Advanced In Vivo Heteronuclear MRS Approaches for Studying Brain Bioenergetics Driven by Mitochondria

Abstract

The greatest merit of in vivo magnetic resonance spectroscopy (MRS) methodology used in biomedical research is its ability for noninvasively measuring a variety of metabolites inside a living organ. It, therefore, provides an invaluable tool for determining metabolites, chemical reaction rates and bioenergetics, as well as their dynamic changes in the human and animal. The capability of in vivo MRS is further enhanced at higher magnetic fields because of significant gain in detection sensitivity and improvement in the spectral resolution. Recent progress of in vivo MRS technology has further demonstrated its great potential in many biomedical research areas, particularly in brain research. Here, we provide a review of new developments for in vivo heteronuclear ³¹P and ¹⁷O MRS approaches and their applications in determining the cerebral metabolic rates of oxygen and ATP inside the mitochondria, in both animal and human brains.

1. Introduction

1.1. Cerebral Bioenergetics and Brain Function

The brain is an extraordinary organ; with its unique structure and complex functions, it distinguishes itself from other organs in many aspects. Unlike cardiac and skeletal muscles, the brain does not perform mechanical work. The major cellular functions in the brain include excitation and conduction resulting in unceasing electrophysiological activities in normal brain, even at rest. These integrated neuronal activities are essential for performing brain functions. Nevertheless, to sustain these activities and functionalities, the brain has a high energy demand which is mainly fulfilled by the energy metabolism at the cellular level through adenosine triphosphate (ATP) production and utilization (1–8).

The vast majority of ATP formation relies on the oxidative phosphorylation occurring inside the mitochondria. The activity of cytochrome oxidase, a key mitochondrial enzyme of oxidative energy metabolism, is regulated by the cell functional activities and their energy demand (9, 10). At normal condition, the cerebral oxidative phosphorylation is expected to be tightly coupled and supported by the oxygen metabolism.

Figure 15.1 illustrates a simplified schema showing the major metabolic processes and ATP energy transportation occurring at various subcellular compartments and the associated hemodynamic processes for supporting normal brain function. Oxygen and glucose are the major chemical substrates for brain metabolism and they are continuously supplied by the circulating blood in the capillary bed. Glucose is first converted to two pyruvate molecules in the cytosol, then the pyruvate enters the mitochondria and is metabolized oxidatively with diffused oxygen molecules through the mitochondrial respiratory chain and the cytochrome oxidase enzyme resulting in substantial oxygen utilization and final products of water and CO₂ (i.e., Reaction 1 or R1 in Fig. 15.1). This oxygen metabolism is coupled with the oxidative phosphorylation for producing ATP from inorganic phosphate (Pi) and adenosine diphosphate (ADP) through the enzyme of F₁F₀-ATP_ase inside the mitochondria (i.e., Reaction 2 or R2 in Fig. 15.1). In general, the mitochondrial oxidative phosphorylation dominates up to 90% of ATP production (11). In contrast, ATP utilization mainly occurs in the cytosol space resulting in ADP and Pi products (i.e., Reaction 5 or R5 in Fig. 15.1), ultimately, providing chemical energy for supporting various cellular activities and brain functions, in which a significant amount of ATP energy is used for neuronal signaling. This ATP utilization is particularly essential for maintaining and restoring the Na⁺/K⁺ ion gradients across the cellular membranes through the enzyme of Na⁺/K⁺-ATP_ase as well as for supporting the signaling process (e.g., neuronal transmission and cycling) at resting and activated brain states (11–14).

Fig. 15.1.

Schematic diagram of simplified major brain network involving metabolisms and hemodynamics occurring in the capillary, subcellular compartments including the mitochondria and cytosol spaces. Oxygen dissociates from hemoglobin (Hb) and enters mitochondria and it is metabolized with pyruvate (Pyr) which is converted from glucose (Glc). This oxygen utilization via Reaction 1 (R1) is tightly coupled with four ATP reactions for generating ATP (R2), consuming ATP (R5), transporting and buffering ATP energy via the paired CK reactions (R3 vs. V4). These four ATP reactions constitute a chemical exchange network PCr↔ATP↔Pi. This neurovascular-metabolic coupled network is essential for brain function.

The high energy demand in the brain causes extremely fast chemical cycling among ATP, ADP and Pi, which requires rapid transportation of these phosphate components between the cytosolic and mitochondrial compartments. This energy transportation could be partially accomplished by phosphocreatine (PCr) through the reversible creatine kinase (CK) reaction, thus, maintaining a stable ATP level in the brain cells (15–17). There are at least two apparently coupled CK reactions: one occurring in the mitochondrial intermembrane space (i.e., Reaction 3 or R3 in Fig. 15.1) and another one occurring in the cytosol space (i.e., Reaction 4 or R4 in Fig. 15.1) although, in reality, these coupled CK reactions likely exist of these subcellular spaces. They play an important role in carrying the ATP molecules generated in the mitochondria into the cytosol for energy utilization, and then to bring the products of ADP and Pi back to mitochondria for sustaining ATP production. Therefore, PCr serves a vital role for energy transportation among subcellular compartments. Four ATP-related reactions (two reactions each for ATP_ase and CK) constitute a complex ATP metabolic process. They are tightly coupled and integrated with the oxygen metabolism and the hemodynamic process as depicted in Figure 15.1 for controlling the dynamics of ATP production and utilization, all of which play a central role in the cerebral bioenergetics and function in normal and diseased brains. Development of in vivo tools being able to noninvasively detect and quantify the cerebral metabolic rate of oxygen utilization (CMRO₂) and ATP formation (CMR_ATP), therefore, become extremely important for studying and understanding the relation between ATP metabolism and cerebral bioenergetics and its impact on brain function.

1.2. In Vivo Heteronuclear MRS Approaches for Studying Brain Bioenergetics and Function

Although there are a number of techniques capable of studying brain metabolism, in vivo heteronuclear magnetic resonance spectroscopy (MRS) allows for noninvasively determining the physiological parameters and their changes that can be linked to brain metabolism, chemical kinetics and cerebral bioenergetics. The most commonly used in vivo heteronuclear MRS approaches for studying brain bioenergetics are in vivo ³¹P, ¹³C and ¹⁷O MRS. Here, we will focus on ³¹P and ¹⁷O MRS in vivo.

In vivo ³¹P MRS allows noninvasive assessment of numerous fundamental biochemical, physiological and metabolic events occurring inside a living brain (e.g., (17–23)). The primary information provided by in vivo ³¹P MRS includes: intracellular pH, intracellular free magnesium concentration ([Mg²⁺]) and high-energy phosphate (HEP) metabolites such as ATP, ADP and PCr. All these phosphate metabolites (except ADP) and Pi can be directly observed in an in vivo ³¹P MR spectrum as demonstrated in Fig. 15.2A which was acquired from the human occipital-lobe at high field (7 tesla) (24). The pH value can be calculated from the chemical shift difference (δ_i) between the Pi and PCr resonance peaks according to the following equation: (25)

$$pH=6.77+\mathit{log}\left[\frac{{\delta }_i-3.29}{5.68-{\delta }_i}\right]$$ (15.1)

and [ADP] can be calculated by the following equation:

$$\left[\mathit{ADP}\right]=\frac{\left[\mathit{ATP}\right]\left(\left[Cr\right]-\left[\mathit{PCr}\right]\right)}{K_{eq}\left[\mathit{PCr}\right]\left[H^{+}\right]}$$ (15.2)

where K_eq is the equilibrium constant of the creatine kinase reaction and [Cr] is the total creatine concentration given by the summation of PCr and non-phosphorylated Cr.

Fig. 15.2.

(A) A typical ³¹P MR spectra acquired from the human occipital lobe at 7T with a total sampling time of 6.4 minutes. The spectrum is characterized by excellent spectral resolution and NMR sensitivity, and a large number of well-resolved resonance peaks from phosphoethanolamine (PE); phosphocholine (PC); inorganic phosphate (Pi); glycerophosphoethanolamine (GPE); glycerophosphocholine (GPC); phosphocreatine (PCr); adenosine triphosphate (ATP); nicotinamide adenine dinucleotides (NAD) and uridine diphospho sugar (UDP). Adapted from Lei et al. of Reference 24. (B) 3D ¹⁷O MRSI of natural abundance H₂ ¹⁷O (top row) and corresponding ¹H anatomical images (bottom row) of rat brain acquired at 9.4T. The ¹⁷O surface RF coil positions and cross sections are indicated in the images.

Besides the aforementioned phosphate compounds and physiological parameters, other detectable phosphate compounds in the human brain ³¹P MRS include: uridine diphospho (UDP) sugar (an important precursor for glycogen metabolism), diphospho nicotinamide adenine dinucleotides (NAD) involving oxidative respiratory chains, and four resolved phosphate compounds of glycerophosphoethanolamine (GPE), glycerophosphocholine (GPC), phosphoethanolamine (PE) and phosphocholine (PC), which are actively involved in the membrane phospholipid metabolism through phospholipid biosynthetic enzymes (26–29). In vivo ³¹P MRS has been widely applied to study both normal and diseased brains and has led to a large number of publications (e.g., (19, 21–24, 26–28, 30–42). The abnormality in the HEP metabolites has been frequently observed in the diseased brains using in vivo ³¹P MRS, and these changes or the change of HEP concentration ratios have been commonly applied in many clinical studies.

Although the steady-state concentrations of cellular HEP metabolites are closely linked to the ATP metabolism, they are relatively stable under normal physiological conditions. This could be attributed to the rigorous regulation of the ATP metabolic reactions and their kinetics (see Fig. 15.1) for maintaining stable chemical energy supply of ATP in the brain. This is likely the case for the brain activation caused by brain stimulation and task performance. Thus, the measurements of the kinetics of ATP metabolism (i.e. reaction rate constants and fluxes) should logically be more sensitive and meaningful for quantifying the cerebral bioenergetics and its change under varied brain activity states as compared to the measurement of steady-state ATP concentrations. In vivo ³¹P MRS, in combination with the magnetization transfer (MT) approach (18, 43–48), is capable of noninvasively determining the chemical reaction fluxes related to the ATP metabolism and enzyme activity; and thus becomes an important tool for studying the brain ATP metabolisms and cerebral bioenergetics. One example is to apply this approach for measuring the metabolic flux of oxidative phosphorylation in the brain (20,49,50). This useful in vivo approach and its new development will be described here.

