Prediction of optimal contrast times post-imaging agent administration to inform personalized fluorescence-guided surgery

Abstract. Significance: Fluorescence guidance in cancer surgery (FGS) using molecular-targeted contrast agents is accelerating, yet the influence of individual patients’ physiology on the optimal time to perform surgery post-agent-injection is not fully understood. Aim: Develop a mathematical framework and analytical expressions to estimate patient-specific time-to-maximum contrast after imaging agent administration for single- and paired-agent (coadministration of targeted and control agents) protocols. Approach: The framework was validated in mouse subcutaneous xenograft studies for three classes of imaging agents: peptide, antibody mimetic, and antibody. Analytical expressions estimating time-to-maximum-tumor-discrimination potential were evaluated over a range of parameters using the validated framework for human cancer parameters. Results: Correlations were observed between simulations and matched experiments and metrics of tumor discrimination potential (p<0.05). Based on human cancer physiology, times-to-maximum contrast for peptide and antibody mimetic agents were <200  min, >15  h for antibodies, on average. The analytical estimates of time-to-maximum tumor discrimination performance exhibited errors of <10% on average, whereas patient-to-patient variance is expected to be greater than 100%. Conclusion: We demonstrated that analytical estimates of time-to-maximum contrast in FGS carried out patient-to-patient can outperform the population average time-to-maximum contrast used currently in clinical trials. Such estimates can be made with preoperative DCE-MRI (or similar) and knowledge of the targeted agent’s binding affinity.

receptor (e.g., a tumor) can be represented as a function of time, t, by: where CT is the concentration of the imaging agent in "tumor" tissue, K1 represents the rate constant governing extravasation of the imaging agent from the blood plasma to the tumor tissue, is the exponential "elimination" decay constant of the imaging agent in the blood, k2 represents the rate constant governing the efflux the imaging agent from the tumor tissue to the blood plasma, BP is the binding potential, and the mathematical operator represents convolution.
The concentration of the same imaging agent in a tissue devoid of targeted receptor (BP = 0) can then be represented as: where CN in this "normal" tissue, and and represent the extravasation and efflux rate constants of the imaging agent in the normal tissue.
It is then possible to find an analytical solution to the convolution terms in Eqs. (S1) and (S2) using the following identity: If signal is shot noise limited (common in fluoresence), noise can be approximated as the square root of the signal intensity. As a corollary, maximum CVR and maximum signal difference Assuming that (i.e., imaging agent distribution to tissue rates are much faster than agent elimination from the blood), Eq. (S7) simplifies to: which further simplifies to: and the time to maximum CVR can be represented as:

Approximation of time to maximum CVR in paired-agent imaging
To get an approximation of time to the maximum CVR for paired-agent imaging, the noise component in the denominator of Eq. (8) in the main manuscript must be treated differently from that in the single-agent imaging equations (S1)-(S10). To simplify the CVR equation for pairedagent imaging, it can be assumed that the noise for a BP estimate can be represented by (1/CU+1/CT) 1/2 , where CU represents the untargeted (control) imaging agent concentration in the "tumor" tissue. Then the CVR for BP can be represented with the additional equivalency noted: (S11) This comes with the assumption that BP in the normal tissue is equal to zero. To find the time at which CVRBP is maximum, a similar process is followed as in the previous section. Assuming that the targeted and untargeted (control) imaging agents exhibit similar K1 values and plasma clearance, the derivative of Eq. (S11) can be simplified to: (S12) Combining like exponential terms yields: (S13) And taking the natural log of both sides of Eq. (S13) yields: (S14) which finally simplifies to: Equation (S15) is an analytical approximation of the time of maximum CVR for paired-agent imaging.

Kinetic data to test the correlation between true values and analytical approximation of time to maximum CVR and finding the CVR Tmax maps
In the last part of the paper, analytical estimations of CVR Tmax for single-and paired-agent imaging techniques were evaluated against simulated "truth." The input parameters for generating Fig. 7 and Table 3 in the main manuscript were taken from Schmidt and Wittrup. 35 Not all the values were explicitly measured in their study but based on the molecular weight of the imaging agents and their radii, approximated ranges for each class of imaging agent were extracted from their paper. Table S1 explicitly displays the ranges of parametric values used. To convert these values to the input parameters of our analytical approximations for CVR Tmax, data from other available resources were incorporated: K1 was estimated from blood flow (F) and vascular permeability (permeability-surface area product, PS), where K1 = F(1-e -PS/F ) and k2 is the product of K1 and tissue-blood partition coefficient (k2 = K1. ). Tumor blood flow and normal T k k k k k k k @ ---l tissue blood flow were approximated as 1 and 0.5 ml.g -1 .min -1 , respectively. 36 Surface area was approximated as 1.7 cm 2 .g -1 , with the partition coefficient assumed to be 1.64. 37