The Bateman function revisited: A critical reevaluation of the quantitative expressions to characterize concentrations in the one compartment body model as a function of time with first-order invasion and first-order elimination

The Bateman function, $A''(e^{ - k_e t} - e^{ - k_a t} )$ , quantifies the time course of a first-order invasion (rate constant k_a) to, and a first-order elimination (rate constant k_e) from, a one-compartment body model where A″=(γDose)k_a/(k _a?k _e) V. The rate constants (whenk _a>3k _e) are frequently determined mined by the “method of residuals” or “feathering”. The rate constantk _a is actually the sum of rate constants for the removal of drug from the invading compartment. “Flip-flop”, the interchange of the values of the evaluated rate constants, occurs whenk _e>3k _a. Whether ?k _a or ?k _e is estimable from the terminal lnC-t slope can be determined from which apparent volume of distribution,V, derived from the Baterman function is the most reasonable. The Bateman function and “feathering” fail when the rate constants are equal. The time course is then expressed byC=γDtk e ^?kt . The determination of such equalk values can be obtained by the nonlinear fitting of suchC-t data with random error to the Bateman function. Also, rate constant equality can be concluded when 1/t _max and the k _min (value ofk _e at the minimum value of $e^{ - k_e t_{max} } /k_e$ plotted against variablek _e values) are synonymous or whenk _min t _max approximates unity. Simpler methods exist to evaluateC-t data. When a drug has 100% bioavailability, regression ofDose/V/C onAUC/C in the nonabsorption phase givesk _e no matter what is the ratio ofm=k _a /k _e . Sincek _e t _max=lnm/(m?1),m can be determined from the given table relatingm andk _e t _max. When γ is unknown,k _e can be estimated from the abscissas of intersections of plots of $C_{max} e^{k_e t_{max} }$ andk _e AUC, both plotted vs. arbitrary values ofk _e, and γD/V values are estimable from the ordinate of the intersection. Also, when γ is unknown,k _e can be estimated from the abscissas of intersections (or of closest approaches) of $e^{k_e t_{max} } /k_e$ andAUC/C _max, both plotted vs. arbitrary values ofk _e. TheC-t plot of the Modified Bateman function, $C = Be^{ - \lambda _2 t} - Ae^{ - \lambda _1 t}$ , does not commence at the origin (i.e., whent _c=0=0 and when a lag time does not exist). However,T _C=0 = ln(A/B/(λ₁-λ₂ whenA>B. AUC ^A″ without time lag is the same asAUC ^A≠B and $A'' = Be^{ - \lambda _2 t} = Ae^{ - \lambda _1 t}$ . Thet _max of theC-t plot of the latter ist _c=0 later than thet _max of theC-t plot of the former which commences att=0. However, (AUMC _uncorr ^A≠B )_∞ =B/λ ₂ ² -A/λ ₁ ² differs fromAUMC _corr ^A≠B ) =A″t _C=0 (1/λ₂-1/λ₁ +A″(1/λ ₂ ² -1/λ ₁ ² ). (AUMC _corr ^A″ ) =A″(1/λ ₂ ² -1/λ ₁ ² ) whenC-t plots start att=0.AUMC _uncorr ^{A ≠ B} is not valid. The (MRT _uncorr ^{A ≠ B} )_∞ is also an invalidMRT estimate, $(B/\lambda _2^2 - A/\lambda _1^2 )/e^{t_{c = 0} } (B/\lambda _2 - A/\lambda _1 )$ , but whenA>B, C-t curves which start at the origin,C _t=0 , haveMRT values displaced byMRT _corr ^{A ≠ B} =MRT ^{[A′ or A' = A = B]} ; +t _C=0 . Thet _max of the Bateman function is also displaced byt _C=0 when theA exceeds theB of its modified form. Dose-dependent pharmacokinetics can be concluded fromC-t data generated by various firstorder invading nonintravenous doses if drug absorption is 100%. Thek _e values can be determined if the apparent volume of distribution of the one-compartment body model is known. Plots ofm/AUC _t ^p vs. timet have a slope of — CL_ME, (the negative of the clearance of the metabolite) and an intercept of the clearance of the precursor, CL_PM, provided that all of the precursor had been absorbed. Similar studies could determine the appararent volume of distribution of the metabolite and the clearance (and thus the rate constant,k _PM=CL_PM/V _P) of the precursor to the metabolite.     

The effects of dopamine agonists on rotational behavior in non-tolerant and caffeine-tolerant rats

Tolerance develops to caffeine-induced stimulation of both locomotor activity and rotational behavior. The role of dopamine in tolerance to the locomotor stimulant effects of caffeine has been documented. However, the role of dopamine in caffeine-induced turning behavior remains to be elucidated. Therefore, the present study determined the role of dopamine receptors in tolerance to caffeine-induced rotational behavior. Rats with a unilateral lesion of the nigrostriatal tract, induced by 6-hydroxydopamine (6-OHDA), were treated chronically with either caffeine (1.0mg/ml) or with drug-free tap water, by a method of scheduled access. Agonists with and without selectivity for dopamine receptor sub-types were tested in both groups of rats (nonselective: apomorphine, d-amphetamine; D1 selective: SKF-38393, SKF-77434; D2 selective: R(-)-propylnorapomorphine (NPA), quinpirole). All drugs produced dose-dependent increases in turning that, with the exception of quinpirole, were comparable in both groups. Quinpirole produced a smaller effect in rats treated with caffeine than in control rats. Thus, there was significant cross-tolerance only to the effects of quinpirole. The concurrent administration of SKF-38393 with NPA produced a synergistic interaction on rotational behavior in control rats, to which cross-tolerance did not develop in caffeine-treated rats. In contrast to what occurs with locomotor activity, in control rats the selective D1 dopamine receptor antagonist SCH 23390 completely blocked SKF-38393-induced turning behavior and the selective D2 dopamine receptor antagonist eticlopride partially attenuated this effect. NPA-induced turning behavior was blocked only by eticlopride; SCH 23390 was without effect. Both SCH 23390 and eticlopride blocked d-amphetamine-induced rotational behavior. The results of this study suggest that D1 dopamine receptors are not involved in tolerance to caffeine-induced rotational behavior. The role of D2 dopamine receptors in this effect is unresolved. Results obtained from rotational behavior studies generally do not parallel those obtained from locomotor activity studies, suggesting that different mechanisms underlie the effects of caffeine on these two behaviors.     