Another alternative in vivo heteronuclear MRS approach which can directly and noninvasively assess the fluxes of oxidative metabolism occurring in the mitochondria (i.e., R1 in Fig. 15.1) is the use of in vivo ¹⁷O MRS approach for imaging CMRO₂ (e.g., (51–54) and a recent review article (55) and the references cited therein). The basic idea underlying this approach is to apply in vivo ¹⁷O MRS for detecting the dynamic change of the ¹⁷O-labeled metabolic water (H₂ ¹⁷O) produced through the metabolism of inhaled ¹⁷O₂ gas, and ultimately for determining and imaging CMRO₂. Recent progress, especially at ultrahigh fields, has advanced the in vivo ¹⁷O MRS methodology for imaging CMRO₂ and great promise has been demonstrated in the animal applications at high fields. This topic is also discussed here in some detail.

Although the metabolic fluxes measured by in vivo ³¹P MRS and in vivo ¹⁷O MRS reflect different metabolic reactions and pathways, these two MRS approaches are quite complementary. They are vital for investigating the coupling between the oxygen utilization and oxidative phosphorylation in the brain mitochondria under normal and pathological conditions.

2. Benefit of In Vivo ³¹P and ¹⁷O MRS at Ultrahigh Magnetic Field

2.1. Challenges of In Vivo Heteronuclear MRS

In practice, in vivo heteronuclear MRS faces many technical challenges due to its unfavorable sensitivity. For instance, the phosphate metabolites detected by in vivo ³¹P MRS and the metabolic H₂ ¹⁷O detected by in vivo ¹⁷O MRS are in a range of few millimolar concentrations, which are approximately 5000 times lower than the tissue water concentration, resulting in a much lower detection sensitivity. Thus, a high number of signal averaging is required to achieve reasonable spectral quality. This low sensitivity is even more manifest for the nuclear spins (e.g., ³¹P and ¹⁷O) with a relatively low magnetogyric ratio (γ) compared to in vivo ¹H MRS. This significantly limits the reliability, applicability, spatial and temporal resolutions of in vivo ³¹P and ¹⁷O MRS for general application, as well as clinical studies. One common trade off is to reduce the spatial and/or temporal resolution of in vivo MRS, thereby gaining detection sensitivity. However, in order to determine the nonuniform distribution of cerebral metabolites and chemical reaction fluxes in different brain regions, there is a high demand on improving the spatial resolution of in vivo MRS. Moreover, the dynamic changes caused by physiological perturbation (e.g., sensory stimulation) may occur in a relatively short time and the magnitudes of the changes are usually subtle compared to those observed under pathological states. Therefore, both reasonably high spatial and temporal resolutions are desired and they rely heavily on the achievable detection sensitivity, which poses the major challenge for in vivo heteronuclear MRS. One way to overcome this challenge is the use of high/ultrahigh field MRS. Besides the sensitivity gain at high fields, the spectral resolution of in vivo MRS is also significantly improved and many overlapped resonance peaks from different metabolites as observed at low fields become resolvable at ultrahigh fields as demonstrated in Fig. 15.2A.

2.2. Sensitivity Improvement of In Vivo Heteronuclear MRS at High Field

One of the most important advantages at ultrahigh fields is the potential gain in detection sensitivity. This is particularly crucial for the low γ nuclei MRS such as in vivo ¹⁷O and ³¹P MRS. However, it is not so straightforward to evaluate and compare detection sensitivity (or signal-to-noise ratio, SNR) at different magnetic field strengths (B₀). The apparent SNR achievable at a given field strength relies not only on the B₀ but also on other B₀-dependent parameters, such as the longitudinal relaxation time (T₁), the apparent transverse relaxation time (T₂*) and the repetition time (TR) for acquiring MRS signal. It is, in general, more useful to determine and evaluate the SNR of signal detected in a given unit sampling time under optimal acquisition condition, which means that the excitation flip angle (α) satisfies the Ernst equation of cos(α_opt) = exp(−TR/T₁) (56). For a simple case with the single pulse and data acquisition scheme, such an averaged SNR can be quantified by Eq. (15.3) (56–60),

$$\mathit{SNR}\left(\text{per unit sampling time}\right)\propto {C_{\gamma }}^{2.5}{B}_0^{\beta }{Q}^{1/2}{\left(\frac{T_2^{\ast }}{T_1}\right)}^{1/2}{(1-E_2^2)}^{1/2}G\left(x\right)$$ (15.3)

where

$$G\left(x\right)={\left[2\frac{1-e^{-x}}{x\left(1+e^{-x}\right)}\right]}^{1/2}x=\frac{\text{TR}}{{\mathrm{T}}_1}\text{and}{E}_2^2=\exp \left(-2\cdot a_t/T_2^{\ast }\right),$$ (15.4)

C is the concentration of the nuclear spin under observation; a_t is the spectrum acquisition time; Q is the radio frequency (RF) coil quality factor. C and γ are B₀-independent and can be treated as constants.

Equation (15.3) accounts for most B₀-dependent parameters that have influences in the apparent SNR, such as T₂* signal loss and the partial saturation effect on signal due to a relatively short TR of ≪ 5T₁. For in vivo ³¹P MRS applications, the term of ${(1-E_2^2)}^{1/2}G\left(TR/T_1\right)$ approximates to 1.0 (60), thus Eq. (15.5) is a simplification

$$\mathit{SNR}\left(\text{per unit sampling time}\right)\propto B_0^{\beta }{Q}^{1/2}{\left(\frac{T_2^{\ast }}{T_1}\right)}^{1/2},$$ (15.5)

or

$$\mathit{SNR}\left(\text{per unit sampling time}\right)\propto B_0^{\beta \ast }{\left(\frac{T_2^{\ast }}{T_1}\right)}^{1/2},$$ (15.6a)

if one applies the approximation of $Q\propto B_0^{1/2}$ resulting β* = β+1/4 (57,60). The values for β* and β based on the theoretical predictions are 1.75 and 1.5 respectively (57).

For precisely quantifying and understanding the sensitivity of in vivo ³¹P MRS as a function of magnetic field strength, it is necessary to quantify all B₀-dependent parameters used in Eq. (15.6A).

2.2.1. Field Dependence of in vivo ³¹P MRS Sensitivity

It has been demonstrated that both SNR and the quality of in vivo ³¹P MRS acquired in human brain are improved at higher fields (24,61–63). Recently, we have quantitatively measured and compared the values of T₁, T₂* and SNR of PCr resonance peak acquired from the human occipitallobe at 4 tesla and 7 tesla (60). We found that not only T₂* of PCr, but also T₁ of PCr (i.e. T_1,PCr) were shortened at 7 tesla compared to 4 tesla. This observation indicates that the field dependence of T_1,PCr is likely determined by two competing relaxation mechanisms, i.e. the chemical shift anisotropy (CSA) and the dipolar interaction that simultaneously influence the ³¹P longitudinal relaxation time (60,64,65). In the case with dominant CSA contribution, the T₁ value decreases with increasing field strength following the relation of $1/T_1\propto {\mathrm{B}}_0^2$; in contrast, the T₁ value increases with increasing field strength when the dipolar interaction mechanism dominates. The opposite trends between these two relaxation mechanisms lead to a decrease in T_1,PCr at higher field and offer an advantage for in vivo ³¹P MRS as a shorter repetition time can be employed which allows more signal averaging within the same sampling time; as a result, improving SNR and leading to a total SNR gain of 56% at 7T as compare to 4T. Moreover, the β value derived from the experimental measurements and Eq. (15.5) in this study was 1.4 (60). This value is in an excellent agreement with the theoretically predicted β value of 1.5 as described in the literature (57).

Another interesting observation of this study is that the linewidth broadening of the phosphate resonance peak with increased field strength is not linearly correlated with the field strength and, thus, at higher field strength, there is a small increase in the line width of phosphate signals (60). Moreover, higher field strength increases the chemical shift dispersion (i.e., in Hz unit) of in vivo ³¹P MRS linearly with field strength. The combination of these two factors (i.e., large increase in chemical shift dispersion and relatively small increase in linewidth broadening) improves the ³¹P spectral resolution at 7T (see Fig. 15.2A). This improvement makes it possible to resolve many adjacent phosphate metabolite resonance peaks (e.g., α-ATP versus NAD) and it is especially helpful for resolving the Pi peak from other adjacent resonance peaks. The well-resolved Pi peak is crucial for measuring the ATP production flux and will be discussed later.

2.2.2. Field Dependence of in vivo ¹⁷O MRS Sensitivity

¹⁷O is a stable oxygen isotope with a spin quantum number of 5/2 and detectable by ¹⁷O MRS. It possesses an electric quadrupolar moment and its natural abundance is only 0.037%, which is almost 30 times lower than that of ¹³C and 2700 times lower than that of ¹H. Moreover, the γ value of ¹⁷O is 7.4 times lower than that of ¹H. These factors attribute to the low inherent ¹⁷O sensitivity that might be the major obstacle for the development and application of in vivo ¹⁷O MRS approaches.

The relaxation mechanism of ¹⁷O spin is distinct from ³¹P spin. The ¹⁷O quadrupolar moment can interact with local electric field gradients and the temporal fluctuations of this interaction induced by molecular motion dominate the ¹⁷O relaxation processes and determine both T₁ and T₂ of H₂ ¹⁷O (66), where T₂ is the transverse relaxation time. Theoretically, the T₁, T₂ and T₂* values of ¹⁷O water spins are expected to be insensitive to B₀ (55, 66). We have experimentally investigated and compared the ¹⁷O relaxation times of the natural abundance H₂ ¹⁷O in rat brain at both 4.7 and 9.4 tesla. We confirmed that the ¹⁷O relaxation times are B₀-independent (67). Recent experimental evidence has indicated that the B₀-independence of ¹⁷O relaxivity can further extend to a much higher magnetic field, such as 17.6 tesla (68). The field independence of ¹⁷O relaxivity reveals that ¹⁷O sensitivity gain at higher fields is not compromised by the relaxation times, and this could lead to a substantial sensitivity gain when the field strength increases according to Eq. (15.6B) if the same acquisition parameters (e.g., TR and a_t) are applied at different field strengths,

$$\mathit{SNR}\left(\text{per unit sampling time}\right)\propto B_0^{\beta \ast }.$$ (15.6b)

Our experimental results showed approximately a four-fold SNR gain in the in vivo ¹⁷O MRS signal measured in the rat brain at 9.4 tesla compared to 4.7 tesla (67). Moreover, the β* value deduced from these experimental measurements and Eq. (15.6B) was ∼2 (67), which is close to the theoretically predicted β* value of 7/4 (57). The significant sensitivity gain provides adequate SNR for acquiring the 3 dimensional ¹⁷O MRS imaging of the natural abundance H₂¹⁷O from the small brain of rat with a temporal resolution of ∼10 seconds at 9.4T (see one example shown in Fig. 15.2B).

