Mathematical models in percutaneous absorption

A number of mathematical models have been used to describe percutaneous absorption kinetics. In general, most of these models have used either diffusion-based or compartmental equations. The object of any mathematical model is to a) be able to represent the processes associated with absorption accurately, b) be able to describe/summarize experimental data with parametric equations or moments, and c) predict kinetics under varying conditions. However, in describing the processes involved, some developed models often suffer from being of too complex a form to be practically useful. In this chapter, we attempt to approach the issue of mathematical modeling in percutaneous absorption from four perspectives. These are to a) describe simple practical models, b) provide an overview of the more complex models, c) summarize some of the more important/useful models used to date, and d) examine sonic practical applications of the models. The range of processes involved in percutaneous absorption and considered in developing the mathematical models in this chapter is shown in Fig. 1. We initially address in vitro skin diffusion models and consider a) constant donor concentration and receptor conditions, b) the corresponding flux, donor, skin, and receptor amount-time profiles for solutions, and c) amount- and flux-time profiles when the donor phase is removed. More complex issues, such as finite-volume donor phase, finite-volume receptor phase, the presence of an efflux. rate constant at the membrane-receptor interphase, and two-layer diffusion, are then considered. We then look at specific models and issues concerned with a) release from topical products, b) use of compartmental models as alternatives to diffusion models, c) concentration-dependent absorption, d) modeling of skin metabolism, e) role of solute-skin-vehicle interactions, f) effects of vehicle loss, a) shunt transport, and h) in vivo diffusion, compartmental, physiological, and deconvolution models. We conclude by examining topics such as a) deep tissue penetration, b) pharmacodynamics, c) iontophoresis, d) sonophoresis, and e) pitfalls in modeling.

Percutaneous absorption of sunscreen agents from liquid paraffin: Self-association of octyl salicylate and effects on skin flux

This study provides an investigation of the availability of octyl salicylate (OS), a common sunscreen agent, from liquid paraffin and the effect of OS on skin permeability. A model membrane system to isolate the vehicle effect from membrane permeability has been developed. Partitioning of OS between liquid paraffin and aqueous receptor phases was conducted. Partition coefficients increased with increase in OS concentration. A range of OS concentrations in liquid paraffin was diffused across human epidermis and synthetic membranes into 4% bovine serum albumin in phosphate-buffered saline and 50% ethanol. Absorption profiles of OS obtained from silicone and low-density polyethylene (LDPE) membranes were similar to each other but higher than for the high-density polyethylene [HDPE (3 times)] membrane and human epidermis (15 times). The steady state fluxes and apparent permeability coefficients (K-p') obtained from the diffusion studies showed the same trends with all membranes, except for the HDPE membrane which showed greater increase in flux and K-p' at concentrations above 30%. IR spectra showed that several bands of OS were shifted with concentrations, and the molecular models further suggested that the main contribution to the self-association is from non-1,4 van der Waals interactions.

Diffusion modeling of percutaneous absorption kinetics: 2. Finite vehicle volume and solvent deposited solids

