The effect of walking and vitamin B supplementation on quality of life in community-dwelling adults with mild cognitive impairment: a randomized, controlled trial

Objectives To examine the effect of walking and vitamin B supplementation on quality-of-life (QoL) in community-dwelling adults with mild cognitive impairment.
Introduction
Especially in older people, both mental and physical function decrease due to multiple age related changes, which in turn may affect quality of life (QoL). The most obvious decrease in mental function is cognitive decline, which is a common aspect of aging. However, in some cases decline is more serious than expected for a certain age. This is specified as Mild Cognitive Impairment (MCI). MCI is considered to be a potential transitional stage between normal cognitive function and Alzheimer’s disease, characterized by (1) subjective memory complaint (2) objective memory impairment (3) normal mental status (4) intact activities of daily living (ADL) (5) absence of dementia [1]. Independent of the latter four criteria, subjective memory complaints are related to lower QoL [2]. Moreover, MCI is associated with poor physical health and high risk of ADL dependence [3, 4]. Since both cognitive and physical decline belong to the most important determinants of QoL in community dwelling elderly subjects [5], subjects with MCI are likely to be susceptible to a decrease in QoL.
The number of adults with MCI is increasing considerably due to the aging population. For multiple reasons, it is important to prevent a decrease in QoL. Apart from the personal benefits, a high rated QoL also reduces medical consumption and helps to maintain independency as long as possible [6]. This in turn may relieve significant others, caregivers and medical society in general. For this reason, attention should be paid to possible interventions contributing towards a higher level of overall QoL and it’s mental and physical components. In this respect, physical exercise and vitamin supplementation are interesting interventions worth investigating. Regular participation in moderate intensity aerobic training is reported to be beneficial in improving QoL and wellbeing, which is an important aspect of QoL [7, 8]. Since walking is the most prevalent physical activity among older adults [9], improving QoL by increasing the time spent on moderate intensity walking seems promising. Indeed, a community based walking program significantly improved both the physical and mental components of health-related QoL in older adults (n = 582) [10]. Inconclusive evidence has been reported on the influence of vitamin B supplementation on QoL. Different aspects of QoL were not responsive to short term supplementation (range 4–12 weeks) with different doses and combinations of B vitamins in men and women [11–13].
Not much is known about QoL in community dwelling elderly with MCI. Moreover, no trials on the effect of exercise and vitamin B supplementation on QoL have been carried out yet in adults with MCI. The FACT-study (Folate physical Activity Cognition Trial) was developed to examine the effect of these interventions on cognition [14]. Aspects of QoL were measured as a secondary outcome. In the present paper, the effectiveness of 1 year moderate intensity walking (two sessions of 60 min per week) and daily vitamin supplementation (5 mg folate, 50 mg vitamin B6 and 0.4 mg B12) on both overall QoL and it’s health-related components is examined in community dwelling older adults with MCI. We hypothesize that 1 year moderate intensity walking benefits QoL. Concerning the effect of vitamin supplementation, this paper should be considered as explorative.
Methods
Study design
The study was designed as a randomized, placebo controlled intervention trial, based on a two-by-two factorial design. The study-protocol has been described in detail elsewhere [14] and was approved by the VU University Medical Center medical ethics committee. Written informed consent was obtained from all participants.
Participants
In a medium-sized Dutch town community dwelling subjects aged 70–80 years with MCI were identified using a population based two-step-screening [15]. The operational criteria for MCI according to the criteria of Petersen et al. [1] and additional inclusion criteria for the RCT are described in Table 1. Subjects were not paid to participate in the study.