Cannabis use and cognitive decline in persons under 65 years of age

The purpose of this study was to investigate possible adverse effects of cannabis use on cognitive decline after 12 years in persons under age 65 years. This was a follow-up study of a probability sample of the adult household residents of East Baltimore. The analyses included 1,318 participants in the Baltimore, Maryland, portion of the Epidemiologic Catchment Area study who completed the Mini-Mental State Examination (MMSE) during three study waves in 1981, 1982, and 1993-1996. Individual MMSE score differences between waves 2 and 3 were calculated for each study participant. After 12 years, study participants' scores declined a mean of 1.20 points on the MMSE (standard deviation 1.90), with 66% having scores that declined by at least one point. Significant numbers of scores declined by three points or more (15% of participants in the 18-29 age group). There were no significant differences in cognitive decline between heavy users, light users, and nonusers of cannabis. There were also no male-female differences in cognitive decline in relation to cannabis use. The authors conclude that over long time periods, in persons under age 65 years, cognitive decline occurs in all age groups. This decline is closely associated with aging and educational level but does not appear to be associated with cannabis use.     

Crystalloid inclusions in brain macrophages and hemopoietic tissue in GFAP-IL3 mice resemble inclusions identified in multiple sclerosis

Crystalloid inclusions or "pole bodies" observed in brain macrophages in human demyelinating disease represent a morphological enigma. Similar inclusions were detected in brain macrophages from the GFAP-IL3 mouse, a transgenic murine model for macrophage mediated demyelination. Mice also showed inclusions in hematopoietic tissue. They appear to be related to phagocytosis and secretion, respectively, as evidenced by the fact that in phagocytosing cells they often merged with lysozomes and that affected cells showed empty channels open to the interstitium. Based on ultrastructural and immunolocalization studies using chaperonin-10, lysozyme, and cathepsin the authors suggest that these inclusions are consistent with phagocytosis-related secretory products. This study may provide insight into the nature and significance of similar macrophage inclusions recently identified in multiple sclerosis.     

温血心停跳液与冷晶体心停跳液对狗心率变异性的影响

为探讨体外循环（ＣＰＢ）导致心脏植物神经系统（ＣＡＳ）损伤的机理,了解温血心停跳液能否防止ＣＰＢ后心率变异性（ＨＲＶ）的降低,采用对照方法观察了温血心停跳液与冷晶体心停跳液对狗ＨＲＶ的影响。结果显示：ＣＰＢ后温血心停跳液组（ＷＢ组）和冷晶体心停跳液组（ＣＣ组）的全频谱（ＴＰ）、低频（ＬＦ）和高频（ＨＦ）均较术前明显降低（Ｐ＜０．０５）,而且ＣＣ组比ＷＢ组降低更明显（Ｐ＜０．０５）,但ＬＦ／ＨＦ在组内及组间均无明显变化（Ｐ＞０．０５）。ＣＰＢ后２４小时平均心率（ＭＨＲ）明显增加（Ｐ＜０．０５）,且ＣＣ组高于ＷＢ组（Ｐ＜０．０５）。本研究表明：采用温血心停跳液或冷晶体心停跳液的ＣＰＢ不会干扰ＣＡＳ平衡,但均能使ＨＲＶ降低,温血心停跳液不能防止ＨＲＶ损害。     

The role of pancreatic venous sampling in the localization of occult insulinomas

The palpation and enucleation of occult insulinomas (less than 15 mm) can be a difficult surgical problem even with good arteriographic localization. In the authors' limited experience, confirmation of arteriographic findings by pancreatic venous sampling provided little additional localizing information. However, if arteriography is negative or equivocal, venous sampling can indicate the segment of pancreas to be "blindly" resected if the adenoma is not palpable. Venous sampling may be misleading in polyendocrine syndromes because of the frequency of multiple adenomas and variable hormone production.     

Commentary and historical perspective of anterior cruciate ligament rehabilitation

This article serves as the introduction and historical perspective of anterior cruciate ligament surgery and rehabilitation. Several physician-therapist teams have been invited to share their "state of the art" techniques and to contrast their programs to that espoused by Shelbourne and Nitz in 1990. Our commentary/review of "Accelerated Rehabilitation After Anterior Cruciate Ligament Reconstruction" (Shelbourne KD, Nitz P, Am J Sports Med 18:292-299, 1990) is provided to contextualize the reader to what most clinicians would recognize as an extremely aggressive rehabilitation approach that is being popularized in the 1990s. A comparison is then presented of the rehabilitation sequence used in the MacIntosh procedures, demonstrating how early motion/functional rehabilitation was the hallmark of this type of extraarticular rehabilitation sequence and how today's pattern has evolved to follow that philosophy. Each of the teamed authors has attempted to present his surgery and rehabilitation/techniques and highlight differences between his program and that of Shelbourne and Nitz. We hope that the readers find this glimpse of the past and present helpful in formulating their rehabilitation sequences and that the future will be predicated on excellent basic science and clinical judgment. J Orthop Sports Phys Ther 1992;15(6):265-269.