The diffusion model for percutaneous absorption is developed for the specific case of delivery to the skin being limited by the application of a finite amount of solute. Two cases are considered; in the first, there is an application of a finite donor (vehicle) volume, and in the second, there are solvent-deposited solids and a thin vehicle with a high partition coefficient. In both cases, the potential effect of an interfacial resistance at the stratum corneum surface is also considered. As in the previous paper, which was concerned with the application of a constant donor concentration, clearance limitations due to the viable eqidermis, the in vitro sampling rate, or perfusion rate in vivo are included. Numerical inversion of the Laplace domain solutions was used for simulations of solute flux and cumulative amount absorbed and to model specific examples of percutaneous absorption of solvent-deposited solids. It was concluded that numerical inversions of the Laplace domain solutions for a diffusion model of the percutaneous absorption, using standard scientific software (such as SCIENTIST, MicroMath Scientific software) on modern personal computers, is a practical alternative to computation of infinite series solutions. Limits of the Laplace domain solutions were used to define the moments of the flux-time profiles for finite donor volumes and the slope of the terminal log flux-time profile. The mean transit time could be related to the diffusion time through stratum corneum, viable epidermal, and donor diffusion layer resistances and clearance from the receptor phase. Approximate expressions for the time to reach maximum flux (peak time) and maximum flux were also derived. The model was then validated using reported amount-time and flux-time profiles for finite doses applied to the skin. It was concluded that for very small donor phase volume or for very large stratum corneum-vehicle partitioning coefficients (e.g., for solvent deposited solids), the flux and amount of solute absorbed are affected by receptor conditions to a lesser extent than is obvious for a constant donor constant donor concentrations. (C) 2001 Wiley-Liss, Inc. and the American Pharmaceutical Association J Pharm Sci 90:504-520, 2001.

Rehabilitation outcomes following percutaneous coronary interventions (PCI)

This prospective study evaluated the effect of an individualized, comprehensive, home-based cardiac rehabilitation program combining exercise training with risk factor modification and psychosocial counseling on risk factors, psychological wellbeing, functional capacity, and work resumption in 99 post-percutaneous coronary interventions (PCI) patients randomized to control (standard care plus telephone follow-up, n = 49) or intervention (individualized, comprehensive, home-based cardiac rehabilitation, n = 50) groups. Data were collected at time 1 (T-1) during hospital admission, time 2 (T-2) approximately 2 months post-PCI, and time 3 (T-3) approximately 12 months post-PCI. Results suggest that the allocation to an individualized, comprehensive, home-based cardiac rehabilitation program provided more advantageous outcomes. At both follow-ups, the intervention group showed within-group improvement in serum cholesterol levels (P < 0.02; P < 0.01) and exercise participation (P < 0.001; P < 0.001) with differences in exercise participation favoring the intervention group (P < 0.01) at T-2 Repeated measures ANOVA showed significant improvements over time in body mass index (BMI) (P < 0.01), psychological well-being (P < 0.001), and functional capacity (P < 0.001) for both groups. More patients in the intervention group had returned to work at T-2 (P < 0.001) and did so more quickly (P < 0.01). These findings suggest that an individualized, comprehensive, home-based cardiac rehabilitation program improves risk factor profiles and work resumption patterns for patients following PCI. (C) 2001 Elsevier Science Ireland Ltd. All rights reserved.

Diffusion modeling of percutaneous absorption kinetics: 3. Variable diffusion and partition coefficients, consequences for stratum corneum depth profiles and desorption kinetics

Stratum corneum (SC) desorption experiments have yielded higher calculated steady-state fluxes than those obtained by epidermal penetration studies. A possible explanation of this result is a variable diffusion or partition coefficient across the SC. We therefore developed the diffusion model for percutaneous penetration and desorption to study the effects of either a variable diffusion coefficient or variable partition coefficient in the SC over the diffusion path length. Steady-state flux, lag time, and mean desorption time were obtained from Laplace domain solutions. Numerical inversion of the Laplace domain solutions was used for simulations of solute concentration-distance and amount penetrated (desorbed)-time profiles. Diffusion and partition coefficients heterogeneity were examined using six different models. The effect of heterogeneity on predicted flux from desorption studies was compared with that obtained in permeation studies. Partition coefficient heterogeneity had a more profound effect on predicted fluxes than diffusion coefficient heterogeneity. Concentration-distance profiles show even larger dependence on heterogeneity, which is consistent with experimental tape-stripping data reported for clobetasol propionate and other solutes. The clobetasol propionate tape-stripping data were most consistent with the partition coefficient decreasing exponentially for half the SC and then becoming a constant for the remaining SC. (C) 2004 Wiley-Liss, Inc.