Clearly, the increase of B₀ should benefit all of the in vivo multinuclear MRS approaches. In vivo ¹⁷O MRS probably benefits the most from the substantial sensitivity gain at ultrahigh fields. On the other hand, in vivo ³¹P MRS can benefit from both the moderate sensitivity gain and the significant spectral resolution improvement, which is crucial for resolving many overlapping resonance peaks of different metabolites. All these benefits provided by high field strength are essential for improving the reliability of in vivo ¹⁷O and ³¹P MRS and for accurately determining cerebral metabolic fluxes.

3. How to Apply In Vivo ¹⁷O MRS for Imaging CMRO₂

In vivo ¹⁷O MRS methodology has two major applications for studying brain function and cerebral bioenergetics through imaging either cerebral blood flow (CBF) or CMRO₂ (51–55, 67, 69–87). Both applications rely upon the measurement of brain H₂ ¹⁷O content and its dynamic change using in vivo ¹⁷O MRS. The CBF measurement is based on monitoring the washout rates of inert H₂ ¹⁷O tracer in the brain tissue following an intravascular bolus injection of ¹⁷O-labeled water. The CMRO₂ measurement is based on monitoring the dynamic changes of metabolically generated H₂ ¹⁷O in the brain tissue from inhaled ¹⁷O-labeled oxygen gas (55). There are two types of magnetic resonance approaches for monitoring brain H₂ ¹⁷O in vivo: a direct approach by using ¹⁷O MRS detection, and an indirect approach by using ¹H magnetic resonance imaging (MRI) to measure the changes in T₂- or T_1ρ-weighted proton signals caused by the ¹⁷O-¹H scalar coupling and proton chemical exchange (see recent review article of (55) and the references cited therein). Both direct and indirect approaches are suitable for CBF measurements. However, recent studies indicated that the in vivo ¹⁷O MRS approach at ultrahigh fields seems to have more advantages for quantifying and imaging CMRO₂, which perhaps is the most important application of in vivo ¹⁷O MRS. Here, the in vivo ¹⁷O MRS approach for imaging CMRO₂ is described in detail.

3.1. Theory and Quantification of CMRO₂ Based on In Vivo ¹⁷O MRS Approach

In general, there is a similarity between in vivo ¹⁷O MRS approach and positron emission tomography (PET) approach (88–91) for measuring CMRO₂ through the use of isotropic labeled oxygen gas (¹⁷O₂ for MRS and ¹⁵O₂ for PET). After gas exchange in the lung, the inhaled and labeled O₂ molecules quickly bind to hemoglobin (Hb) in the blood, forming O₂-hemoglobin complexes (HbO₂) (see Fig. 15.1). Through the feeding arteries and arterioles, the HbO₂ complex enters the brain capillaries. The O₂ molecules are dissociated from hemoglobin in the capillaries, then cross the brain blood barrier (BBB) in the form of free gas, diffuse into the brain tissue (intra- and extracellular space), and finally enter mitochondria where they are metabolized and produce the water with the isotope label following the chemical reaction (3):

$$\text{Carbon substrate}+{\mathrm{O}}_2\to \text{Oxidized carbon substrate}+2{\mathrm{H}}_2\mathrm{O}$$ (15.7)

According to this reaction (equivalent to R1 in Fig. 15.1), one oxygen molecule produces two isotopic labeled water molecules (H₂ ¹⁷O for ¹⁷O MRS and H₂¹⁵O for PET), which can move out of the mitochondria (traversing the opposite pathway as O₂ entry) and finally be washed out from the brain through venules and veins. The dynamic change of the isotope labeled water in the brain is tightly linked to the cerebral oxygen utilization rate. It provides the vital signal source for determining CMRO₂ for both ¹⁵O PET and ¹⁷O MRS.

Though the principle underlying the ¹⁷O MRS approach for measuring CMRO₂ was historically adopted from the well-established ¹⁵O PET approach, there is significant distinction between these two neuroimaging approaches. For instance, one complication in PET is that it is unable to distinguish the ¹⁵O signal contribution from ¹⁵O₂ molecules versus the metabolically generated H₂¹⁵O molecules. This limits the robustness of PET technique for imaging CMRO₂ (55, 90). In contrast, the ¹⁷O MRS approach specifically detects the metabolically generated H₂¹⁷O without confounding signals from ¹⁷O₂ molecules because of the “invisibility” of ¹⁷O₂ in an in vivo ¹⁷O spectrum (55). This unique magnetic resonance specificity leads to a great advantage which significantly simplifies the in vivo ¹⁷O MRS methodology for measuring and quantifying CMRO₂ (55, 87). Nevertheless, the dynamic change of the metabolically generated H₂¹⁷O concentration in the brain during an ¹⁷O₂ inhalation is interplayed by three parallel processes (see Fig. 15.3): (i) Cerebral oxygen utilization for generating the metabolic H₂ ¹⁷O in the brain tissue, (ii) Cerebral blood perfusion resulting in H₂ ¹⁷O washout from the brain, and (iii) Blood recirculation bringing the metabolically generated H₂ ¹⁷O in the entire body back to the brain. All contributions from these three processes have to be considered for quantifying CMRO₂. Based on the Kety – Schmidt theory (92–94), the mass balance of the isotope labeled H₂¹⁷O in the brain tissue during an ¹⁷O₂ gas inhalation can be derived as (52,54,55,87):

$$\frac{\mathit{dCb}\left(t\right)}{\mathit{dt}}=2\alpha f_1\mathit{CMR}{O}_2+\mathit{mCBF}\left(f_{2}Ca\left(t\right)-\frac{\mathit{nCb}\left(t\right)}{\mathrm{\lambda }}\right)$$ (15.8)

where C_a(t), C_b(t) and C_v(t) are the metabolic H₂¹⁷O concentrations in excess of the natural abundance of H₂¹⁷O concentration in the arterial blood, brain tissue and venous blood respectively, as a function of ¹⁷O₂ inhalation time (t, unit = minute); α is the ¹⁷O enrichment fraction of the oxygen atoms in the inhaled ¹⁷O₂ gas; λ is the brain/blood partition coefficient (95). The factor of two accounts for the fact that one O₂ converts to two H₂O molecules through oxidative metabolism according to Eq. (15.7); f₁ and f₂ are two unit conversion factors (54, 87). The correction factor m is used in Eq. (15.8) to account for the water permeability restriction across the brain blood barrier (96), and n is another correction factor that accounts for the permeability restriction occurring when H₂ ¹⁷O molecules which are metabolically generated inside the mitochondria across the mitochondrial membranes (54,87). Both m and n depend on CBF (54,87). The function of C_a(t) (or artery input function) is determined by the total metabolic H₂¹⁷O generated in all aerobic organs of a living body. It can approximate as a linear function of ¹⁷O₂ inhalation time (i.e., C_a(t)=At, A is a constant) (52, 54, 78, 87). Under this approximation, the solution for solving the differential equation of Eq. (15.8) is:

$$\mathit{CMR}{O}_2\left(t\right)=\frac{\left\{\left[\frac{C_b\left(t\right)-\frac{A{f}_2{\mathrm{\lambda }}^2}{m{n}^2\mathit{CBF}}\left(\frac{\mathit{mnCBF}}{\mathrm{\lambda }}t{e}^{-\frac{\mathit{mnCBF}}{\mathrm{\lambda }}t}+e^{-\frac{\mathit{mnCBF}}{\mathrm{\lambda }}t}-1\right)}{1-e^{-\frac{\mathit{mnCBF}}{\mathrm{\lambda }}t}}\right]-\frac{A{f}_2\mathrm{\lambda }t}{n}\right\}}{\frac{2\alpha \mathrm{\lambda }{f}_1}{\mathit{mnCBF}}}.$$ (15.9)

According to this equation, the CMRO₂ value at each data point measured at different inhalation time (t) can be calculated by using the experimentally measured CBF, A, n, C_b(t) values and other known constants (f₁, f₂, m, α and λ). The quantification approach based on Eq. (15.9) is a complete model which accounts for all required parameters for precisely determining CMRO₂ (54,55,87).

Fig. 15.3.

Schematic illustration of a “complete model” describing three parallel processes of the ¹⁷O -labeled metabolic water (H₂ ¹⁷O) occurring in the brain when the ¹⁷O-labeled oxygen gas molecules are introduced via an inhalation. In this model, only the metabolic H₂ ¹⁷O is considered because the ¹⁷O-labeled O₂ is invisible by in vivo ¹⁷O NMR. Ca(t), Cb(t) and Cv(t) stand for the H₂ ¹⁷O concentration in arteriole, brain tissue and venule, respectively, as a function of the ¹⁷O₂ inhalation time.

3.2. Measurement and Imaging of CMRO₂ using In Vivo ¹⁷O_MRS Approach

The complete model as described by Eq. (15.9) requires multiple experimental measurements of four variables (A, n and C_b(t) and CBF) in order to calculate CMRO₂. Figure 15.4 illustrates the procedures for performing these in vivo ¹⁷O MRS measurements and the results of a rat brain study with α-chloralose anesthesia at 9.4 T (54,55).

Fig. 15.4.