Table 1Inclusion and exclusion criteria for participation in the trial Operationalization of Petersen criteria for MCI (1–5) and additional inclusion criteria for the RCT (6–12)1. Memory complaints (answer yes to question ‘do you have memory complaints’, or at least twice sometimes at cognition scale of Strawbridge [16]2. Objective memory impairment; 10 WLT delayed recall ≤5 + percentage savings ≤ 100 [17]3. Normal general cognitive functioning; TICS ≥ 19 + MMSE ≥ 24 [18, 19]4. Intact daily functioning: no report of disability in activities of daily living on GARS-scale, except on the item ‘taking care of feet and toe nails’ [20]5. Absence of dementia; TICS ≥ 19 + MMSE ≥ 246. Being able to perform moderate intensity physical activity, without making use of walking devices, e.g., a rollator or a walking frame 7. Not using vitamin supplements/vitamin injections/drinks with dose of vitamin B6, B11 or B12 comparable to vitamin supplement given in intervention8. Not suffering from epilepsy, multiple sclerosis, Parkinson’s disease, kidney disorder requiring haemodialysis, psychiatric impairment9. Not suffering from depression as measured by the GDS (cut off ≤5) [21]10. Not using medication for rheumatoid arthritis or psoriasis interfering with vitamin supplement11. No alcohol abuse (men < 21 consumptions a week, women < 15 consumptions a week)12. Not currently living in a nursing home or on a waiting list for a nursing homeMCI = Mild Cognitive Impairment, RCT = Randomized Controlled Trial, 10 WLT = 10 Word Learning Test, TICS = Telephone Interview for Cognitive Status, MMSE = Mini Mental State Examination, GARS = Groningen Activity Restriction Scale, GDS = Geriatric Depression Scale
Randomization
After the baseline interview, subjects were randomly assigned to the interventions using the statistical computer program SPSS. Intervention groups were: (1) walking program or placebo activity program; and (2) vitamin B supplementation or placebo supplementation. Randomization was stratified for physical activity level at baseline in minutes per day as measured by the LASA physical activity questionnaire [22]. For the flow of participants see Fig. 1.
Fig. 1Flow chart. TI = Telephone Interview, WP = Walking Program, PAP = Placebo Activity Program, FA/B12/B6 = Folic Acid, Vitamin B12, Vitamin B6 supplementation, SO = significant other, T6 = follow-up after 6 months, T12= follow-up after 12 months, *reason for exclusion: only baseline data available
Exercise intervention
Subjects assigned to the walking program (WP) participated twice a week 60 min in group-based moderate intensity walking during 1 year. Each session consisted of a warming up, moderate intensity walking exercises and a cooling down. The WP was based on ‘Sportive Walking,’ an existing aerobic walking program [23] aimed at improving cardiovascular endurance. Therefore, duration and intensity of the walking exercises increased gradually during the program. Sessions took place outdoor in municipal parks. Subjects not assigned to the WP participated in a placebo activity program (PAP) with the same frequency, session duration and program duration. However, the PAP consisted of low intensity exercise, such as light range of motion movements and stretching. Sessions were divided into five themes: relaxation, activities of daily living, balance, flexibility, posture and a combination of all. For each theme three sessions were developed and the entire series of 18 sessions was repeated during the intervention period. The PAP was carried out in community centers. Both programs were supervised by qualified and trained instructors. Attendance to both programs was assessed by the percentage of attended sessions.
Vitamin supplementation (FA/B12/B6)
Subjects in the vitamin supplementation group took one pill containing 5 mg vitamin B11 (Folic Acid), 0.4 mg vitamin B12 (Cyanocobalamin) and 50 mg vitamin B6 (Pyridoxine-hydrochloride) daily during 1 year. This vitamin supplement is available on prescription in The Netherlands. Subjects randomized to the control group took an identically looking placebo pill. The pills were packed in blister packs for 1 week, which were labeled for each day of the week. Compliance with the vitamin supplementation was verified by pill counts in returned blister packs during the intervention.
