experimental setup when using a tiltable coil**. The tiltable coil allows us to control the pitch orientation of the participant's head. We have demonstrated an overall test-retest similarity of estimated fibre-tract orientations in the default position, whereas there were clear differences with the tilted head position. However, some differences in fibre orientation of the CST between the test and retest could be observed, particularly in the inferior segments, while differences in fibre orientation in the IFOF tract were less obvious. Given the apparent stability of the IFOF tract profiling and insensitivity of fibre orientation to the head rotation around **B**0 in the default head position (yaw), the test-retest differences in the CST could be a result of an additional roll head orientation with respect to the coil between the two scans. Such additional differences in orientation could be mitigated by further restricting head position within the coil, e.g. additional padding or performing the experiments with differences in tilt immediately after each other without a break. Whereas this introduces a confound in assessing test-retest variability, the estimation of fibre-orientations is done in each coil orientation independently and as such we do not expect this to be detrimental in the overall assessment of *T*2-anisotropy.

**Range of orientations**. By re-purposing a coil that was designed to maximise patient comfort in clinical situations means that the range of coil orientations was limited. A larger range of orientations would allow the θ versus 1/*T*2 relationship to be elucidate more robustly. Nevertheless, these initial experiments demonstrate the utility of this hardware design for uncovering orientational-anisotropy effects in vivo.

#### *4.2 Origin of T***2***-Contrast and -Anisotropy in WM*

The water signal from each WM voxel is a superposition of the signal from different water pools (e.g. intra- and extra-axonal, and at short TE also myelin water), therefore the macroscopic *T*2-values measured in this study could be approximated as the weighted average of the *T*2-values from each of the two compartments. This means that the macroscopic *T*2 will depend on individual *T*2-values of the compartments, but also on the relative contribution to the signal. As such, tracts with the same apparent *T*2 but differences in signal fractions and *T*2-values between the intra- and the extra-axonal compartments could exhibit very different apparent orientational anisotropy.

A clear separation of macroscopic *T*2-values in some tracts and segments between the default and the tilted head orientations suggests that macroscopic *T*2 is also a function of orientation to**B**0. Fibre tract re-orientation in the magnetic field will cause local changes in the local magnetic field due to differences between the magnetic susceptibility of the myelin sheath and the surrounding tissue. Following the hollowcylinder model [26], the magnitude of these microscopic **B**0-field perturbations is expected to be larger in the extra-axonal compartment and, in combination with molecular Brownian motion, will cause an additional faster relaxation in the extrarelative to the intra-axonal compartment [46]. Future work will explore the effects of fibre orientation on individual compartments [47, 48].

#### *4.3 Considerations in Data Processing*

**Tractometry versus image registration** In this work we adopted tract profiling for comparing the *T*2-diffusion-correlation data in default and tilted head positions, instead of a voxel-based analysis; image registration was used for visualisation purposes only. Voxel-based analysis is known to suffer from confounds related to misregistration and data interpolation, an effect we visually observed in our study likely amplified by the large imaging voxels (3 mm isotropic) and imperfect correction for geometric distortions due to gradient nonlinearities. With the tractometry approach, spatial correspondence between coil orientations was established while keeping the data in native space, and each segment consitutes information from multiple voxels improving robustness to noise. We were able to reproduce *T*2-values from test-retest along the tracts.

**Correction for subject motion** The individual images have been corrected for subject motion, which could also involve head re-orientation with respect to the magnetic field. Subjects who participated in this study were experienced MR scanner participants, therefore the maximum rotation around any axis rarely exceeded 1.5◦. However, when considering the application of this method on less compliant subjects, subject motion could become a confounding factor.

#### **5 Conclusion**

Including a tiltable coil into the experimental set-up for diffusion-*T*2 correlation measurements paves the way for a more reliable assessment of orientational *T*2 dependence. Microstructural origins of the differences in *T*2 could include differences in pathway properties (e.g. axon diameter) or susceptibility effects. *T*2 orientationaldependence would furthermore impact analyses frameworks that assume constant *T*2 along pathways [49]. Voxel-wise comparison of *T*2 from different head-orientations remains challenging due to complications in experiment setup, imperfect correction for geometric distortions, and intrinsic scan-variability. Using a tractometry framework, we found indications of regional changes in *T*2 upon tilting of the head. Studying this effect in a larger population is necessary to increase statistical power. In future work, the diffusion-*T*2 correlation experiments can be used to study compartmental *T*2 orientation-dependence.

**Acknowledgments** CMWT is supported by a Rubicon grant (680-50-1527) from the Netherlands Organisation for Scientific Research (NWO) and a Sir HenryWellcome Fellowship (215944/Z/19/Z).

The data were acquired at the UK National Facility for In Vivo MR Imaging of Human Tissue Microstructure funded by the EPSRC (grant EP/M029778/1), and The Wolfson Foundation.

We are grateful to Fabrizio Fasano, Peter Gall, and Matschl Volker from Siemens Healthcare GmbH for their support.

#### **References**

**Open Access** This chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence and indicate if changes were made.

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## **Anisotropy in the Human Placenta in Pregnancies Complicated by Fetal Growth Restriction**

**Paddy J. Slator, Alison Ho, Spyros Bakalis, Laurence Jackson, Lucy C. Chappell, Daniel C. Alexander, Joseph V. Hajnal, Mary Rutherford, and Jana Hutter**

**Abstract** The placenta has a unique structure, which enables the transfer of oxygen and nutrients from the mother to the developing fetus. Abnormalities in placental structure are associated with major complications of pregnancy; for instance, changes in the complex branching structures of fetal villous trees are associated with fetal growth restriction. Diffusion MRI has the potential to measure such fine placental microstructural details. Here, we present in-vivo placental diffusion MRI scans from controls and pregnancies complicated by fetal growth restriction. We find that after 30 weeks' gestation fractional anisotropy is significantly higher in placentas associated with growth restricted pregnancies. This shows the potential of diffusion MRI derived measures of anisotropy for assessing placental function during pregnancy.