Schematic diagram showing the multiple in vivo ¹⁷O measurements for determining CMRO₂ using the complete model according to the mass balance equation of Equation (15.8) which links Cb(t), Ca(t), CBF and n with CMRO₂. To simplify the equation, three known constants of 2α₁, mf₂ and m/λ used in Equation (15.8) are replaced by k1, k2 and k3, respectively. (A) Stacked plot of the ¹⁷O spectra of cerebral H₂ ¹⁷O tracer from one representative rat brain voxel as indicated by the circle in the anatomical image (low center insert). The spectra were acquired before and after a bolus injection of H₂ ¹⁷O for CBF measurements. (B) Stacked plot of the ¹⁷O spectra of the metabolic H₂ ¹⁷O from the same representative voxel acquired before (natural abundance), during (as indicated by the gray bar under the stacked plot) and after a two-minute ¹⁷O₂ inhalation. (C) Measurement of Ca(t) by using an implanted ¹⁷O RF coil (the left insert). The middle insert illustrates a ¹⁷O spectrum of natural abundance H₂ ¹⁷O obtained from the rat carotid artery blood by using the implanted RF coil before H₂¹⁷O inhalation. The right insert shows the time course of Ca(t) (circle symbol) and Cb(t) from a representative 3D ¹⁷O CSI voxel (square symbol) in the same rat during a two-minute inhalation of ¹⁷O₂. Finally, the ratio between the ¹⁷O signal decay detected after a bolus injection of H₂ ¹⁷O (see Fig. 15.4A) versus the ¹⁷O signal decay detected after the cessation of ¹⁷O₂ inhalation (see Fig. 15.4B) gives the constant of n. Adapted from Zhu et al. of Ref (54).

3.2.1. Imaging CBF

The CBF measurement was performed via bolus injection of a small amount of ¹⁷O-enriched water into one internal carotid artery and monitoring the washout process of the H₂ ¹⁷O tracer in the brain using 3 dimensional ¹⁷O chemical shift imaging (CSI) (67). Figure 15.4A demonstrates the stacked plots of H₂ ¹⁷O spectra acquired from a single voxel (as indicated in the brain anatomy image) of 3 dimensional ¹⁷O CSI data set in a representative rat before and after the H₂ ¹⁷O bolus injection. The peak height of the H₂ ¹⁷O spectra shows an exponential decay and its decay rate determines the CBF value in the CSI voxel (54,55,67).

3.2.2. Imaging C_b(t)

The crucial step for CMRO₂ measurements is to monitor and image the dynamic changes of the metabolic H₂ ¹⁷O content in the brain (i.e., C_b(t)) during an inhalation of ¹⁷O₂ gas. Figure 15.4B illustrates the stacked plots of ¹⁷O spectra of cerebral H₂ ¹⁷O from the CSI voxel acquired before, during and after a 2-minute inhalation of ¹⁷O₂ (54). It indicates excellent ¹⁷O sensitivity for detecting the cerebral H₂ ¹⁷O signal and its change during the inhalation; and the approximately linear increase of H₂ ¹⁷O during a short ¹⁷O₂ inhalation is evident, and the slope is tightly coupled to CMRO₂.

One practical challenge for most in vivo MRS approaches is the difficulty for measuring the absolute concentrations of metabolites of interest. Nevertheless, the natural abundance H₂ ¹⁷O signal which can be accurately measured in the brain before the introduction of ¹⁷O-labeled oxygen gas (see Fig. 15.4B) provides an excellent internal reference for quantifying the absolute concentration of C_b(t) for each CSI voxel (54, 87). This self-calibration method is independent of the ¹⁷O detection sensitivity. This is particularly valuable when a surface RF coil with nonuniform spatial distribution of detection sensitivity is applied.

3.2.3. Other Measurements

The arterial input function of C_a(t) was measured in vivo by an implanted ¹⁷O RF coil (97) wrapped around a carotid artery (in the rat). Figure 15.4C illustrates the implanted ¹⁷O RF coil, the natural abundance H₂ ¹⁷O signal detected from the rat carotid blood and C_a(t) measured during a two-minute inhalation of ¹⁷O₂ (54). The experimental result showed an approximately linear relation between the arterial H₂ ¹⁷O concentration and the ¹⁷O₂ inhalation time, and the linear fitting of C_a(t) gave the value of constant A required by Eq. (15.9). Note that the C_a(t) (see Fig. 15.4C) and C_b(t) (see Fig. 15.4B) measurements could be conducted simultaneously with the configuration of dual ¹⁷O RF coils and receivers (97).

Finally, the ratio between the decay rates of H₂ ¹⁷O signal measured after the cessation of ¹⁷O₂ inhalation (see Fig. 15.4B) versus that after a H₂ ¹⁷O bolus injection (see Fig. 15.4A) gives the constant of n, reflecting the H₂ ¹⁷O permeability restriction across the mitochondrial membranes (54,87).

3.2.4. Imaging CMRO₂ in Rat Brain

The values of C_b(t), CBF and n measured from each ¹⁷O MRS imaging (MRSI) voxel and the value of A measured from each ¹⁷O inhalation measurement in the same animal as demonstrated in Fig. 15.4 can be used to calculate the absolute CMRO₂ value as a function of inhalation time according to Eq. 15.9. Figure 15.5A shows one example of CMRO₂ time course from a representative ¹⁷O MRSI voxel with a temporal resolution of 11 seconds (54). It is evident that the CMRO₂ values are independent of ¹⁷O₂ inhalation time if the first two CMRO₂ values characterized with relatively large fluctuations are excluded. These CMRO₂ values were averaged for improving measurement accuracy. The same procedure and calculation can be applied to all ¹⁷O MRSI voxels for generating 3D CMRO₂ images in the rat brain (54, 77). Figure 15.5B demonstrates three adjacent CMRO₂ images in the coronal orientation from a representative rat brain. The averaged CMRO₂ and CBF values in the rat brains anesthetized with α-chloralose were 2.19 ± 0.14 μmol/g/min and 0.53 ± 0.07 ml/g/min (n=7), respectively (54). The CMRO₂ value is consistent with the reported values in the literature, which were measured by other independent techniques under similar physiological condition (98–100).

Fig. 15.5.

(A) Plot of the calculated CMRO₂ values using the complete model as described by Equation (15.9) as a function of ¹⁷O₂ inhalation time. (B) Three-dimensional coronal CMRO₂ images of rat brain measured by in vivo ¹⁷O MRS approach during a two-minute ¹⁷O₂ inhalation. Adapted from Zhu et al of Ref. (s). (See Color Plate)

3.3. Establishing a Robust and Noninvasive ¹⁷O MRS Approach for Imaging CMRO₂

3.3.1. Noninvasive Approach

The major technical limitation of the complete model for determining CMRO₂ using in vivo ¹⁷O MRS is the requirement of invasive measurements (e.g., CBF, C_a(t), n). This could significantly limit the potential of this in vivo approach for broad biomedical applications, especially in humans. Thus, it is crucial to examine the feasibility of developing a completely noninvasive ¹⁷O approach for imaging CMRO₂. Attempts have been made to simplify the experimental procedures and the models for determining CMRO₂ based on a number of approximations (52, 53, 73, 79, 81, 87). We discuss one of these models, in which the invasive measurements could be eliminated by using the simplified model based on the Taylor’s and Polynomial Theorems (87). Briefly, the C_b(t) time course can be expressed by a polynomial expansion

$${\mathrm{C}}_{\mathrm{b}}\left(\mathrm{t}\right)={\mathrm{a}}_1{\text{t+a}}_2{\mathrm{t}}^2+{\mathrm{a}}_3{\mathrm{t}}^3+\cdots .$$ (15.10)

In this expansion, the first-order (or linear) coefficient of a₁ is directly proportional to CMRO₂ according to the following equation (87)

$${\text{CMRO}}_2=\frac{{\mathrm{a}}_1}{2\alpha {\mathrm{f}}_1}$$ (15.11)

where α and f₁ are known constants (see above). Thus, using this simplified model, only the time course of C_b(t) measured noninvasively by in vivo ¹⁷O CSI approach is needed and it can be fitted to the polynomial function given by Eq. (15.10) to calculate the linear coefficient of a₁, and ultimately determining CMRO₂ according to Eq. (15.11). For practical applications, a quadratic polynomial function provides a good approximation for fitting the time course of C_b(t) with moderate measurement fluctuation (101). We have demonstrated that the CMRO₂ value obtained based on the complete model with invasive procedures has no statistical difference from that based on the simplified model and quadratic function fitting where only a single noninvasive measurement of C_b(t) is required (87). Moreover, our results also validated that the linear fitting of C_b(t) could provide a good approximation for determining CMRO₂ in the rat brain when the ¹⁷O₂ inhalation time is relatively short (e.g., 2 minutes) (87). This is consistent with the prediction based on either Eq. (15.8) or (15.10). During the initial ¹⁷O₂ inhalation period, both C_a(t) and C_b(t) have not built up significantly resulting in near zero value of the second term on the right side of Eq. (15.8). Therefore, Eq. (15.8) can be approximated as a linear differential equation, and C_b(t) becomes a linear function of the inhalation time. This is also evident in Eq. (15.10) in which the high-order terms become negligible when t is short. Therefore, it is possible to use the simplified model for determining and imaging CMRO₂ based on a single and completely noninvasive ¹⁷O spectroscopic imaging measurement of C_b(t) (55,86,87).

Recently, we have further examined the simplified model for determining CMRO₂ under varied physiological conditions (86). In this study, we compared the CMRO₂ results obtained with the complete model versus the simplified model using linear fitting of C_b(t) under normothermia (37°C) condition and hypothermia (32°C) condition, which is a well known factor leading to significant suppression of both CBF and CMRO₂. Figure 15.6 demonstrates an excellent consistency of the CMRO₂ results between the complete and simplified models for either the voxel-wised comparison (Fig. 15.6A) or the averaged CMRO₂ comparison (Fig. 15.6B) at both brain temperatures (86). The comparison results reveal the validity of the simplified ¹⁷O approach for imaging CMRO₂ applicable at a wide physiological range. Additional technical development which further advances the in vivo ¹⁷O methodology could ultimately provide the simplest and completely noninvasively ¹⁷O neuroimaging approach for imaging CMRO₂ (in humans).

Fig. 15.6.

(A) Voxel based CMRO₂ calculation and comparison using the completed and simplified models from a representative rat (total voxel number used was 224 for 32°C and 254 for 37°C, voxel size = 75μ). (B) Averaged CMRO₂ values in the same rat brain at normothermia (37°C) and hypothermia (32°C) conditions, calculated with simplified and completed model, respectively. Adapted from Zhu et al of Ref. (86).