Increased platelet-derived microparticles in the coronary circulation of percutaneous transluminal coronary angioplasty patients

Platelet-derived microparticles that are produced during platelet activation are capable of adhesion and aggregation. Endothelial trauma that occurs during percutaneous transluminal coronary angioplasty (PTCA) may support platelet-derived microparticle adhesion and contribute to development of restenosis. We have previously reported an increase in platelet-derived microparticles in peripheral arterial blood with angioplasty. This finding raised concerns regarding the role of platelet-derived microparticles in restenosis, and therefore the aim of this study was to monitor levels in the coronary circulation. The study population consisted of 19 angioplasty patients. Paired coronary artery and sinus samples were obtained following heparinization, following contrast administration, and subsequent to all vessel manipulation. Platelet-derived microparticles were identified with an anti-CD61 (glycoprotein IIIa) fluorescence-conjugated antibody using flow cytometry. There was a significant decrease in arterial platelet-derived microparticles from heparinization to contrast administration (P=0.001), followed by a significant increase to the end of angioplasty (P=0.004). However, there was no significant change throughout the venous samples. These results indicate that the higher level of platelet-derived microparticles after angioplasty in arterial blood remained in the coronary circulation. Interestingly, levels of thrombin-antithrombin complexes did not rise during PTCA. This may have implications for the development of coronary restenosis post-PTCA, although this remains to be determined.

A cost-effectiveness analysis of fluvastatin in patients with diabetes after successful percutaneous coronary intervention

Background: The Lescol Intervention Prevention Study (LIPS) was a multinational randomized controlled trial that showed a 47% reduction in the relative risk of cardiac death and a 22% reduction in major adverse cardiac events (MACEs) from the routine use of fluvastatin, compared with controls, in patients undergoing percutaneous coronary intervention (PCI, defined as angioplasty with or without stents). In this study, MACEs included cardiac death, nonfatal myocardial infarction, and subsequent PCI and coronary artery bypass graft. Diabetes was the greatest risk factor for MACEs. Objective: This study estimated the cost-effectiveness of fluvastatin when used for secondary prevention of MACEs after PCI in people with diabetes. Methods: A post hoc subgroup analysis of patients with diabetes from the LIPS was used to estimate the effectiveness of fluvastatin in reducing myocardial infarction, revascularization, and cardiac death. A probabilistic Markov model was developed using United Kingdom resource and cost data to estimate the additional costs and quality-adjusted life-years (QALYs) gained over 10 years from the perspective of the British National Health Service. The model contained 6 health states, and the transition probabilities were derived from the LIPS data. Crossover from fluvastatin to other lipid-lowering drugs, withdrawal from fluvastatin, and the use of lipid-lowering drugs in the control group were included. Results: In the subgroup of 202 patients with diabetes in the LIPS trial, 18 (15.0%) of 120 fluvastatin patients and 21 (25.6%) of 82 control participants were insulin dependent (P = NS). Compared with the control group, patients treated with fluvastatin can expect to gain an additional mean (SD) of 0.196 (0.139) QALY per patient over 10 years (P < 0.001) and will cost the health service an additional mean (SD) of 10 (E448) (P = NS) (mean [SD] US $16 [$689]). The additional cost per QALY gained was;(51 (US $78). The key determinants of cost-effectiveness included the probabilities of repeat interventions, cardiac death, the cost of fluvastatin, and the time horizon used for the evaluation. Conclusion: Fluvastatin was an economically efficient treatment to prevent MACEs in these patients with diabetes undergoing PCI.