Outcome measures
Baseline data on sociodemographic and background variables were collected using a postal screening questionnaire. The measurement of other baseline variables, as reported in Table 2, has been described elsewhere [14]. In the present manuscript a distinction was made between ‘overall quality of life,’ referring to a subjects overall enjoyment of life and ‘health-related quality of life,’ referring to health-related factors affecting quality of life. The term QoL was used as an umbrella term for both overall and health-related QoL. The population-specific Dementia Quality of Life questionnaire (D-QoL) [24] was used to assess overall QoL and the generic Short Form 12 (SF12) [25] to assess health-related QoL. The D-QoL is a 29 item measure especially developed for elderly with cognitive decline and dementia. The participant is asked about how much they enjoyed activities that were reported to be important for elderly such as ‘watching animals.’ Moreover, the frequency of certain positive and negative feelings such as ‘lovable’ or ‘worried’ were asked for. Finally, they were asked to rate their overall quality of life. The participant was instructed to choose the best fitting answer from five item response scales. The answers were divided into five domains of QoL measuring sense of aesthetics, feelings of belonging, negative affect, positive affect/humor and self esteem. A mean score ranging from one to five was calculated for these subscales and for the total D-QoL. A higher score indicated better quality of life. Median internal consistency reliability of the D-QoL was 0.80 and median test–retest reliability was 0.72 in a sample of 95 older adults with different stages of cognitive decline [24]. The SF12 consists of 12 items measuring eight concepts of both mental and physical health, i.e., physical functioning, role-physical, bodily pain, general health, energy, social functioning, role emotional and mental health. These concepts are subdivided into two summary scores using a norm-based criterion: i.e., mental and physical component summary scales (SF12-MCS and SF12-PCS). The mean score is 50 with a standard deviation of 10. For example, a score of 60 corresponds to a-QoL rating of one standard deviation above the average ratings in the general population. Test retest reliability for the SF-12 MCS was 0.76 in a sample of 187 adults in the United Kingdom and 0.77 in a sample of 232 adults in the United States. Reliability coefficients of the SF-12 PCS in these populations were 0.86 and 0.89, respectively [25]. In the present study, measurement took place during a personal interview at baseline and after 6 and 12 months. Both the D-QoL and the SF-12 were administered by a trained interviewer who was unaware of the participants’ group allocation.
Table 2Baseline characteristics of participants (n = 152)Exercise interventionVitamin interventionWP (n = 77)PAP (n = 75)FA/B12/B6 (n = 78)Placebo-pill (n = 74)Age (Mean (SD))75 (2.9)75 (2.8)75 (2.8)75 (2.9)Gender (% male)48*645655MMSE (Median (10th–90th ‰))29 (26–30)29 (27–30)29 (25–30)29 (27–30)Education (% low/middle/high) 61/22/1752/29/1957/26/1755/26/19Marital status (% living together)75686973Physical activitya (min/day) (Median (10th–90th ‰))44 (10–155)39 (11–120)45 (13–155)38 (9–111)Vitamin status (% deficient FA/B12/B6)b46/8/048/8/049/9/045/7/0Homocysteine statusc (% hyperhomocysteinemia)27232723Blood pressure (% hypertension)d27*142516BMI (kg/m2) (Median (10th–90th p‰))26.7 (23.1–31.5)26.6 (23.5–32.7)26.5 (23.3–32.8)26.7 (23.5–31.2)Smoking (% smokers)13151711Number of self-reported diseases (% 0,1,2)e52/42/669/27/466/28/655/41/4WP = Walking Program, PAP = Placebo Activity Program, FA/B12/B6 = Folic Acid, Vitamin B12, Vitamin B6 supplementation, MMSE = Mini Mental State Examination, Education: low = no education, primary education, lower vocational training; intermediate = intermediate level secondary education, intermediate vocational training; high = higher level secondary education, higher vocational training, university training. BMI = Body Mass Indexa ≥3.0 metabolic equivalents b Cut off points: FA red blood cell <337 nmol/l or FA plasma < 6,3 nmol/l; B12 ≤ 150 pmol/l; B6 < 20 nmol/lc Homocysteine > 14 mmol/ld Hypertension = diastole ≥ 90 and systole ≥160e Cardiovascular disease, chronic obstructive pulmonary disease, diabetes, epilepsy, multiple sclerosis, Parkinson’s disease, psychiatric disease, renal failure requiring dialysis and/or rheumatoid arthritis * Significantly different from PAP (P < 0.05)
Statistical analyses
Differences between groups on baseline characteristics were tested using independent t-tests (normally distributed variables), Mann–Whitney U tests (not normally distributed variables) and χ2 (categorical variables). Within group differences were tested using dependent t-tests.