3.3.2. Robustness and Reliability

Another merit of the ¹⁷O CMRO₂ imaging approach is its ability for performing repeated CMRO₂ imaging measurements with a short interval between two measurements. This is due to the fact that the cerebral H₂ ¹⁷O concentration can quickly reach a new and steady level within a few minutes after the cessation of ¹⁷O₂ inhalation, which allows repeated CMRO₂ measurements in the same subject and experimental session (see Fig. 15.7A). Figure 15.7B shows the excellent reproducibility of repeated CMRO₂ measurements in five rats (1st and 2nd measured CMRO₂ values were 2.26 ± 0.18 and 2.20 ± 0.14 μmol/g/min giving a ratio of 1.03 ± 0.05 between the consecutive measurements) (86). The results demonstrate the robustness and reliability of the simplified in vivo ¹⁷O approach for noninvasively and rapidly imaging CMRO₂ repeatedly in a small brain of rat. This capability is particularly valuable for studies aiming at CMRO₂ changes induced by physiological or pathological perturbations in which multiple measurements are required under different conditions (e.g., control versus stimulation for brain function study). Therefore, the combination of the simplified model and ultrahigh field in vivo ¹⁷O MRS may potentially provide an alternative neuroimaging modality for studying the central role of oxidative metabolism in brain function and neurological diseases (55,77).

Fig. 15.7.

(A) Stacked plots of H₂¹⁷O spectra from a representative voxel of 3D ¹⁷O MRSI data acquired before, during and after two consecutive two-min ¹⁷O₂ inhalations in a rat brain. (B) The comparison results between two repeated CMRO₂ measurements in five rat brains. Adapted from Zhu et al of Ref. (86).

3.3.3. Demonstration of in vivo ¹⁷O MRS Application for Studying Brain Bioenergetics

It is well documented that the basal CMRO₂ is sensitive to the brain temperature (see (3, 102) and the references cited therein). However, most studies reported in the literature were based on the global CMRO₂ measurements of entire brain using the Kety-Schmidt method (92, 93), and were limited by the lack of spatial information regarding regional CMRO₂. We have conducted a CMRO₂ imaging study using 3D in vivo ¹⁷O CSI combined with the simplified model at 9.4 tesla for quantifying absolute CMRO₂ values in the rat brain at normal brain temperature (37°C) (i.e., normothermia) and mild hypothermia (32°C) conditions (86). Figure 15.8A illustrates an example showing three representative slices of 3D CMRO₂ maps from a rat brain under normothermic and hypothermic conditions. These images clearly show significant reduction of CMRO₂ crossing the entire brain induced by lowering brain temperature several degrees. This metabolic suppression occurring at hypothermia was consistently observed in all five rats studied (Fig. 15.8B), resulting in an average of 45% CMRO₂ reduction as compared to normothermic condition (86). These results indicate that the established in vivo ¹⁷O MRS approach is sensitive to determine the dynamic CMRO₂ change and its spatial distribution due to physiological perturbation. The measured CMRO₂ can be quantitatively correlated to other associated physiological parameter changes. Figure 15.9 illustrates one example showing the quantitative relation between CMRO₂ and CBF: both of them were measured by in vivo ¹⁷O MRS in the α-chloralose anesthetized rat under a wide range of physiological conditions from normothermia to hypothermia (86). It shows a strong correlation between CBF and CMRO₂ with a linear correlation coefficient of R = 0.97 indicating a tight vascular-metabolic coupling in the rat brain.

Fig. 15.8.

(A) 3D CMRO₂ maps of a representative rat brain obtained at normothermia (left column) and hypothermia (right column), and their corresponding anatomic images (middle column). (B) Summary of CMRO₂ results measured at normothermia and hypothermia conditions (n = 5). Adapted from Zhu et al of Ref. (86). (See Color Plate)

Fig. 15.9.

Correlation of CBF and CMRO₂ values in the rat brains anesthetized with α-chloralose at brain temperature range of 32–37°C. The linear correlation coefficient (R) was 0.97. Adapted from Zhu et al. of Ref. (86).

4. How to Apply In Vivo ³¹P MRS for Studying Cerebral ATP Metabolic Fluxes and Bioenergetics

The ATP metabolism for regulating both ATP production and utilization plays a fundamental role in cerebral bioenergetics, brain function and neurodegenerative diseases. Two important chemical reactions that contribute to the brain ATP metabolism are the ATP_ase and CK reactions. They are coupled together and constitute a three-³¹P-spin chemical exchange system involving ATP, PCr and Pi (i.e., PCr↔ATP↔Pi). One vital function of this exchange system is to maintain a stable cellular ATP concentration ensuring continuous energy supply for sustaining electro-physiological activity in the brain. Logically, the measures of ATP metabolic fluxes should be more sensitive to the brain activity and energy state and their change than that of steady-state ATP and other HEP concentration. Therefore, they should provide a useful index reflecting cerebral bioenergetics under various brain states. It would be, thus, essential to find a noninvasive and reliable technique being able to assess the cellular exchange rates (or fluxes) of PCr↔ATP↔Pi in brain in situ. The sole approach for serving this purpose is the use of in vivo ³¹P MRS combined with magnetization transfer method (20,43–47,50,103). However, to completely determine the kinetics and fluxes involved in the PCr↔ATP↔Pi exchange requires extensive measurements and information including three steady-state phosphate metabolite concentrations (i.e., [ATP], [PCr] and [Pi]) and their intrinsic T₁ values, and four pseudo first-order chemical reaction rate constants (forward and reverse rate constants for the CK reaction and the ATP_ase reaction, respectively) (50). The products of the rate constants and their related phosphate concentrations can provide four ATP metabolic fluxes along both forward and reverse reaction directions in the PCr↔ATP↔Pi exchange system (see Fig. 15.10).

Several in vivo ³¹P MT methods have been developed such as conventional two-spin magnetization saturation transfer (CST), inversion recovery transfer (IT) and two-dimensional chemical exchange spectroscopy (2D-EXSY) (44, 45, 49, 104). They have been applied to physiological studies of ATP metabolism in a variety of organs, from hearts to brains (20, 24, 45, 46, 49, 50, 103, 105–111). Among these methods, the CST method is most commonly used in biomedical research, perhaps due to its methodological simplicity and high efficiency. This method is particularly useful in measuring the forward rate constants and fluxes in the chemical exchange system of PCr↔ATP↔Pi when a frequency-selective RF saturation pulse train is applied to fully saturate the γ-ATP spin. Under this circumstance, the three-spin chemical exchange system of PCr↔ATP↔Pi can be treated as two independent two-spin chemical exchange systems (i.e., PCr↔ATP and ATP↔Pi); consequently, the forward rate constants and fluxes for both the CK reaction (i.e., R4 in Figs. 15.1 and 15.13) and ATP_ase reaction (i.e., R2 in Figs. 15.1 and 15.13) can be explicitly determined. These forward metabolic fluxes reflect the ATP synthesis or production rates catalyzed by ATP_ase and CK, respectively. However, the measurements of the reverse CK flux (ATP→PCr) using CST (i.e., by saturating PCr) resulted in an inequality between the forward and reverse CK fluxes (112–114), which is paradoxical, in the sense that the CK fluxes into and out of the PCr pool must be equal when the CK reaction is under chemical equilibrium condition. One possible explanation is that the ATP metabolism involves other chemical exchange reactions besides the CK reaction, for example the ATP hydrolysis reaction (115). Consequently, neglecting ATP hydrolysis may lead to an error in estimating the reverse CK flux. Therefore, it is necessary to consider PCr→ATP↔Pi as a three-spin chemical exchange system in order to accurately determine all kinetic parameters; in particular, the reverse rate constants and fluxes (45,46,50,115,116).

Fig. 15.13.

Chart showing the three-step measurements of in vivo ³¹P MSS MT approach for determining the entire ATP kinetic network and associated metabolic rate constants and fluxes, and the measurement results from the human occipital lobe. Step 1 measures two forward reactions (R2 and R4) along the solid arrows. Step 2 measures the indirectly coupled reverse reaction (R3) along the double-line arrows. Step 3 measures another reverse reaction (R5) along the dotted-line arrows. All results point to the fact that flux ratios satisfy the chemical equilibrium condition.

We will discuss a newly introduced in vivo ³¹P MT approach being able to noninvasively study the PCr↔ATP↔Pi exchange in the brain explicitly through the in vivo measurements of the following rate constants and fluxes associated with four coupled reactions in different subcellular compartments (50):

1. The forward flux $(F_f^{{\mathit{ATP}}_{\mathit{ase}}})$ of ATP_ase reaction (i.e., R2 in Figs. 15.1 and 15.13) occurring inside the mitochondria;

2. The forward flux $(F_f^{\mathit{CK}})$ of CK reaction (i.e., R4 in Figs. 15.1 and 15.13),

3. The reverse flux $(F_r^{{\mathit{ATP}}_{\mathit{ase}}})$ of ATP_ase reaction (i.e., R5 in Figs. 15.1 and 15.13) occurring in the cytosol space;