#### **1 Introduction**

Fetal growth restriction (FGR) is a condition where the developing fetus does not reach its full growth potential in-utero [13]. It constitutes a major pregnancy complication and is associated with a high degree of fetal mortality, morbidity and life-long complications [19]. Early onset FGR (defined as that diagnosed before 32 weeks' gestation) affects 0.5–1% of pregnancies and late onset FGR (diagnosed after 32

e-mail<EMAIL_ADDRESS>
A. Ho · S. Bakalis · L. C. Chappell Women's Health Department, King's College London, London, UK

L. Jackson · J. V. Hajnal · M. Rutherford · J. Hutter Centre for the Developing Brain, School of Biomedical Engineering and Imaging Sciences, King's College London, London, UK e-mail<EMAIL_ADDRESS>
L. Jackson · J. V. Hajnal · J. Hutter Biomedical Engineering Department, School of Biomedical Engineering and Imaging Sciences, King's College London, London, UK

P. J. Slator (B) · D. C. Alexander

Centre for Medical Image Computing, Department of Computer Science, University College London, London, UK

weeks') affects 5–10% of pregnancies [6, 9]. Early diagnosis and close monitoring are essential to optimize the outcome for pregnancies affected by FGR. Recently, pharmacological treatments have shown promise for severe early onset FGR cases [31]. However, while routine antenatal monitoring utilising symphysis-fundal height and ultrasound measurements can identify a significant proportion of FGR cases [10], detection remains a major problem—only 31% of cases were diagnosed during a previous study [11]. Detection is crucial as FGR is a leading cause of late unexpected stillbirth [11].

Post-delivery histopathological analysis shows a significant degree of characteristic pathologies in FGR placentas [15, 33], emphasising its importance and involvement in the cascade of events leading ultimately to sub-optimal growth. However, while post-delivery detection or confirmation plays an important role in increasing knowledge and possible causes of FGR, it comes too late to influence clinical care for these pregnancies. Therefore, recent novel developments, mainly using Magnetic Resonance Imaging (MRI) focus on studying the placenta during pregnancy to complement available antenatal screening.

#### *1.1 Placental Microstructure*

The placenta constitutes the key connection between mother and baby in utero and acts as the life support system for the growing fetus. Among its many functions are the exchange of oxygen and nutrients from the maternal blood circulation to the fetal blood, and the removal of waste products. The placenta comprises 10–40 individual lobules each constituting one key exchange unit. The transfer relies on a delicate and dynamically evolving microstructure within these units, focused around the fetal villi and depicted in Fig. 1A. These tree-like structures originate from the umbilical cord and contain fetal arteries and veins. They are bathed in maternal blood that enters the intervillous spaces from the spiral arteries at the level of the basal plate. A thin membrane called the syncytiotrophoblast separates maternal and fetal circulation, and allows the transport of oxygen and nutrients through it. Several histopathological features are associated with FGR, including elongated villous trees without the appropriate branching patterns [21] as illustrated schematically in Fig. 1B.

#### *1.2 Placental MRI*

Specific challenges of in-utero placental MRI include motion, such as maternal breathing and fetal movements, various air-tissue interfaces such as amniotic fluid, abdominal fat and bowel gas, and the suboptimal position of the imaging coil with respect to the organ of interest, especially for placentas located on the posterior wall of the uterus [5]. Another important limitation specifically for diffusion MRI arises

**Fig. 1** Schematic representation of single fetal villous trees in the placenta. Fetal blood flows through the convoluted branching structures, allowing nutrient exchange with the surrounding maternal blood. Panel **A**: complex branching structure of a healthy placenta. Panel **B**: pathological branching structure, associated with prengancy complications such as fetal growth restriction

from the safety requirement to reduce the acoustic sound level of the sequence to protect the fetal hearing. Therefore, typically the gradient slew rate is reduced, in consequence increasing the read-out length and thus the echo time resulting in lower Signal-to-Noise Ratios (SNR) [5, 16].

Diffusion MRI can reveal fine tissue microstructure details through sensitivity to the diffusion of water. By varying the strength and direction of diffusion gradients, the MRI sequence can be specifically tailored to microstructural features of interest. For example, sequences with a high number of distinct gradient directions can inform on tissue anisotropy and directionality. Such diffusion MRI sequences are commonly used to image white matter fibre tracts in the brain, however applications elsewhere in body exist, including in the placenta [3, 20, 27].

#### **2 Methods**

Pregnant women, recruited as part of a larger cohort for the Placental Imaging Project (PIP), underwent an MRI scan between 20 and 40 weeks of gestation. Informed consent was obtained (REC 14/LO/1169) and the scan was performed on a clinical 3T Philips Achieva (Best, The Netherlands) scanner using the 32-channel cardiac coil. All women were scanned in supine position under frequent monitoring of heart rate, saturation and blood pressure throughout the scan. Dedicated padding was provided to increase maternal comfort and verbal interaction was maintained.

