Twelve healthy male Sprague–Dawley rats (median mass of 330 g) were injected with hyperpolarized 13
-pyruvate through a tail vein catheter. Two male wild type and ten TRAMP mice (median mass of 35.5 g) were injected with hyperpolarized 13
-pyruvate through a jugular vein catheter. The TRAMP mice were serially studied to monitor tumor progression and treatment response, whereas healthy rats and mice were sacrificed immediately after imaging. The TRAMP mice received up to 12 13
-pyruvate injections over multiple studies and the healthy mice and rats received a maximum of three 13
-pyruvate injections. Imaging and spectroscopy were performed on a GE 3T MR scanner (GE Healthcare, Waukesha, WI) with a dual-tuned (1
C) quadrature coil, either customized for rats (8 cm inner diameter, 9 cm length, sensitive volume: 75 mm diameter and 90 mm length) or customized for mice (5 cm inner diameter, 8 cm length) [7
]. The specifics of the animal handling procedure have been reported previously [7
]. All experiments were conducted under a protocol approved by our institutional animal care and use committee.
-pyruvate was generated with either a prototype DNP polarizer [19
] or a Hypersense®
system (Oxford Instruments, Abingdon, UK). Polarization levels ranged from 16% to 23%. Animals were given a range of pyruvate concentrations and volumes to assess the effects of dose on metabolite exchange. Rats received 13
-pyruvate at concentrations of 9.6–80 mM with volumes of 1.0–3.4 mL, yielding a 13
-pyruvate dose between 28.1 and 724.2 µmol/kg. In TRAMP and wild type mice, doses ranged from 92.4 to 857.9 µmol/kg (10–80 mM, 300–400 µL). The injections lasted between 4 and 13 s in rats, but were consistently 12 s in the mice.
In 12 of the rats (21 scans), dynamic spectroscopy data were acquired from a single 15 mm axial slice centered on the kidneys (Flip angle = 5°, spectral bandwidth (BW) = 5 kHz, 2048 spectral points) using a spin-echo RF pulse sequence. Data acquisition began simultaneously with the 13
-pyruvate injection and was repeated every 3 s (TR = 3 s) over a duration of 189 s (64 time points). The same acquisition was used for six TRAMP mice (11 scans) with a 10 mm axial slice centered on the primary tumor in the prostate. Chemical shift mis-registration between pyruvate and lactate for the 2.8 kHz hyperbolic secant RF selection pulses [7
] was estimated at approximately 2 mm for the 15 mm slice selection and 1.4 mm for the 10 mm slice selection. Volumes of tumor that were estimated to be within the observed 10 mm slices ranged from approximately 0.6–3.2 cc.
A one-dimensional flyback echo-planar spectroscopic imaging (1D-EPSI) technique was used to acquire dynamic data in two healthy wild type mice (3 scans) and five TRAMP mice (15 scans) [20
]. The readout gradient was applied in the superior–inferior (SI) dimension during acquisition to allow spatial encoding with a 10 mm slice resolution and a 160 mm field of view (FOV). The readout trajectory was designed for a spectral bandwidth of 581.4 Hz with 288 spectral points [21
]. The other acquisition parameters remained the same.
-weighted anatomical 1
H images were acquired to reference the spectroscopic data in both rats and mice. Acquisition details for these images have been published previously [7
Data were processed using an algorithm that was implemented in the Interactive Data Language (IDL, ITT Visual Information Solutions, Boulder, CO). For the single slice data, a 10 Hz Lorentzian apodization was applied to each free-induction decay (FID) prior to Fourier transforming the data. Zero-order phasing was applied to maximize the value of the first point in the FID. The average baseline signal was then subtracted and the real peak heights for 13
-lactate, and 13
-alanine were used as input data for the models described below. The 1D-EPSI data were processed similarly, with additional phase corrections to account for the time delays in the FID that result from the spatial encoding [22
]. These data were zero-filled spatially in the SI dimension to 1.25 mm resolution in order to more precisely reference the metabolite levels to specific tissues.
A model for the change in 13
-pyruvate signal over time was first fit to the pyruvate peak height data according to the following piecewise equation:
) represents 13
-pyruvate peak height as a function of time. The parameters fit by this model are: kpyr
, the rate constant for pyruvate signal decay (in s−1
, the rate of pyruvate arrival (in a.u. s−1
); and tarrival
, the time of pyruvate arrival (in s). The signal was assumed to be zero for all metabolites prior to tarrival
. The variable, tend
, can be calculated as the sum of the fitted arrival time, tarrival
, and the known injection duration. The three estimated pyruvate parameters (kpyr
) were then used to fit the following equation with 13
-lactate and 13
-alanine dynamic data:
Here, x represents either lactate (lac) or alanine (ala), and Mx(t) represents either 13C1-lactate or 13C1-alanine peak heights over time. Two parameters were estimated: kpyr→lac (or kpyr→ala), the rate constant for pyruvate to lactate (or alanine) exchange (s−1), and klac (or kala), the rate constant for lactate (or alanine) signal decay (s−1). Metabolite signal decay rate constants (kpyr, klac, and kala) were assumed to consist of both metabolite T1 decay and signal loss from the 5° RF flip angles. This meant that T1 values could be estimated for lactate and alanine after accounting for RF excitations and for pyruvate after also accounting for metabolic exchange rate constants. The robustness of parameter estimation was assessed based upon multiple scans on a healthy rat that was given three similar 13C1-pyruvate doses (321.4–321.9 µmol/kg).
In addition to metabolism, T1
effects, and RF excitations, all rate constants may be influenced by other sources of signal change or variation, and they should be thought of as apparent, rather than absolute, rate constants. Also note that reverse exchange of metabolites back to pyruvate was assumed to be negligible in this model to allow the estimation of irreversible Michaelis–Menten kinetics. This was further shown to be a reasonable assumption in previous studies that used hyperpolarized 13
-lactate as the injected substrate [23
The dose effects were represented by a Michaelis–Menten-like model with maximum reaction velocity (Vmax
) and Michaelis constant (Km
) according to the following equation:
The kinetics are described here using kpyr→lac
instead of initial reaction rates (V0
). This modified Michaelis–Menten equation is simply the inverse of the Hanes–Woolf equation [24
]. To adhere to the traditional Michaelis–Menten equation, the initial reaction rates (V0
) relative to pyruvate dose were also estimated as the product of dose (Dosepyr
) and exchange rate constants (kpyr→lac
). Parameter estimates from nineteen scans (11 rats) were used to fit Eq. (3)
and estimate Vmax
for exchange with lactate and exchange with alanine. The robustness of the model fit was assessed via the scaled fitting error [25
Metabolic parameters from ten TRAMP mouse tumors (26 scans) and two wild type mice (3 scans) were considered. In wild type mice, comparison data came from the region containing normal prostate. Three TRAMP mice underwent serial studies at a constant pyruvate dose (two with hormone deprivation treatment of casodex administered immediately after the first scan, one without treatment) to investigate how metabolic parameters change with disease progression. Tumor stage was assessed by size and appearance. Four TRAMP mice (two mid-stage tumors, two late-stage tumors) received a range of three 13
-pyruvate doses on studies performed within a short time period (7 days for one, 4 h for the other three); these data were used to separately fit Eq. (3)
and to describe the individual dose–responses. Four TRAMP mice underwent only one dynamic spectroscopy scan.