4. The reverse flux $(F_r^{\mathit{CK}})$ of CK reaction (i.e., R3 in Figs. 15.1 and 15.13).

4.1. In vivo ³¹P MT Approach for Determining Entire PCr↔ATP↔Pi Exchange

A newly introduced in vivo ³¹P MT approach for determining all kinetic parameters of the PCr↔ATP↔Pi exchange is called the Multiple Single-site Saturation (MSS) MT approach (50). The MSS approach requires a total of four in vivo ³¹P spectra: one control spectrum in the absence of RF saturation plus three single-site, RF-saturated spectra with the saturation frequency on PCr, γ-ATP and Pi, respectively (50). The quantification of the ATP metabolic fluxes relies on solving three coupled Bloch equations based on the three-spin chemical exchange model. For simplifying the mathematical derivation, the symbols of a, b and c were used which stand for PCr, ATP and Pi, respectively. The Bloch equations describing the magnetizations of a, b and c and their changes as a function of time are given by (43),

$$\begin{array}{r}\mathrm{PCr}\underset{k_1}{\overset{k_{-1}}{\rightleftarrows }}\gamma -\mathit{ATP}\underset{k_2}{\overset{k_{-2}}{\rightleftarrows }}{P}_i\\ abc\\ \frac{d{M}_a}{\mathit{dt}}=-\frac{(M_a-M_a^0)}{T_{1a}}-k_1{M}_a+k_{-1}{M}_b\end{array}$$ (15.12a)

$$\frac{d{M}_b}{\mathit{dt}}=-\frac{(M_b-M_b^0)}{T_{1b}}-k_{-1}{M}_b-k_2{M}_b+k_1{M}_a+k_{-2}{M}_c$$ (15.12b)

$$\frac{d{M}_c}{\mathit{dt}}=-\frac{(M_c-M_c^0)}{T_{1c}}-k_{-2}{M}_c+k_2{M}_b$$ (15.12c)

where M_a, M_b and M_c are the magnetizations of PCr, γ-ATP and Pi; $M_a^0$, $M_b^0$ and $M_c^0$ are the magnetizations at Boltzmann thermal equilibrium; k₁ and k₋₂ are the pseudo first-order forward rate constants involving ATP production through the CK reaction and the ATP_ase reaction, respectively; k₋₁ and k₂ are the pseudo first-order reverse rate constants involving ATP utilization through the CK reaction and the ATP_ase reaction, respectively; T_1a, T_1b and T_1c are the intrinsic spin-lattice relaxation times of PCr, γ-ATP and Pi, which are B₀ dependent. Four rate constants involving the PCr↔ATP↔Pi exchange and their four associated ATP metabolic fluxes can be determined by the following three-step measurements with frequency-selective RF saturation on the γ-ATP (Step 1), Pi (Step 2) and PCr (Step 3) resonance peak, respectively.

Step 1: Progressive saturation of γ-ATP for determining intrinsic spin-lattice relaxation times of PCr and Pi, forward rate constants and fluxes

The first step of the ³¹P MT measurements is to apply a frequency-selective RF pulse train for completely saturating the γ-ATP resonance peak with varied saturation time (t) (i.e., the progressive saturation experiment commonly used in the CST approach). For this case, the three-spin chemical exchange system of PCr↔ATP↔Pi can be treated as two independent two-spin chemical exchange systems (i.e., PCr↔ATP and ATP↔Pi) Solving Eqs. (15.12a) and (15.12c) with the boundary condition of Mb = 0 results in Eqs. (15.13a) and (15.13b) (47),

$$M_a\left(t\right)=M_a^0\left[\left(\frac{k_1}{{\alpha }_a}\right)e^{-{\alpha }_{a}t}+\left(\frac{1}{{\alpha }_a{T}_{1a}}\right)\right]$$ (15.13a)

$$M_c\left(t\right)=M_c^0\left[\left(\frac{k_{-2}}{{\alpha }_c}\right)e^{-{\alpha }_{c}t}+\left(\frac{1}{{\alpha }_c{T}_{1c}}\right)\right]$$ (15.13b)

with

$${\alpha }_a=\frac{1}{T_{1a}^{\mathit{app}}}=\left(k_1+\frac{1}{T_{1a}}\right);{\alpha }_c=\frac{1}{T_{1c}^{\mathit{app}}}=\left(k_{-2}+\frac{1}{T_{1c}}\right).$$

Therefore, the parameters of apparent spin-lattice relaxation rates (α_a and α_c) and intrinsic spin-lattice relaxation times (T_1a and T_1c) at a given B₀ can be determined via regressions as a function of t, where both k₁ and k₋₂ are replaced by their apparent spin-lattice relaxation rate and intrinsic spin-lattice relaxation time (see Eqs. (15.13a) and (15.13b)). Then, the forward rate constants (k₁ and k₋2) can be calculated by their relations with the apparent spin-lattice relaxation rate and intrinsic spin-lattice relaxation time as depicted above.

When a steady-state condition is approached with complete saturation of γ-ATP (i.e., dM_a/dt = 0 and dM_c/dt = 0), Eqs. (15.13a) and (15.13b) can be further simplified to the following formulae:

$$k_1=\frac{M_a^0-M_a^{\ast b}}{M_a^0}{\alpha }_a=\frac{M_a^0-M_a^{\ast b}}{T_{1a}{M}_a^{\ast b}}$$ (15.13c)

$$k_{-2}=\frac{M_c^0-M_c^{\ast b}}{M_c^0}{\alpha }_c=\frac{M_c^0-M_c^{\ast b}}{T_{1c}{M}_c^{\ast b}}$$ (15.13d)

where $M_a^{\ast b}$ and $M_c^{\ast b}$ are the steady-state magnetizations of a and c when b is fully saturated. Therefore, the forward rate constants of k₁ and k₋₂ can be calculated by using Eqs. (15.13c) and (15.13d). For this case, only two steady-state spectra acquired in the presence and absence of saturating b are needed to determine both k₁ and k₋₂, if T_1a and T_1c have already been determined at a given B₀ through the progressive saturation measurement accordingly to Eqs. (15.13a) and (15.13b). Finally, the forward fluxes for the CK and ATP_ase reactions can be determined by the following relations,

$$F_f^{\mathit{CK}}=k_1\left[\mathit{PCr}\right]\text{and}{F}_f^{{\mathit{ATP}}_{\mathit{ase}}}=k_{-2}\left[Pi\right]$$ (15.13e)

Step 2: Steady-state saturation of Pi for determining CK reverse rate constant and flux

The second step of the in vivo ³¹P MSS MT measurements is to apply a frequency-selective RF pulse train for completely saturating the Pi resonance peak with a sufficiently long saturation time resulting in steady-state magnetizations of a and b. For this case, M_c = 0, dM_a/dt = 0, dM_b/dt = 0, and Eqs. (15.12a) and (15.12b) yield

$$k_{-1}={\alpha }_a\left(\frac{M_a^{\ast c}}{M_a^0}-\frac{1}{T_{1a}{\alpha }_a}\right)\frac{M_a^0}{M_b^{\ast c}}$$ (15.14a)

$$k_1={\alpha }_b\left(\frac{M_b^{\ast c}}{M_b^0}-\frac{1}{T_{1b}{\alpha }_b}\right)\frac{M_b^0}{M_a^{\ast c}}$$ (15.14b)

with

$${\alpha }_b=\frac{1}{T_{1b}^{\mathit{app}}}=\left(k_2+k_{-1}+\frac{1}{T_{1b}}\right)$$

where $M_a^{\ast c}$ and $M_b^{\ast c}$ are the steady-state magnetizations of a and b when Pi is fully saturated. Only Eq. (15.14a) is needed in the MSS MT approach to determine the CK reverse rate constant (k₋₁) by using the measured magnetizations (i.e., $M_a^0$, $M_a^{\ast c}$ and $M_b^{\ast c}$) and other relaxation parameters (i.e., α_a and T_1a), which are determined by the measurement in Step 1. The reverse flux of CK reaction can be calculated by the following relation:

$$F_r^{\mathit{CK}}=k_{-1}\left[\mathit{ATP}\right].$$ (15.14c)

Step 3: Steady-state saturation of PCr for determining ATP_ase reverse rate constant and flux

The third step of the in vivo ³¹P MSS MT measurements is to apply a frequency-selective RF pulse train for completely saturating the PCr resonance peak with a sufficiently long saturation time resulting in steady-state magnetizations of b and c. For this case, M_a=0, dM_b/dt=

$$k_2={\alpha }_c\left(\frac{M_c^{\ast a}}{M_c^0}-\frac{1}{T_{1c}{\alpha }_c}\right)\frac{M_c^0}{M_b^{\ast a}}$$ (15.15a)

$$k_{-2}={\alpha }_b\left(\frac{M_b^{\ast a}}{M_b^0}-\frac{1}{T_{1b}{\alpha }_b}\right)\frac{M_b^0}{M_c^{\ast a}}$$ (15.15b)

where $M_b^{\ast a}$ and $M_c^{\ast a}$ are the steady-state magnetizations of b and c when PCr is fully saturated. Only Eq. (15.15a) is needed in the MSS MT approach to determine the ATP_ase forward rate constant (k₂) by using the measured magnetizations (i.e., $M_a^0$, $M_a^{\ast c}$ and $M_b^{\ast c}$) and other relaxation parameters (i.e., α_c and T_1c), which are determined by the measurement in Step 1. The reverse flux of the ATP_ase reaction can be calculated via following relation:

$$F_r^{{\mathit{ATP}}_{\mathit{ase}}}=k_2\left[\mathit{ATP}\right].$$ (15.15c)

Therefore, by combining these three measurement steps, one is able to measure all kinetic parameters which determine the entire exchange of PCr↔ATP↔Pi including all four ATP metabolic fluxes for both forward and reverse reaction directions as schematically summarized in Figs. 15.1 and 15.13. In total, a minimal number of three selective saturated in vivo ³¹P spectra plus one control in vivo ³¹P spectrum (for quantifying [ATP], [Pi], [PCr], i.e., $M_a^0$, $M_b^0$ and $M_c^0$) are required by the MSS MT approach for the measurements (50).

4.2. Application of in vivo ³¹P MSS MT Approach in Human Brain at 7T

The in vivo ³¹P MT measurements can significantly benefit from the high-field advantages of improved MR detection sensitivity and spectral resolution. We have conducted extensive measurements at 7T for validating the in vivo ³¹P MSS MT approach, and ultimately, determining the entire chemical exchange of PCr↔ATP↔Pi in the human occipital lobe (20,50).