After initial structural T2-weighted sequences of the entire uterus and the fetal brain in multiple orientations, a B0 map was acquired. An in-house developed tool for image based shimming was employed [12] to focus the shim on the placental parenchyma, avoiding air-tissue interfaces with bowel gas as much as possible. We next acquired a diffusion-prepared spin echo sequence. For some participants we used a modified sequence which acquires additional gradient-echos after the initial Spin Echo (e.g. [28]), although in this study we only utilised the first spin echo measurement. Conventional Stejskal-Tanner diffusion preparation was performed, with a total of 65 b-value/b-vector combinations, optimized specifically for the placenta as previously described [17, 26], with three diffusion gradient directions at b = [5, 10, 25, 50, 100, 200, 400, 600, 1200, 1600] s/mm2, eight directions at b = 18 s/mm2, seven at b = 36 s/mm2, fifteen at b = 800 s/mm2, and six b = 0 volumes. Further parameters include FOV = [300–340] × 320 × 84 mm, TR = 7 s, SENSE = 2.5, halfscan = 0.6, resolution = 3 mm3 for scans with additional gradient-echos and 2 mm3 otherwise. The total acquisition time was 8 min 30 s. Fat was suppressed with SPIR saturation pulses. The acquisition plane was coronal to the mother, chosen to assure that the in-plane direction coincides with the longest placental dimensions in mostly anterior and posterior placentas.

To correct for motion, the diffusion weighted volumes were registered non-rigidly to a common template using the ANTs multivariate template construction tool with the cross-correlation similarity metric [1]. Subsequently, a region of interest (ROI) comprising the whole placenta and adjacent basal placenta was manually segmented in all slices of the first b = 0 volume. We estimated diffusion tensor, mean diffusivity (MD), and fractional anisotropy (FA) maps—using all diffusion weightings—for the motion corrected scans using MRTrix [32].

#### *2.1 Recruitment*

We include a total of twenty-nine participants in this study, who were categorised as follows. Sixteen women were normal uncomplicated control pregnancies; their outcomes were obtained and checked to ensure that no new diagnosis of pre-eclampsia, gestational hypertension, fetal growth restriction or gestational diabetes had occurred, and their birthweight was greater than the 5th centile (by INTERGROWTH-21st). Seven women were diagnosed with fetal growth restriction, detected from antenatal ultrasound assessments. We also include six women recruited as uncomplicated control pregnancies who gave birth to a baby under the 5th centile, but did not have a formal antenatal FGR diagnosis. Although these could simply be constitutionally small babies, they could also be undiagnosed FGR cases, so we hence analysed them as a separate cohort. Five of the six below the 5th centile had co-morbidities, such as chronic hypertension in pregnancy (CHTN), or pre-eclampsia (PE). The patient population characteristics are given in Table 1.

**Table 1** Scan details for all participants. FGR denotes participants diagnosed with fetal growth restriction according to guidelines [13]. Under 5% denotes participants with no FGR diagnosis who delivered a baby weighting under the 5th percentile

#### **3 Results**

Figures 2 and 3 display FA maps, ordered by gestational age (GA) at scanning time, for control and growth restricted participants respectively. We next examine the evolution of FA values over gestation (Fig. 4). Finally, we compare FA values

#### 268 P. J. Slator et al.

**Fig. 2** Fractional anisotropy maps for all control participants. The boundary between the uterine wall (higher FA) and placenta (lower FA) is clear in most placentas with gestational age less than 30 weeks

**Fig. 3** Fractional anisotropy maps for FGR and low birthweight cohorts

**Fig. 4** Mean FA across placenta and uterine wall as a function of gestational age

**Fig. 5** Mean FA across placenta and uterine wall for the three cohorts, split at 30 weeks gestational age

between control and growth-restricted pregnancies (Fig. 5), assessing the potential of FA to inform on FGR-associated placental abnormalities.

The FA maps for all control participants (Fig. 2) show distinctive patterns in agreement with the literature [27]—the FA is lower in the placenta, and higher in the adjacent uterine wall. These observations likely represent isotropic nature of maternal blood pools and fetal villous tree branching within the placenta, and the prevalence of anisotropic fibrous muscle tissue in the uterine wall. Another factor in the high FA in the uterine wall may be the coherent orientation of vasculature in these areas. On the other hand, the distinction between the uterine wall and placenta is less clear in the growth restriction placentas (Fig. 3), and many of these maps show areas of high FA within the placenta.

Figure 4 plots the mean FA value within the ROI comprising the placenta and uterine wall. Control scans (Fig. 4, black dots) show an apparent decrease in mean FA over gestation, potentially reflecting microstructural changes during normal placenta maturation. On the other hand, growth restriction scans (Fig. 4, red and yellow dots), do not show a clear trend over gestation. At early gestational ages, control and compromised placentas have comparable mean FA values. Due to the downward FA trend in control placentas, from around 30 weeks gestation growth restriction placentas appear to have considerably lower FA values than control placentas. This difference was statisically significant, both when comparing controls with the combined FGR and low birth weight cohorts (*p* = 0*.*005, independent samples t-test), and when comparing controls to these two cohorts separately (Fig. 5). We tested if trends over GA differ between controls and growth restriction (i.e. FGR and under 5%) cohorts by calculating a linear regression to predict mean FA based on GA, cohort, and the interaction between GA and cohort. The coefficients and p-values are given in Table 2, and Fig. 6 visualises the fits. The coefficient of the interaction term between GA and low birth weight is statistically significant (p = 0.002), suggesting a different trend over gestation.

**Table 2** Coefficients and corresponding statistics from linear regression to predict mean FA based on GA, cohort, and GA × cohort (interaction term)

**Fig. 6** Linear regression to predict mean FA based on GA, cohort, and GA × cohort

#### **4 Discussion and Conclusion**

This study visualizes and quantifies fractional anisotropy in placentas of both control pregnancies and those affected by growth restriction. Encouragingly we find that the FA is significantly different across gestation in growth restricted pregnancies compared to controls. The fractional anisotropy is a coarse measurement that averages over a number of tissue properties. There are hence a number of microstructural or functional changes that could explain this observation. Our initial speculations of plausible factors behind the changes in FA are as follows.

