The quantification with FDG as seen by a physician

Premise

Although, at the present, in the routine practice, the qualitative analysis of PET with F-18 Fluoro-deoxyglucose (FDG) remains indispensable and sufficient for clinical purposes, a quantitative approach may add a significant contribution, when rigorous and reliable. In particular, a quantitative analysis may already be clinically applied for indications as a better definition of a specificity's threshold, a more precise prognostic stratification, a correct evaluation of the tumor response

Reminder

The FDG classic compartmental model can be represented by the scheme reported in Fig. 1. With K as the transfer constant. K₁ represents the concentration's fraction (activity per volume unit, e.g. KBq/ml) of labeled FDG that in the time unit moves from the plasma compartment into the tissue compartment of free FDG. In the literature, this constant is usually denoted by a capital K, the others being indicated with a blood/ml of tissue/min (tissue density = 1.04 g/ml), while k₂, k₃ and k₄ are rate

Autoradiographic method

It is precisely based on the three compartment model showed in Fig. 1 and used by Sokoloff to study glucose metabolism in the brains of normal albino rats n 1977 [2]. This model is thus valid for the normal brain but, afterwards, has been extended (without much critical evaluation) to other tissues and considered valid even in pathological situations. The operational formula that allows in the autoradiographic method to obtain MR_glu is:$M{R}_{\mathit{glu}}=\frac{\mathit{Gl}\left[C_i\left(T\right)-K_1\cdot {exp}^{\left(-\left(k_2+k_3\right)\cdot T\right)}\cdot {\displaystyle \underset{0}{\overset{T}{\int }}{C}_p\left(t\right)\cdot {exp}^{\left(k_2+k_3\right)\cdot t}\cdot \mathit{dt}}\right]}{\mathit{LC}\cdot \left[{\displaystyle \underset{0}{\overset{T}{\int }}{C}_p\left(t\right)\cdot \mathit{dt}}-\right]}$

Simplified methods

After that, technological advances have allowed the collection of dynamic curves, the autoradiographic method has gradually transferred the role of reference system to the Non Linear Regression (NLR) method (a complex procedure that cannot be certainly included between the simplified methods: see below).

At this point, do we have to think that the proposed formula (10) from Sokoloff has only historical interest? No, because many simplified methods, after all, may be considered an application of

SUV

What has been said about the simplified methods also applies for that over-simplified index that is the SUV. In the ordinary sense, SUV, if we use, as example, the known corrected formula for SUV using body weight,$\mathit{SUV}=\frac{C_i\left(T\right)}{A_0/\mathit{bw}}=\frac{C_i\left(T\right)}{\mathit{NF}}$where A₀ is the administered Activity and bw is the body weight. In formula (11c) we considered the ratio administered Activity/body weight as a normalization factor indicated with NF. It follows, by rewriting formula (11c), that C_i(T) = SUV × NF and, if we substitute,

Non linear regression (NLR) method

Non linear regression (NLR) has been used by Phelps since 1979 for FDG quantitative analysis [5]. Contrary to static methods (autoradiography and related simplified procedures) previously discussed, and to dynamic methods (Patlak and Blomqvist) described below, NLR represents a very complex way to use compartmental models. Consequently, being very difficult to calculate MR_glu with NLR, a consolidated experience in the mathematical non linear fitting process is required.

The NLR method became the

Rutland-Patlak's method

Generally known only by the name of Patlak [13], who gave it a good mathematical formulation [14], or as Patlak-Gjedde method, this procedure was firstly conceived, but for completely different purposes, by Rutland [15], [16], who tried to have it recognized, but without much success.

The method of Rutland-Patlak is connected to the three constants K₁, k₂ and k₃ defined for the FDG compartment model, without k₄. Starting from the compartmental model, it is in fact possible to demonstrate that,

Blomqvist's method

The method is based on an artifice: the disaggregation of compartments according to the scheme reported in Fig. 3.

In this model P₁, P₂ and P₃, which can be determined with a linear regression, are related to the k constants from relationships which allow to get k₁, k₂ and k₃. C₁ and C₂ do not correspond to the compartments of free and that phosphorylated FDG. Instead Blomqvist shows that it is their sum that corresponds to them, i.e.:$C_1+C_2=C_f+C_b$

Blomqvist shows that the disaggregation does not

Thinking about methods

To better compare and understand different methods, below you can see an example from our series also reported in Fig. 4. It is a case of a lung tumor, studied with a dynamic acquisition for 45 minutes.

Fig. 4 shows TACS from blood vessel (input function) and from tissue region of interest (tissue response).

Proceeding to the determination of K_i in our example with the outlined methods, we have obtained results reported in Table 1, Table 2.

It is interesting to note that the value of K_i, calculated

The “Lumped constant”

To finish this paper, we want briefly make few comments concerning the lumped constant (LC), which, as you recall, it is the ratio between MR_FDG and MR_glu. Given the relationship in formula (1), it is clear that the value of MR_glu depends essentially on the value of LC. Usually values for LC are ​​taken from literature, but these are far from unanimous. For normal brain, as example, different values for LC are proposed by three pioneers as Phelps (LC = 0.42), Sokoloff (0.46) and Reivich (0.52)

Focus on

We conclude this paper that, as you remember, is the transcription of an informal talk to residents in nuclear medicine, with some personal recommendations:

• 1.

  Unless you want to become a “reference center”, do not worry about the NLR method and do not waste money to buy commercial software.

• 2.

  Utilize the good old Rutland-Patlak. But do it very well!

• 3.

  Remember that Patlak presupposes that the transfer of the tracer is irreversible (i.e. K₄ = 0 in the compartmental model). This may be true for some tissues

Acknowledgment

This manuscript was taken in part from a publication written by Professor Galli and included inside the “Notiziario di Medicina Nucleare ed Imaging Molecolare” published on the web (www.aimn.it) by the Associazione Italiana di Medicina Nucleare on October 12, 2012.