4.2.1. Progressive Saturation for Measuring Intrinsic T₁, Forward Rate Constants And Fluxes

Figure 15.10A illustrates the progressive saturation transfer measurements and related in vivo ³¹P spectra when the γ-ATP resonance peak was completely saturated (i.e., Step 1 measurement used in the in vivo ³¹P MSS MT approach). It shows a gradual decrease of Pi signal when the γ-ATP saturation time increases because of the chemical exchange between γ-ATP and Pi (i.e., ATP↔Pi) and the increased magnetization transfer effect (20). This MT effect was observed on the chemical-exchangeable Pi resonance but not for those adjacent and non-chemical-exchangeable phosphate metabolites such as PDE and PME groups. Moreover, the MT effect on Pi disappeared when the RF saturation frequency was moved to the opposite side of the in vivo ³¹P spectrum with the same chemical shift difference as shown in Figure 15.10B. Figure 15.10C plots the quantitative relation between the normalized Pi signal intensity (i.e., $M_a^{\left(t\right)}/M_a^0$ in Eq. (15.13a)) under the γ-ATP saturation with the saturation time of t. This plot can be used to calculate the intrinsic T₁ of Pi (i.e., T_1a) and the forward ATP_ase reaction rate constant (k₁) by the regression fitting according to Eq. (15.13a). Then, the forward ATP_ase reaction flux can be determined according to Eq. (15.13e). The same in vivo ³¹P MT spectral data can be applied to quantify the MT effect on the PCr resonance as a function of the γ-ATP saturation time, ultimately, to determine the intrinsic T₁ of PCr (i.e., T_1c) and the forward CK reaction rate constant and flux according to Eqs. (15.13b) and (15.13e).

Fig. 15.10.

(A) Progressive saturation measurements and averaged in vivo ³¹P spectra (partially displayed) as a function of γ-ATP saturation time (t), and (B) their corresponding control ³¹P spectra. The arrows point to the Pi resonance peak. (C) Normalized Pi signal change as a function of t and regression fitting (solid line) according to Eq. (15.13a). Adapted from Lei et al. of Ref. (20).

4.2.2. Steady-State Saturation for Measuring Forward Rate Constants And Fluxes

One technical limitation of progressive saturation approach is the requirement of a number of saturated in vivo ³¹P spectra with varied saturation time (e.g., Fig. 15.10). One alternative but more robust approach is the use of steady-state saturation if the intrinsic T₁ values have been determined at a given B₀ (see details in the discussion of Step 1 measurement above). Figure 15.11 demonstrates such a measurement (i.e., Step 1) and the in vivo ³¹P MT spectra acquired in the absence (control spectrum; Fig. 15.11A) and presence (saturated spectrum; Fig. 15.11B) of sufficiently long RF saturation for ensuring complete saturation of the γ-ATP resonance peak and approaching steady-state magnetizations for both Pi and PCr. Figure 15.11C shows the difference spectrum by subtracting the control and γ-ATP saturated spectra (20, 50). The relative Pi signal reduction can be used to calculate the forward rate constant and flux for the ATP_ase reaction according to Eqs. (15.13d) and (15.13e). Similarly, the relative PCr signal reduction can be used to calculate the forward rate constant and flux for the CK reaction according to Eqs. (15.13c) and (15.13e).

Fig. 15.11.

In vivo ³¹P spectra acquired from a health human occipital lobe in the absence (A) and presence (B) of complete γ-ATP saturation, and the difference spectrum (C) between the two. Only the Pi and PCr resonance peaks show the magnetization transfer effect due to the saturation. The intensity reduction of Pi can be used to determine the forward rate constant and flux for the ATPase reaction, and the intensity reduction of PCr can be used to determine the forward rate constant and flux for the CK reaction. Adapted from Lei et al. of Ref. (20).

4.2.3. In vivo ³¹P MSS MT Measurements for Determining all ATP Metabolic Fluxes Involving PCr↔ATP↔Pi Exchange in Human Occipital Lobe

Figure 15.12 illustrates one example of in vivo ³¹P MSS MT measurements in the human occipital lobe (50). A total of four in vivo ³¹P spectra were collected in the absence (Fig. 15.12A) and presence of complete RF saturation on the resonance peak of Pi (Step 2; Fig. 15.12B), PCr (Step 3; Fig. 15.12C) and γ-ATP (Step 1; Fig. 15.12D), respectively. It reveals that single-site saturation on one phosphate spin can lead to significant magnetization reductions in the other two coupled phosphate spins through the three-spin chemical exchange system of PCr↔ATP↔Pi. For instance, the PCr saturation results in a significant signal reduction for both γ-ATP and Pi as shown in Fig. 15.12C. All required steady-state saturated magnetizations can be determined by using the three saturated in vivo ³¹P spectra as shown in Fig. 15.12B–D, and all equilibrium magnetizations can be determined by using the control in vivo ³¹P spectrum as shown Fig. 15.12A. The values of these magnetizations were used to determine four rate constants (k₁, k₂, k₋₁ and k₋₂) and four fluxes ( $F_f^{{\mathit{ATP}}_{\mathit{ase}}}$, $F_r^{{\mathit{ATP}}_{\mathit{ase}}}$, $F_f^{\mathit{CK}}$ and $F_r^{\mathit{CK}}$ associated with the PCr↔ATP↔Pi exchange in the human brain. These measured results and the ratios between the forward and reverse fluxes are summarized in Fig. 15.13 indicating several important observations. First, there is no statistical difference between the forward and reverse exchange fluxes for both the CK reaction (i.e., $F_f^{\mathit{CK}}$ versus $F_r^{\mathit{CK}}$; p = 0.38) and the ATP_ase reaction (i.e., $F_f^{{\mathit{ATP}}_{\mathit{ase}}}$ versus $F_r^{{\mathit{ATP}}_{\mathit{ase}}}$; p = 0.46) (50). Second, the ratios between the forward and reverse fluxes for the CK reaction $(F_f^{\mathit{CK}}/F_r^{\mathit{CK}}=0.95\pm 0.12)$ and the ATP_ase reaction $(F_f^{{\mathit{ATP}}_{\mathit{ase}}}/F_r^{{\mathit{ATP}}_{\mathit{ase}}}=1.08\pm 0.21)$ are close to unity. In general, the CK fluxes reflect the nonoxidative phosphorylation and the ATP_ase fluxes, in contrast, reflect oxidative phosphorylation. Both of these phosphorylation pathways can contribute to the total ATP production flux (i.e., $F_f^{\mathit{total}}=F_f^{\mathit{CK}}+F_f^{{\mathit{ATP}}_{\mathit{ase}}}=73.9\mathrm{\mu }\mathrm{mol}/\mathit{g}/\min$) and the total ATP utilization flux (i.e., $F_r^{\mathit{total}}=F_r^{\mathit{CK}}+F_r^{{\mathit{ATP}}_{\mathit{ase}}}=76.9\mathrm{\mu }\mathrm{mol}/\mathit{g}/\min$). The ratio between $F_f^{\mathit{total}}$ and $F_r^{\mathit{total}}$ is again close to unity (=0.96) indicating that the total ATP production flux equals the total ATP utilization flux. These results lead us to conclude that the fluxes measured by the in vivo ³¹P MSS MT approach satisfy the chemical equilibrium conditions for the CK and ATP_ase reactions in the human brain, and indicate that the MSS MT approach is able to explicitly determine four rate constants in the PCr↔ATP↔Pi kinetic process and their associated ATP metabolic fluxes in the brain noninvasively. Nevertheless, such equal forward and reverse flux relations are unable to be obtained for the saturation transfer measurement if the three-spin PCr↔ATP↔Pi exchange system was treated as two independent two-spin change systems (i.e., PCr↔ATP and ATP↔Pi) even when the same experimental MSS MT data were analyzed (50). These findings clearly indicate that the chemical exchange system of PCr↔ATP↔Pi has to be treated as a three-spin exchange system in order to accurately determine the reverse rate constants and fluxes for both the CK and ATP_ase reactions.

Fig. 15.12.

In vivo ³¹P MSS MT measurements and four spectra acquired from a representative human occipital lobe in the absence (A) and presence of complete RF saturation on the resonance peak of (B) Pi (Step 2), (C) PCr (Step 3) and (D) γ-ATP (Step 1), respectively. The narrow arrows indicate the saturation sites and the wide arrows indicate the signal reductions due to the magnetization transfer. Adapted from Du et al. of Ref. (50).

The PCr↔ATP↔Pi exchange system in a normal brain likely reaches chemical equilibrium (or near equilibrium) under most circumstances. As long as the equilibrium condition is satisfied, one can further simplify the in vivo ³¹P MT measurement procedure by using the chemical equilibrium relation (50). In this case, only two in vivo ³¹P spectra (one control and another with full saturation of γ-ATP as illustrated in Fig. 15.11) are practically required to determine the entire PCr↔ATP↔Pi exchange process (50). Thus, this simplification can make the in vivo ³¹P MT measurement more robust for rapidly determining the ATP metabolic flux changes induced by either physiological or pathological perturbations.

5. Perspective and Discussion

Despite its low detection sensitivity compared to 1H MRS, researchers in the past three decades have revealed the great merits of in vivo heteronuclear MRS for a broad range of biomedical applications. Two of them (i.e., ³¹P and ¹⁷O) have been discussed here in great detail and each method provides a unique tool for noninvasively studying specific metabolic pathways in the brain through the measurements of metabolite concentrations and biochemical reaction fluxes. The combination of different in vivo multinuclear MRS approaches may significantly enhance the MR capability to perform comprehensive studies concerning brain physiology, neurochemistry, bioenergetics and their relations to brain function. This point is addressed by answering the following questions:

5.1. Why is in vivo ³¹P MT Approach Attractive and Promising for Studying Brain Bioenergetics?

A large amount of research efforts have been spent since early 1980s for exploring the possibility of determining the ATP metabolic fluxes using a variety of in vivo 31P MRS MT approaches and great progress has been made (20, 44–46, 49, 50, 103–110, 115, 117). Nevertheless, the course for advancing the in vivo ³¹P MRS MT methodology and its clinical application has been significantly slowed down particularly in brain studies during the last decade. One of the major causes is probably in regard to two controversial observations in this research field. The first one is the inconsistency in the results of the measured reverse ATP fluxes in the literature (e.g., (112–114)). In our opinion, this inconsistency is likely caused by the lack of comprehensive spin-exchange models used in the early research work. And this controversy can be resolved by using more sophisticated three-spin exchange models for accurately determining the reverse ATP fluxes for both the CK and ATP_ase reactions (45,46,50,115,116).