We observed a clear pattern of decreasing FA with gestational age for control placentas, suggesting that normal placental development causes a reduction in coherently orientated tissue. A consistent hypothesis is that this reduction in FA reflects the normal onset of terminal villi formation along the surfaces of intermediate villi, which occurs predominately during the third trimester [2]. On the other hand, we observed higher FA for placentas associated with growth restricted pregnancies after 30 gestational weeks. This is consistent with histological findings that FGR placentas show a lack of side-branching terminal villi [2].

In this study, we utilised an MR protocol with multiple b-values and gradient directions. However, we only fit a relatively simple model to the data, the diffusion tensor. This data can support more complex models, such as anisotropic IVIM-type models, which separately consider the perfusion (i.e. low b-value) and diffusion (high b-value) signal components (e.g. [26]), and may help disentangle the tissue microstructure changes underlying the observed difference in FA. Another potential approach is to use orientation distribution functions, which might reveal differences in complexity of the orientation of villi (e.g. [23]).

There are a number of MRI-derived biomarkers that show promise for detecting placental dysfunction. These include: T2\* relaxometry [18, 24, 25], which relates to oxygenation levels; structural measures [7]; apparent diffusion coefficient (ADC) [4, 14, 30], relating to global tissue structure; and intravoxel incoherent motion (IVIM) MRI perfusion fraction [8, 22, 29], which relates to blood flow. Thus far, dMRI-derived potential biomarkers (ADC and perfusion fraction) have considered tissue to be isotropic. Our results strongly suggest that the FA is also sensitive to placental dysfunction, and hence that quantifying tissue anisotropy is an additional important avenue for assessing placental health. It may be the case that multiple biomarkers need to be combined in order to best assess the health of an individual placenta. The fact that we see higher FA values for placentas with birth weight under the 5th percentile, as well as those diagnosed with FGR is interesting and merits further investigation. It is likely that a significant proportion of cases under the 5th percentile are undiagnosed FGR. Our results suggest that quantifying tissue anisotropy in the placenta could have a role to play in the detection of FGR, We will investigate this by combining further scanning with post-delivery placental histology to test the ability to distinguish FGR cases from small but otherwise healthy babies.

**Acknowledgments** We thank all mothers, midwives, obstetricians, and radiographers who played a key role in obtaining the datasets. This work was supported by the NIH Human Placenta Project grant 1U01HD087202-01 (Placenta Imaging Project [PiP]); Wellcome Trust (201374/Z/16/Z); EPSRC (N018702, M020533, EP/N018702/1); NIHR (RP-2014-05-019); the Wellcome EPSRC Centre for Medical Engineering at Kings College London (WT 203148/Z/16/Z) and by the National Institute for Health Research (NIHR) Biomedical Research Centre based at Guy's and St Thomas' NHS Foundation Trust and Kings' College London. The views expressed are those of the authors and not necessarily those of the NHS, the NIHR or the Department of Health.

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**Author details**

Nilisha Itankar1 , Viraja Bhat2 , Jayati Chourey2 , Ketaki Barve2 , Shilpa Kulkarni2 , Prakash Rao2 and Yogesh Patil3\*

\*Address all correspondence to<EMAIL_ADDRESS>
1 Symbiosis Institute of Technology (SIT), Symbiosis International University (SIU), Near Lupin Research Park, Lavale, Pune, India

2 Symbiosis Institute of International Business (SIIB), Symbiosis International University (SIU), Rajiv Gandhi Infotech Park, Hinjewadi, Pune, Maharashtra, India

3 Symbiosis Institute of Research and Innovation (SIRI), Symbiosis International University (SIU), Lavale, Pune, Maharashtra, India


**3.2. Mineralogical characterization**

The gasoline hydrocarbons, for possessing volatile and low-density compounds require a special sealed cell to avoid losses due to evaporation and leakage and to support the applied tensions. The material selected for the construction of the special cells was stainless steel, to avoid reaction and adsorption problems in the walls, which is the case of plastics and acrylics

The system used to perform the gasoline's hydraulic conductivity was similar to that applied by Fernandes (1989). The special cell may be disassembled, and is made up of three parts. The first part is a cylinder, where the test material and reservoir are found. This part is 5 mm thick, 110 mm long and has an internal diameter of 77.2 mm. The other two parts are the upper and lower lids. Both have cavities filled with rubber rings which are able to prevent the reaction of the hydrocarbons in the gasoline and act as a seal when the cylinder is assembled. The upper lid has two openings, one for the entry of fluid and the other for the application of vertical tension with compressed air. The lower lid is made up of an outgoing flow register which is

connections were made out of aluminum, due to its low cost and flexibility; the connecting joints were sealed with 3M automotive glue and winding sealing thread, in order to prevent

The conductivity test was performed with test material 5 cm long, compacted at normal Proctor energy at optimal water content condition, in the cylinder of the hydraulic conductivity cell. Then, a thin disk of porous ceramic was placed top of the sample. The small space between the disk and the cylinder wall was filled with 3M glue to prevent preferential flows along the wall, and to ensure that the gasoline only passed through the porous ceramic disk. The cell was then assembled, and the upper and lower lids were connected to the cylinder. The cylinder is 11 cm high, of which the remaining 6 cm were filled with type C gasoline. After the cell was totally sealed and connected to the compressed air system, with pressure controlled by a manometer, it was connected with plastic tubes able to support high pressure. The conduc‐ tivity tests were performed for various applied vertical pressures. For each pressure applied, the hydraulic conductivity was measured. The pressures were varied to see how the soil sample behaved with an increase in hydraulic gradient upon the flow of gasoline. The hydraulic conductivity was measured in the laboratory at static tensions **σv** of 50, 100, 150, 200,

and 300 kPa, with respective hydraulic gradients of 75, 150, 225, 300, and 450.

hydrocarbons of the gasoline through infrared technique.