Prevalence and patterns of anxiety and depression in patients undergoing elective percutaneous transluminal coronary angioplasty

Background The use of elective percutaneous transluminal coronary angioplasty (PTCA) as a treatment for coronary heart disease is increasing. Despite this, little is known about the prevalence and patterns of anxiety and depression experienced by patients undergoing and recovering from this procedure. Anxiety and depression are factors known to negatively influence recovery after a cardiac event. Objective The purpose of this study was to (1) describe the levels of anxiety and depression reported by patients pre- and postelective PTCA, and (2) determine associations evident between anxiety and depression and the sociodemographic and clinical variables of gender, marital status, history of acute myocardial infarction, and attendance at cardiac rehabilitation. Methods In this descriptive, repeated-measures investigation, patients (n = 140) were requested to complete the Spielberger State Trait Anxiety Inventory and Cardiac Depression Scale (CDS) at three time points: 0(1) before admission for elective PTCA (T1); (2) 6 to 8 weeks (T2) after PTCA; and (3) 6 to 8 months (T3) after PTCA. Results A typical participant was male (75%), of European ethnicity (90%), aged 62 years (standard deviation = 10.7) with single or double vessel disease, and had attended cardiac rehabilitation in the past. At T1, 16% of men and 24% of women had state anxiety scores comparable to those experienced by neuropsychiatric patients. Trait anxiety scores remained relatively constant over time; higher scores at T1 were associated with past acute myocardial infarction. CDS scores at T2 and T3 were significantly lower than those at T1. However, an unexpected increase in CDS scores occurred at T3, compared with T2. At T3, 14% of men and 10% of women were depressed, relative to T1. Conclusion The findings lend support for the closer surveillance of emotional status in this population. Specialist nurses have the potential to play a greater role in identifying those at risk of developing anxiety and depression. However, this unmet need will remain unmet until specialist nurses who spend the most face-to-face time with patients are equipped with the skills and resources to systematically identify those “at risk.”

Percutaneous absorption of steroids: Determination of in vitro permeability and tissue reservoir characteristics in human skin layers

The skin localization of steroids following topical application is largely unknown. We determined the distribution of five steroids in human skin using excised epidermal, dermal, and full-thickness membranes in vitro. There was no significant difference in steroid maximum flux through epidermal and full-thickness membranes, other than significantly lower fluxes for the most polar steroid, aldosterone. Hydrocortisone had the highest dermal diffusivity and dermal penetration, and the accumulation of hydrocortisone and corticosterone was higher than that of the other steroids. Slower penetration and higher accumulation in the viable epidermis of progesterone in full-thickness skin were consistent with dermal penetration limitation effects associated with high lipophilicity. Copyright (c) 2006 S. Karger AG, Basel

Topical penetration of commercial salicylate esters and salts using human isolated skin and clinical microdialysis studies

Aims The penetration of active ingredients from topically applied anti-inflammatory pharmaceutical products into tissues below the skin is the basis of their therapeutic efficacy. There is still controversy as to whether these agents are capable of direct penetration by diffusion through the tissues or whether redistribution in the systemic circulation is responsible for their tissue deposition below the application site. Methods The extent of direct penetration of salicylate from commercial ester and salt formulations into the dermal and subcutaneous tissue of human volunteers was determined using the technique of cutaneous microdialysis. We also examined differences in the extent of hydrolysis of the methylester of salicylate applied topically in human volunteers and in vitro skin diffusion cells using full-thickness skin and epidermal membranes. Results The present study showed that whilst significant levels of salicylate could be detected in the dermis and subcutaneous tissue of volunteers treated with the methylsalicylate formulation, negligible levels of salicylate were seen following application of the triethanolamine salicylate formulation. The tissue levels of salicylate from the methylsalicylate formulation were approx. 30-fold higher than the plasma concentrations. Conclusion The absorption and tissue concentration profiles for the commercial methylsalicylate formulation are indicative of direct tissue penetration and not solely redistribution by the systemic blood supply.

