A theoretical model of blood-brain exchange is developed to analyze multiple-time tissue uptake data and determine whether a unidirectional transfer process was dominant. The model assumes linear transfer kinetics and includes a blood-plasma compartment, a reversible tissue region with multiple compartments, and one or more irreversible tissue regions. The solution of the model equations shows that plotting the ratio of total tissue solute concentration to plasma concentration against the ratio of arterial plasma concentration-time integral to plasma concentration should yield a curve that becomes linear with a slope equal to the influx constant $ K_i $. This method allows for the determination of $ K_i $, which quantifies blood-brain transport for most solutes and is the only transfer constant accurately determined for slowly crossing solutes. The model is general and does not assume specific time courses or compartment arrangements. The influx constant $ K_i $ is defined as the steady-state rate of solute flux across the blood-brain barrier (BBB) divided by the plasma concentration of the solute. The model can be applied to any membrane system, including the BBB, when the source solution's concentration is not constant. The multiple-time/graphical approach allows for the assessment of unidirectionality of uptake and provides physiological information about the distribution of the test material within the BBB complex. It also eliminates the need for vascular space markers and provides a lower limit for rapidly reversible volumes. The method involves plotting the ratio of tissue/plasma concentration against the integral of plasma concentration over time. If the resulting curve is linear, the influx constant can be determined from the slope. This approach is model-independent and provides information about the size and exchange rate of compartments that rapidly and reversibly exchange with plasma. It is particularly useful for analyzing data from positron emission tomography (PET) studies, as timed data can be obtained from a single subject. The method has been applied to various solutes, including amino acids and glucose, and has been shown to be effective in assessing the transport of solutes across the BBB. The approach is also applicable to other organ systems for assessing irreversible processes. The multiple-time/graphical method is preferred over compartmental analysis due to its simplicity and ability to provide physiological insights without model dependency.A theoretical model of blood-brain exchange is developed to analyze multiple-time tissue uptake data and determine whether a unidirectional transfer process was dominant. The model assumes linear transfer kinetics and includes a blood-plasma compartment, a reversible tissue region with multiple compartments, and one or more irreversible tissue regions. The solution of the model equations shows that plotting the ratio of total tissue solute concentration to plasma concentration against the ratio of arterial plasma concentration-time integral to plasma concentration should yield a curve that becomes linear with a slope equal to the influx constant $ K_i $. This method allows for the determination of $ K_i $, which quantifies blood-brain transport for most solutes and is the only transfer constant accurately determined for slowly crossing solutes. The model is general and does not assume specific time courses or compartment arrangements. The influx constant $ K_i $ is defined as the steady-state rate of solute flux across the blood-brain barrier (BBB) divided by the plasma concentration of the solute. The model can be applied to any membrane system, including the BBB, when the source solution's concentration is not constant. The multiple-time/graphical approach allows for the assessment of unidirectionality of uptake and provides physiological information about the distribution of the test material within the BBB complex. It also eliminates the need for vascular space markers and provides a lower limit for rapidly reversible volumes. The method involves plotting the ratio of tissue/plasma concentration against the integral of plasma concentration over time. If the resulting curve is linear, the influx constant can be determined from the slope. This approach is model-independent and provides information about the size and exchange rate of compartments that rapidly and reversibly exchange with plasma. It is particularly useful for analyzing data from positron emission tomography (PET) studies, as timed data can be obtained from a single subject. The method has been applied to various solutes, including amino acids and glucose, and has been shown to be effective in assessing the transport of solutes across the BBB. The approach is also applicable to other organ systems for assessing irreversible processes. The multiple-time/graphical method is preferred over compartmental analysis due to its simplicity and ability to provide physiological insights without model dependency.