The residual water of the soil pores mixed with gasoline collected in the test was previously run through a separating funnel to remove the aqueous phase to later take a reading of

The test material of the lateritic soil sample, before and after the hydraulic conductivity test conducted with water, and the other with the flow of gasoline, were dried at room temperature. Micromorphological analyses were performed on Thin Lamina (TL) in vertical sections, prepared by impregnating the sample with plastic resin (Cardoso, 1995; Martins, 2002). The instrumental technique used for the microscopic views of the TL was Optical Microscopy.

square, 10 mm thick. The

connected to a collecting container. The two lids are 120 x 120 mm2

leaks and to make the system more secure.

(Doanhue *et al.*, 1999).

642 Environmental Risk Assessment of Soil Contamination

The identification and quantification of minerals in the sample were carried out by the method developed by Martins (2000). This method involves the use of X-ray diffraction (XRD) technique for identifying the minerals, chemical analysis for the determination of major elements (Al, Fe, Si, Ca, Mg and Ti), thermogravimetric analysis (TGA), and the use of Munsell color code (Munsell color company Inc., 1975). The determination of major chemical elements was performed by ICP-AES after the fusion of samples with alkaline NaOH as fondant at a temperature of 450 ° C for 40 minutes using the nickel crucible. Determinations of elements by ICP / AES (atomic emission spectrometry of Plasma Induced Coupling) were performed with Thermo Jarrell ASH equipment, model Iris / AP.

The thermogravimetric analysis were applied to quantify the kaolinite and gibbsite. For this used the TGA Shimadzu equipment with temperature ramp of 20 °C to 1500 °C, with speeds ranging from 0.2 to 60 ° C / min, using the software TAS60WS for the treatment of data. The Munsell code was used for determining the ratio of hematite and goethite in the soil samples. The CEC of soil was determined using the principle of the simple as the sum total of the exchangeable cations that a soil can adsorb. The determination of the organic matter content was done prior to extraction using wet oxidation method with potassium dichromate in sulfuric medium. The excess of dichromate after oxidation was titrated with standard solution of ferrous ammonium sulfate (Mohr salt).


**Economics of CCS**

#### **Chapter 11**

**Provisional chapter**

#### **Economics of Carbon Capture and Storage Economics of Carbon Capture and Storage**

John C. Bergstrom and Dyna Ty John C. Bergstrom and Dyna Ty

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/67000

#### **Abstract**

Human-engineered capture of CO2 emissions at the point source and subsequent longterm storage of this CO2 underground represent a potential mitigation strategy for global warming. The so-called carbon capture and storage (CCS) projects are technically feasible but have not been well established from an economic efficiency perspective. This chapter uses economic theory to describe the costs, benefits, and economically efficient level of CCS provision. Achieving the economically efficient level of CCS provision requires consideration of both the private and public costs and benefits of CCS and will also likely require some degree of government intervention in the form of economic incentives and/or direct regulation.

**Keywords:** CO2 , emissions, point source, capture, storage, economics, costs, benefits

#### **1. Introduction**

Since the late twentieth century, a newly developed technology has become one of the tools that can help mitigate the negative impacts on climate change from rising levels of greenhouse gases, especially CO2 . This technology is commonly known as the carbon capture and storage (CCS). CCS technology involves "capturing" CO2 emissions, say from a coal-fired power plant, and then depositing the captured CO2 gas in a storage site, such as an underground geological formation, where it will not enter the atmosphere. CCS projects are currently being tested and implemented throughout the world. However, economic feasibility of human-engineered CCS is not well established [1–4]. The purpose of this chapter is to discuss the economic benefits and costs of CCS projects from both private and public perspectives in order to shed light and provide insight on the potential for CCS technology to

and reproduction in any medium, provided the original work is properly cited.

© 2017 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, provide a viable mitigation strategy for helping to meet twenty-first century global CO2 emission reduction goals, such as set forth in the 2015 United Nations Climate Change Conference in Paris, France.

#### **2. Carbon and oxygen cycles1**

Carbon (C) is the basic building block for plant, animal and human life—all are "carbonbased" organisms. Plants, animals, and humans also depend on oxygen (O2 ) for survival. The cycling of carbon and oxygen in ecosystems is ultimately powered by solar energy. In photosynthesis, plants combine carbon dioxide (CO2 ), water (H2 O), and solar energy to produce sugars, oxygen, and energy. In cellular respiration, animals and humans combine sugars and oxygen to produce carbon dioxide, water, and energy. Carbon-oxygen-hydrogen compounds (e.g., sugars) pass through the food chain or web in ecosystems via herbivores, carnivores, and omnivores. In the food chain, some of the carbon and oxygen stored in organic compounds are returned to the environment in the form of CO2 and H2 O via cellular respiration. When a large organism such as a plant or an animal dies and is decomposed by microorganisms, more of the CO2 and H2 O stored within the plant or animal is returned to the environment where it can be taken up again by plants to produce more carbon-oxygen-hydrogen compounds which can then be taken up again by animals and humans.

Not all carbon and oxygen are recycled in the relatively short-term cycle described above. Some carbon and oxygen from decomposing plants and animals are converted by relatively long-term geologic processes into rocks (e.g., carbonate rock formations such as limestone) and minerals (e.g., coal, oil, and natural gas) stored in the earth's crust. When coal, oil, and natural gas enter economic systems, they are termed fossil fuels. The "fossil" part of this term derives from the fact that they come from fossilized remains of plants and animals. The "fuel" part is derived from the fact that coal, oil and natural gas, and their processed derivatives (e.g., gasoline) are burned as fuel in engines and other machinery found throughout our economic system (e.g., planes, trains, automobiles, electricity power plants, and home furnaces). When fossil fuels are burned, CO2 (and other emission gases—CH4 , N2 O) stored in these minerals is released back into the environment. The release of CO2 from burning fossil fuels is the focus of recent concern and debate over global climate change.