Another surprising observation has raised question regarding whether the measured forward ATP_ase reaction flux truly reflects the oxidative phosphorylation in the mitochondria in a living organ. The ATP synthesis reaction (i.e., R2 in Figs. 15.1 and 15.13) catalyzed by the coupled activities of glycolytic enzymes glyceraldehyde-3-phosphate dehydrogenase (GAPDH) and phosphoglycerate kinase (PGK) have been shown to be a major contributor to the Pi → ATP reaction flux measured by the ³¹P MT approaches in E. coli (118), yeast (119), liver (120), and the myocardium (121). For instant, in the perfused rat heart, GAPDH/PGK mediated exchange dominates the Pi → ATP flux measured by the ³¹P MT approach in the myocardium (121). Under these circumstances, only if the GAPDH/PGK effect was eliminated either directly using exogenous inhibitor iodoacetate or indirectly by eliminating all exogenous and endogenous sources of glucose, the myocardium Pi → ATP flux determined by the in vivo ³¹P MRS MT measurement was found to be the same as the net rate of oxidative ATP synthesis calculated as the product of the cardiac oxygen consumption rate and the P:O ratio, and then the correlation between the measured flux and oxygen consumption rate became evident (121). These observations and findings reveal the complexity of biological systems and potential limitation of in vivo ³¹P MRS MT approaches for directly measuring the ATP metabolic flux related to oxidative phosphorylation in some organs such as heart and liver. Interestingly, in contrast to the observations in the myocardium, and analogous observations in yeast, E. coli and liver, the Pi → ATP flux measured by in vivo ³¹P MRS MT in the human brain is similar to the net oxidative ATP synthesis rate which can be estimated by the available CMRO₂ data and the P:O ratio based on a tight link between the cerebral oxidative phosphorylation and oxygen utilization under normal physiological condition (20, 50). The CMRO₂ value in the human occipital lobe has been measured to be 1.71 μmol/g/min by PET (91). The ATP synthesis rate attributed by oxidative phosphorylation can be calculated by multiplying this CMRO₂ value by the P:O ratio of ∼2.5 (122) and factor of 2, resulting in an estimated value of 8.6 μmol/g/min. This rate is almost identical to the cerebral ATP synthesis rate of $F_f^{{\mathit{ATP}}_{\mathit{ase}}}=8.8\mathrm{\mu }\mathrm{mol}/\mathit{g}/\min$, which was directly measured by in vivo ³¹P MRS MT (50). A similar relation was also evident in the animal studies showing a tight correlation between the measured Pi → ATP flux and the estimated oxidative phosphor rate (49,123). These comparisons of results, thus, lead us to conclude that in the brain, the Pi→ATP flux measured by the in vivo ³¹P MT approach equals the net oxidative ATP synthesis rate linking to the cerebral oxidative phosphorylation, and this flux should provide a vital index reflecting the major bioenergetics for supporting brain activity and function (7, 12, 20, 123). This conclusion makes in vivo ³¹P MT attractive for studying the central role of the cerebral bioenergetics associated with oxidative phosphorylation and brain activity, though the underlying mechanism for explaining the discrepancy in the ³¹P MT measurements between the brain and other organs (e.g., heart and liver) remains to be explored (20).

5.2. What Is the Possible Role that in vivo ³¹P and ¹⁷O MRS can Play for Studying Brain Activation and Function?

As mentioned earlier, both in vivo ³¹P and ¹⁷O MRS methods can provide noninvasive tools for studying brain metabolism and bioenergetics. Each of these methods has unique features for probing the metabolic functions in mitochondria. Specifically, the in vivo ¹⁷O MRS imaging approach is useful for mapping the absolute CMRO₂ within a relatively short ¹⁷O₂ inhalation time. The CMRO₂ images should reflect the total metabolic rate of oxygen utilization (i.e., R1 in Fig. 15.1) and its spatial distribution in the brain. In contrast, the in vivo ³¹P MT approach is powerful for measuring all the cerebral ATP metabolic fluxes associated with four ATP reactions (i.e., R2 to R5 in Fig. 15.1) occurring in different subcellular compartments. All of these measured physiological parameters can be linked to brain ATP energy and ATP transportation. Therefore, the combination of in vivo ³¹P and ¹⁷O MRS methods may provide an essential in vivo MR tool being able to studying the crucial roles of both oxygen and ATP metabolisms in cerebral bioenergetics and brain functions.

One relevant question in the brain function and neuroimaging research fields is how much extra brain energy is needed during the brain stimulation and/or task performance. This topic is still in intense debate, especially regarding how much CMRO₂ is induced by brain stimulation (7, 8, 91, 124–136). A more important question, perhaps, is how many more ATP molecules are consumed during brain activation as compared to the resting brain because of a close relation between the ATP utilization and energy consumption (3, 7, 8). The answers to these questions are central for understanding the mechanisms underlying most modern neuroimaging techniques including two most popular methods of the functional MRI (fMRI) based on the blood oxygenation level dependent (BOLD) contrast (137–142) and PET (7,8,143). One major hurdle for addressing the questions is the lack of sophisticated and robust neuroimaging modalities for directly assessing the absolute CMRO₂ and CMR_ATP, which is equivalent to $F_{f{\text{ATP}}_{\text{ase}}}$ in this article, and their changes elevated by brain activation. Therefore, the in vivo ³¹P and ¹⁷O MRS approaches as described here could fill this methodological gap and make significant contribution in understanding the relation between brain bioenergetics and function. This notion is convincingly supported by several lines of evidence provided by recent research progresses. One example of these progresses was to apply the in vivo ¹⁷O MRS imaging approach for successfully mapping CMRO₂ images in the cat brain under resting and visual stimulation conditions (144). A significant CMRO₂ increase was observed in the activated cat visual cortex. This initial observation indicates the possible central role of oxygen metabolism for supporting the elevated brain activity during activation.

Another significant progress is related to the in vivo ³¹P MT application in the rat brain for studying the quantitative correlation between the CMR_ATP and the varied brain activity from mild anesthesia state to the isoelectric state (123). In this study, we observed a strong correlation between the Pi→ATP flux measured by the in vivo ³¹P MT approach and the brain activity quantified by EEG signal (123). This result indicates a tight correlation between the ATP synthesis rate and brain bioenergetic demand under varied brain activity states. Therefore, the measurement of Pi→ATP flux should provide a sensitive energy index for quantifying the brain bioenergetics. In contrast, the steady-state HEP concentrations (e.g., [ATP], [PCr] and [Pi]) and pH are relatively stable in a wide range of brain activity level (123). These results support the view that one of the major functions of the PCr↔ATP↔Pi exchange process is to sustain the balance between the ATP supply and demand in the brain resulting in a stable ATP concentration under the normal physiological condition. Such a balance is likely maintained by the rapid adjustments of both forward and reverse metabolic fluxes involved in the PCr↔ATP↔Pi exchange according to the change of brain energy. We conclude that the ATP metabolic flux measurements using the in vivo ³¹P MT approach should be more useful for studying the brain bioenergetic change in response to brain activation as compared to the steady-state HEP concentration measurements using conventional in vivo ³¹P MRS. This is evident from two high-field in vivo ³¹P MRS studies showing a few percents of decrease in the PCr signal in contrast to a >30% increase in the CK forward flux in the human visual cortex during visual stimulation (108, 145). It is conceivable that the in vivo ³¹P MT approach, as a sole in vivo tool being able to directly and quantitatively measure the cerebral ATP metabolic fluxes, will play a vital role for studying the brain bioenergetics associated with brain function and activation. One particularly interesting question possibly to be addressed by this in vivo ³¹P MT approach is whether more ATP utilization is required by the elevated neuronal activity, and if yes, how much more is needed? The answers should advance our understanding regarding the central roles of cerebral oxidative phosphorylation and mitochondria in supporting brain function.

5.3. What are the Potential Applications of in vivo ³¹P and ¹⁷O MRS for Clinical Research and Diagnosis?

In vivo MRS methodology can provide detailed metabolite fingerprints in the living organs, and it is perhaps one of the most classic molecular imaging modalities. Many metabolites and their abnormal changes, detectable by in vivo MRS, have been proved to be tightly linked to various brain diseases and disease progression.

Both of the in vivo ¹⁷O MRS and ³¹P MRS MT approaches as discussed here are especially useful for studying the brain oxidative metabolism and the mitochondrial metabolic function. They would provide opportunities for a variety of clinical brain research and potentially for clinical diagnosis because of the obvious role of oxidative metabolism in the pathology associated with many brain disorders and neurodegenerative diseases such as schizophrenia, Alzheimer’s disease, Huntington’s disease, Parkinson’s disease, mitochondrial dysfunction and aging problems (e.g., (146–150)). One line of evidence is the histopathological findings indicating that the activity of cytochrome oxidase, the key mitochondrial enzyme that catalyzes the reduction of oxygen to form water, is significantly impaired in schizophrenic (146) and Alzheimer’s patients (147, 148). Another line of evidence is from the studies of diseases caused by mitochondrial DNA mutations suggesting that a variety of degenerative processes in Parkinson’s disease and Alzheimer’s disease may be associated with defects in mitochondrial oxidative phosphorylation (151, 152). Thus, the in vivo ¹⁷O MRS and ³¹P MT approaches may play vital roles for investigating the neurodegenerative diseases associated with the mitochondrial abnormality and metabolic syndrome with great potential in clinical diagnosis and monitoring the brain functional recovery after medical treatment.

6. Conclusion

Although, in reality, in vivo heteronuclear MRS has not been widely applied compared to ¹H MRI/MRS due to its lower detection sensitivity, the currently available ultrahigh MRI/MRS scanners, technology and their associated high field merits have undoubtedly stimulated the in vivo heteronuclear MRS research and methodological development (153). Significant progresses have been made for advancing in vivo MRS in brain research. One of the unique in vivo MRS utilities is to noninvasively measure the cerebral metabolic fluxes and their dynamic changes, which may lead to many important applications in medical research. Two interesting and exciting applications of the in vivo ¹⁷O MRS approach and/or ³¹P MRS MT approach are: (i) to study the dynamic changes in oxygen utilization and oxidative ATP metabolism during activation in normal brains; (ii) to explore the possibility for detecting abnormality in the oxidative metabolic fluxes during the progression of brain diseases prior to showing metabolite concentration abnormality. The outcomes from these applications will be essential for better understanding of brain function and dysfunction. Finally, the in vivo ¹⁷O and ³¹P MRS can be readily combined with many other MRI utilities for imaging brain anatomy, perfusion, diffusion and BOLD etc within the same scanning session. This combined MRS/MRI strategy can make it particularly powerful in neuroscience research.