In vitro human epidermal and polyethylene membrane penetration and retention of the sunscreen benzophenone-3 from a range of solvents

Purpose. To study epidermal and polyethylene membrane penetration and retention of the sunscreen benzophenone-3 (BP) from a range of single solvent vehicles and evaluate solvent effects on permeability parameters. Methods. The solubility of BP was measured in a number of solvents. Penetration of BP across human epidermis and high density polyethylene (HDPE) membranes was studied from 50% saturated solutions in each solvent. Results. Maximal BP fluxes from the solvents across the two membranes varied widely. Highest fluxes were observed from 90% ethanol (EtOH) for epidermis and from isopropyl myristate (IPM) and C12-15 benzoate alcohols (C12-15 BA) for HDPE membrane. Both the flux and estimated permeability coefficient and skin-vehicle partitioning of BP appeared to be related to the vehicle solubility parameter (delta(v)). The major effects of solvents on BP flux appear to be via changes in BP diffusivity through the membranes. Conclusions. Minimal penetration of sunscreens such as BP is best achieved by choosing vehicles with a delta(v) substantially different to the solubility parameter of the membrane.

Tension regulation during lengthening and shortening actions of the human soleus muscle

In the present study we investigated tension regulation in the human soleus (SOL) muscle during controlled lengthening and shortening actions. Eleven subjects performed plantar flexor efforts on an ankle torque motor through 30 degrees of ankle displacement (75 degrees-105 degrees internal ankle angle) at lengthening and shortening velocities of 5, 15 and 30 degrees s(-1). To isolate the SOL from the remainder of the triceps surae, the subject's knee was flexed to 60 degrees during all trials. Voluntary plantar flexor efforts were performed under two test conditions: (1) maximal voluntary activation (MVA) of the SOL, and (2) constant submaximal voluntary activation (SVA) of the SOL. SVA trials were performed with direct visual feedback of the SOL electromyogram (EMG) at a level resulting in a torque output of 30% of isometric maximum. Angle-specific (90 degrees ankle angle) torque and EMG of the SOL, medial gastrocnemius (MG) and tibialis anterior (TA) were recorded. In seven subjects from the initial group, the test protocol was repeated under submaximal percutaneous electrical activation (SEA) of SOL (to 30% isometric maximal effort). Lengthening torques were significantly greater than shortening torques in all test conditions. Lengthening torques in MVA and SVA were independent of velocity and remained at the isometric level, whereas SEA torques were greater than isometric torques and increased at higher lengthening velocities. Shortening torques were lower than the isometric level for all conditions. However, whereas SVA and SEA torques decreased at higher velocities of shortening, MVA torques were independent of velocity. These results indicate velocity- and activation-type-specific tension regulation in the human SOL muscle.

Mortality and recurrent cardiac events after coronary artery bypass graft: long term outcomes in a population study

Objective: To determine 30 day mortality, long term survival, and recurrent cardiac events after coronary artery bypass graft (CABG) in a population. Design: Follow up study of patients prospectively entered on to a cardiothoracic surgical database. Record linkages were used to obtain data on readmissions and deaths. Patients: 8910 patients undergoing isolated first CABG between 1980 and 1993 in Western Australia. Main outcome measures: 30 day and long term survival, readmission for cardiac event (acute myocardial infarction, unstable angina, percutaneous transluminal coronary angioplasty or reoperative CABG). Results: There were 3072 deaths to mid 1999. 30 day and long term survival were significantly better in patients treated in the first five years than during the following decade. The age of the patients, proportion of female patients, and number of grafts increased over time. An urgent procedure (odds ratio 3.3), older age (9% per year) and female sex (odds ratio 1.5) were associated with increased risk for 30 day mortality, while age (7% per year) and a recent myocardial infarction (odds ratio 1.16) influenced long term survival. Internal mammary artery grafts were followed by better short and long term survival, though there was an obvious selection bias in favour of younger male patients. Conclusions: This study shows worsening crude mortality at 30 days after CABG from the mid 1980s, associated with the inclusion of higher risk patients. Older age, an acute myocardial infarction in the year before surgery, and the use of sephenous vein grafts only were associated with poorer long term survival and greater risk of a recurrent cardiac event. Female sex predicted recurrent events but not long term survival.