As indicated in the discussion above, human activities affect global climate change through impacts on the carbon and oxygen cycle. Burning of fossil fuels is a major contributor to releasing more CO2 into the atmosphere, primarily from terrestrial sources of stored carbon (e.g., coal deposits, oil deposits, and trees). Human activities can also help to remove CO2 from the atmosphere, with one of the primary means being increasing the storage of carbon in terrestrial plants. For example, taking actions to protect "green space" including farmland from development (and managing forests in a sustainable manner following an optimal harvest and replanting schedule) helps to remove CO2 in the atmosphere through carbon sequestration in plants via photosynthesis. Farms, forests, and other green space

¹This section appears also in Ref. ([5], p. 16–18).

areas thus act as "carbon sinks" helping to counteract the greenhouse effect. Another means for storing carbon is through human-engineered carbon capture and storage projects.

## **3. CCS costs**

emis-

) for survival. The

O), and solar energy to produce

O via cellular respiration. When a

, N2

O) stored in these min-

from burning fossil fuels is the

in the atmosphere through

provide a viable mitigation strategy for helping to meet twenty-first century global CO2

in Paris, France.

of the CO2

and H2

When fossil fuels are burned, CO2

¹This section appears also in Ref. ([5], p. 16–18).

releasing more CO2

CO2

**2. Carbon and oxygen cycles1**

242 Recent Advances in Carbon Capture and Storage

tosynthesis, plants combine carbon dioxide (CO2

are returned to the environment in the form of CO2

can then be taken up again by animals and humans.

erals is released back into the environment. The release of CO2

focus of recent concern and debate over global climate change.

optimal harvest and replanting schedule) helps to remove CO2

sion reduction goals, such as set forth in the 2015 United Nations Climate Change Conference

Carbon (C) is the basic building block for plant, animal and human life—all are "carbon-

cycling of carbon and oxygen in ecosystems is ultimately powered by solar energy. In pho-

sugars, oxygen, and energy. In cellular respiration, animals and humans combine sugars and oxygen to produce carbon dioxide, water, and energy. Carbon-oxygen-hydrogen compounds (e.g., sugars) pass through the food chain or web in ecosystems via herbivores, carnivores, and omnivores. In the food chain, some of the carbon and oxygen stored in organic compounds

large organism such as a plant or an animal dies and is decomposed by microorganisms, more

can be taken up again by plants to produce more carbon-oxygen-hydrogen compounds which

Not all carbon and oxygen are recycled in the relatively short-term cycle described above. Some carbon and oxygen from decomposing plants and animals are converted by relatively long-term geologic processes into rocks (e.g., carbonate rock formations such as limestone) and minerals (e.g., coal, oil, and natural gas) stored in the earth's crust. When coal, oil, and natural gas enter economic systems, they are termed fossil fuels. The "fossil" part of this term derives from the fact that they come from fossilized remains of plants and animals. The "fuel" part is derived from the fact that coal, oil and natural gas, and their processed derivatives (e.g., gasoline) are burned as fuel in engines and other machinery found throughout our economic system (e.g., planes, trains, automobiles, electricity power plants, and home furnaces).

(and other emission gases—CH4

into the atmosphere, primarily from terrestrial sources of stored car-

As indicated in the discussion above, human activities affect global climate change through impacts on the carbon and oxygen cycle. Burning of fossil fuels is a major contributor to

bon (e.g., coal deposits, oil deposits, and trees). Human activities can also help to remove

carbon sequestration in plants via photosynthesis. Farms, forests, and other green space

 from the atmosphere, with one of the primary means being increasing the storage of carbon in terrestrial plants. For example, taking actions to protect "green space" including farmland from development (and managing forests in a sustainable manner following an

), water (H2

and H2

O stored within the plant or animal is returned to the environment where it

based" organisms. Plants, animals, and humans also depend on oxygen (O2

#### **3.1. Components of total fixed costs and total variable costs**

CCS projects are not cheap. For example, in the United States, NRG Energy and JX Nippon Oil and Gas Exploration, Inc., are investing around \$1 billion USD on the Petra Nova CCS project. This project when completed in late 2016 is projected to capture and store about 1.4 million tons of carbon per year from one of NRG's existing coal-fired power plants in the State of Texas, USA [6, 7]. In this section, we discuss the concepts and components of CCS costs.

First, we need to realize that CCS projects are actually two interconnected projects in one. The first project is "carbon capture" and the second project is "carbon storage." Each of these projects has various options with different costs. As indicated in the previous section, ecosystems via the carbon and oxygen cycle will naturally capture carbon dioxide from the air (e.g., through photosynthesis) and then store the captured carbon in plants, the soil, and rocks and minerals. While CCS through natural ecosystem processes and functions is a viable mitigation strategy in response to CO2 -induced global climate change concerns (e.g., planting trees), the focus of this chapter is on human-engineered CCS.

In the case of carbon capture, human-engineered means of capturing carbon focus on "endof-pipe technologies" that remove CO2 from industrial emissions, particularly fossil fuel-fired (e.g., coal) electricity power plants. The "best available technology" (BAT) in the current time period (2016) is chemical absorption of CO2 from emissions at the point source (e.g. power plant smokestack). Once the CO2 has been removed from emissions, say from a coal-fired power plant, the CO2 can then be converted by pressurization to a liquid for transportation and storage [1, 2, 8].

Thus, one component of the costs of human-engineered carbon capture is the costs of the equipment (e.g., "scrubbers") and absorption chemicals used to remove CO2 from emissions [4, 9]. From a neoclassical microeconomics theory perspective, the "scrubber" equipment costs are "fixed costs" and the absorption chemicals are "variable costs." Fixed costs are so-called because they are a sunk cost which does not vary with the level of production. For example, once purchased and installed, a coal-fired power plant owner must incur the costs of scrubber equipment whether they are producing electricity or not (e.g., they still have to pay off the equipment as a capital cost).

Variable costs are so-called because they vary with the level of production. For example, as more (less) electricity is produced from a coal-fired power plant, more (less) emissions are generated, and more (less) absorption chemicals must be purchased. The fixed costs of humanengineered carbon capture can be quantified by multiplying the units of equipment purchased by the market price of equipment per unit (plus loan fees and interest if the equipment is financed). The variable costs can be quantified by multiplying, say the units of absorption chemicals purchased by the market price of chemicals per unit.

In addition to the direct, out-of-pocket fixed and variable costs of carbon capture discussed above, there are also opportunity costs of human-engineered carbon capture. For example, from an energy use perspective, human-engineered carbon capture at an electricity power plant comes with an energy use cost in the form of electricity generation that must be given up in support of carbon capture at the plant. This so-called energy penalty can be quantified by multiplying the amount of electricity lost in order to support carbon capture times the market price of electricity [2, 9–11].

After carbon is captured at a point source such as a coal-fired electricity power plant, it must be transported to and stored at a long-term storage site. At the time this chapter is being written, the most practical long-term storage sites appear to be various forms of natural underground geologic cavities (NUGCs). One option under this category is NUGC which once held crude oil and/or natural gas deposits but has been depleted through mining (e.g., oil and gas wells). Oil and gas companies already inject CO2 into operational oil and gas wells in order to squeeze more oil and gas out of the resource deposit. Thus, the technology for injecting CO2 captured from point source emissions into NUGCs where oil and gas deposits have been depleted through mining is well proven [9, 12, 13].

Because natural deposits of oil and gas have been stored by the carbon and oxygen cycle (see above) in NUGCs for thousands and millions of years, NUGCs have displayed the ability to store new CO2 injected into these formations for long periods of time with minimal leakage of CO2 back into the atmosphere. In addition to NUGCs where oil and gas deposits have been depleted, geologists and engineers can locate new NUGCs capable of storing large quantities of CO2 with minimal leakage for long time periods [9, 13].2

In order for carbon captured at the point source to be stored at long-term storage site, it must be transported from the point source to the storage site. The process for transport is generally to convert CO2 captured at the point source to a liquid through pressurization, and then move this liquid to the storage facility by truck, train, or pipeline. Assuming that NUGCs are used for long-term storage, the costs of carbon storage will mostly be the fixed and variable costs of converting CO2 to a liquid, transporting it to the storage site, and then injecting it into the NUGCs [9, 13]. After injecting the CO2 into an NUGC, the ongoing costs of storage should be minimal (e.g., limited to costs of monitoring for leakages).

The fixed costs of carbon storage (including transportation) include the costs of pressurized transport trucks and train cars, and the costs of installing a pipeline. Fixed costs also include the costs of any equipment needed to remove captured CO2 from a truck, train car, or pipeline and inject it into NUGCs. These fixed costs can be quantified by multiplying the units of equipment (e.g., transport truck or rail car) purchased by its market price per unit. The variable costs of carbon storage include payments to labor (e.g., workers who operate and main-

²As discussed in Section 2, natural chemical cycles covert carbon to hard rock and mineral deposits which further enhances long-term storage with minimal leakage.

tain trucks, trains, pipelines, and injection equipment), purchase of replacement parts, and the costs of fuel and power needed to operate and maintain trucks, trains, pipelines, and injection equipment. These variable costs can be quantified by multiplying the units employed (e.g., number of workers) or purchased (e.g., number of replacement parts) by the market wage rate for labor or the market price for replacements parts [8, 9, 13].

We can now define the total costs of carbon capture and storage (*T C*ccs) as

$$T\,\mathbf{C}\_{\rm as} = \left(T\,\mathbf{F}\,\mathbf{C}\_{\rm as}^{\rm c} + T\,\mathbf{V}\,\mathbf{C}\_{\rm as}^{\rm c}\right) + \left(T\,\mathbf{F}\,\mathbf{C}\_{\rm as}^{\rm T} + T\,\mathbf{V}\,\mathbf{C}\_{\rm as}^{\rm T}\right) + \left(T\,\mathbf{F}\,\mathbf{C}\_{\rm as}^{\rm s} + T\,\mathbf{V}\,\mathbf{C}\_{\rm as}^{\rm s}\right) \tag{1}$$

where

financed). The variable costs can be quantified by multiplying, say the units of absorption

In addition to the direct, out-of-pocket fixed and variable costs of carbon capture discussed above, there are also opportunity costs of human-engineered carbon capture. For example, from an energy use perspective, human-engineered carbon capture at an electricity power plant comes with an energy use cost in the form of electricity generation that must be given up in support of carbon capture at the plant. This so-called energy penalty can be quantified by multiplying the amount of electricity lost in order to support carbon capture times the market

After carbon is captured at a point source such as a coal-fired electricity power plant, it must be transported to and stored at a long-term storage site. At the time this chapter is being written, the most practical long-term storage sites appear to be various forms of natural underground geologic cavities (NUGCs). One option under this category is NUGC which once held crude oil and/or natural gas deposits but has been depleted through mining (e.g., oil and gas

to squeeze more oil and gas out of the resource deposit. Thus, the technology for injecting

Because natural deposits of oil and gas have been stored by the carbon and oxygen cycle (see above) in NUGCs for thousands and millions of years, NUGCs have displayed the ability to

In order for carbon captured at the point source to be stored at long-term storage site, it must be transported from the point source to the storage site. The process for transport is generally

this liquid to the storage facility by truck, train, or pipeline. Assuming that NUGCs are used for long-term storage, the costs of carbon storage will mostly be the fixed and variable costs

The fixed costs of carbon storage (including transportation) include the costs of pressurized transport trucks and train cars, and the costs of installing a pipeline. Fixed costs also include

line and inject it into NUGCs. These fixed costs can be quantified by multiplying the units of equipment (e.g., transport truck or rail car) purchased by its market price per unit. The variable costs of carbon storage include payments to labor (e.g., workers who operate and main-

²As discussed in Section 2, natural chemical cycles covert carbon to hard rock and mineral deposits which further en-

captured from point source emissions into NUGCs where oil and gas deposits have been

 back into the atmosphere. In addition to NUGCs where oil and gas deposits have been depleted, geologists and engineers can locate new NUGCs capable of storing large quantities

injected into these formations for long periods of time with minimal leakage

captured at the point source to a liquid through pressurization, and then move

to a liquid, transporting it to the storage site, and then injecting it into the

into an NUGC, the ongoing costs of storage should be

from a truck, train car, or pipe-

into operational oil and gas wells in order

chemicals purchased by the market price of chemicals per unit.

price of electricity [2, 9–11].

244 Recent Advances in Carbon Capture and Storage

CO2

of CO2

of CO2

store new CO2

to convert CO2

of converting CO2

NUGCs [9, 13]. After injecting the CO2

hances long-term storage with minimal leakage.

wells). Oil and gas companies already inject CO2

depleted through mining is well proven [9, 12, 13].

with minimal leakage for long time periods [9, 13].2

minimal (e.g., limited to costs of monitoring for leakages).

the costs of any equipment needed to remove captured CO2

*TF Cccs c* = is the total fixed costs of carbon capture at the point source;

*TV C*ccs *c* = the total variable costs of carbon capture at the point source;

*TF C*ccs *T* the total fixed costs of captured carbon transportation to storage site;

*TV C*ccs *T* the total variable costs of captured carbon transportation to storage site;

*TF C*ccs *s* the total variable costs of carbon storage at storage site;

*TV C*ccs *s* is the total variable costs of carbon storage at storage site.

With respect to economic efficiency, it is imperative we measure the marginal costs of human-engineered CCS. The short-run marginal costs (MCCCS) of human-engineered CCS are defined as

$$M\,\mathcal{C}\_{\rm ccs} = \frac{\partial T\,\mathcal{C}\_{\rm ccs}}{\partial Q\_{\rm O\_{i}}}\tag{2}$$

where *Q*CO2 = is the quantity of CO2 captured and stored.

#### **3.2. Measures of total marginal fixed costs and marginal variable costs**

In practice, there are two common measures used in the cost-benefit analysis to make per-unit CSS costs and benefits comparably equivalent for any given potential level of optimal quantities of carbon dioxide (CO2 ) being captured and stored. These units are measured through time and space either in millions of tons of carbon (MtC) or of CO2 (MtCO2 ) avoided per year, that is, MtC/year or MtCO2 /year.

As described above in the definition of the total costs of carbon capture and storage (TCCCS), TCCCS consists of total fixed costs and total variable costs of carbon capture at the point of source, captured carbon transportation to storage, and carbon storage at the storage site. With respect to economic efficiency, the marginal cost (MCccs) is the imperative measure of the costs of human-engineered carbon capture and storage technology. In this chapter, marginal costs of employed CCS technology (MCccs), as well as marginal benefits received from employed CCS technology (MBccs), are quantified as US dollar per ton carbon (\$/tC) or US dollar per ton carbon dioxide (\$/tCO2 ),3 where one ton of carbon equals 3.67 tons of carbon dioxide.4

According to recent literature, an estimated avoided total cost of CCS per unit (MCccs) is between US \$225/tC and \$315/tC (or US \$61/CO2 and \$86/tCO2 ), but a considerable reduction in MCccs can arise in the near future because of continuously technological improvements in CCS [8]. To give a breadth of findings, estimates of marginal cost avoided can be shared in three cost components: (1) marginal costs of carbon captured at the point of source, which range from US \$200/tC to \$250/tC [8]; (2) marginal costs of captured carbon transportation to storage, which range from US \$5/tC to \$10/tC per 100 km [8]5 ; and (3) marginal costs of carbon stored at the storage site, which range from US \$20/tC to \$55/tC [14].6


**4. Conclusions**

**Author Contributions:** Formal analysis (J.I.R.-S. and E.d-.l.M.-D.l.F.); Funding acquisition (J.I.R.-S.); Investigation (J.I.R.-S.); Methodology (J.I.R.-S. and E.D.l.M.-D.l.F.); Project administration (J.I.R.-S.); Supervision (J.I.R.-S.); Validation (E.D.l.M.-D.l.F.); Visualization (J.I.R.-S.); Writing—original draft (J.I.R.-S. and E.D.l.M.-D.l.F.); Writing—review & editing (J.I.R.-S. and E.D.l.M.-D.l.F.).

**Funding:** This research was funded by the Spanish Ministry of Economic Affairs and Competitiveness (MINECO), under the Spanish Plan of Scientific and Technical Research and Innovation (2013–2016) and European Fund Regional Development (FEDER) under grant number [HAR2015-63503-P].

**Acknowledgments:** We are very grateful to the Fundación Canaria Orotava de Historia de la Ciencia for permission to use the material of Project Betancourt available at their website. Also, we sincerely appreciate the work of the reviewers of this article.

**Conflicts of Interest:** The authors declare no conflict of interest.