Subsequently, data were analyzed according to a modified intention-to-treat principle, based on data from all randomized participants who provided data at baseline and at least one follow-up measurement. To evaluate the effects of the walking program and the vitamin supplementation on QoL, longitudinal regression analysis was used. The two follow-up measurements were defined as dependent variable and multi level analysis with two levels was used, (1) time of follow-up measurement (values corresponding with performance after six and 12 months intervention); (2) individual. According to the study protocol [14], the effect of both interventions was examined independently from each other. Data were analyzed using a crude and an adjusted model. Independent variables were exercise intervention and vitamin intervention. By analyzing both interventions in the same model, results were adjusted for the possible influence of the other intervention. Moreover, all analyses were adjusted for baseline performance on the outcome measure by adding this as a covariate. In the adjusted model, education, baseline activity level, baseline vitamin status, attendance to the exercise program and compliance with the supplementation were added as covariates. Interaction between gender and the WP or FA/B6/B12-supplementation was checked in the adjusted model. In the case of significant interaction, results were reported for men and women separately. In the case of no interaction, gender was added to the adjusted model as an additional covariate. Also, in the ‘adjusted model’ an interaction effect of the exercise program with attendance to the exercise program was checked. Finally, data were analyzed according to the per protocol principle, including all participants who attended at least 75% of the sessions. This cut-off point is in concordance with previous exercise intervention studies in older adults [26, 27].
Data were analyzed using SPSS for Windows (release 12.0.1). A significance level of 5% was used for between group comparisons and of 10% for interaction terms. For all analyses, regression coefficients and 95% confidence intervals for the adjusted models were reported, with the regression coefficients directly indicating the difference in QoL ratings between the WP and the PAP or the FA/B12/B6-supplementation versus placebo supplementation. In the case of significant interaction, regression coefficients and the 95% confidence intervals of the interaction terms were reported.
Results
Patient characteristics
Hundred-seventy-nine participants were randomized to the interventions. Twenty-seven of them were excluded from the analyses, because they only provided baseline data. These subjects were more often married (71% vs. 52%, P = 0.05) and less often current smokers (0% vs. 14%, P = 0.04) than the remaining 152 participants who provided QoL data at baseline and at at least one follow-up measurement. The latter 152 participants were included in the analyses (see Fig. 1). Their mean age (SD) was 75 (2.9) years. Fifty-six percent was male. Additional baseline variables are described per factor in Table 2. Compared to the PAP, the WP included fewer men (48% in WP vs. 64% in PAP) and more subjects with hypertension (27% in WP vs. 14% in PAP). Ratings for both overall and health-related QoL at baseline and after 6 and 12 months intervention are presented in Table 3. No baseline differences were observed on these measures, except for a higher rating of D-QoL self-esteem in subjects in the FA/B12/B6-group compared to subjects in the placebo-supplementation group.
Table 3Means (standard deviations) of QoL ratings at baseline and after 6 and 12 months in older adults with MCIaWP PAPFA/B12/B6 Placebo T0 (n = 77)T6 (n = 77)T12 (n = 71)T0 (n = 75)T6 (n = 75)T12 (n = 67)T0 (n = 78)T6 (n = 78)T12 (n = 71)T0 (n = 74)T6 (n = 74)T12 (n = 67)D-QoL sumscore3.5 (0.26)3.5 (0.29)3.5 (0.27)3.5 (0.32)3.5 (0.34)3.5 (0.34)3.5 (0.32)3.5 (0.32)3.5 (0.33)3.4 (0.24)3.5 (0.31)3.5 (0.27)D-QoL aesthetics3.5 (0.63)3.5 (0.64)3.6 (0.60)3.5 (0.70)3.5 (0.71)3.5 (0.65)3.5 (0.64)3.5 (0.68)3.6 (0.61)3.4 (0.68)3.5 (0.67)3.6 (0.64)D-QoL belonging3.7 (0.50)3.7 (0.49)3.7 (0.44)3.8 (0.45)3.7 (0.47)3.7 (0.46)3.8 (0.50)3.6 (0.50)3.6 (0.48)3.7 (0.44)3.8 (0.45)3.8 (0.40)D-QoL negative affect2.7 (0.45)2.7 (0.46)2.8 (0.50)2.7 (0.55)2.8 (0.54)2.8 (0.52)2.7 (0.54)2.8 (0.47)2.8 (0.53)2.7 (0.47)2.7 (0.53)2.8 (0.49)D-QoL positive affect3.8 (0.39)3.7 (0.46)3.8 (0.40)3.8 (0.40) 3.7 (0.44)3.8 (0.43)3.8 (0.41)3.7 (0.47)3.8 (0.44)3.8 (0.39)3.8 (0.43)3.8 (0.39)D-QoL self esteem3.6 (0.45)3.8 (0.41)3.8 (0.40)3.7 (0.48)3.7 (0.49)3.8 (0.48)3.8 (0.48)*3.8 (0.48)3.9 (0.48)3.6 (0.43)3.7 (0.43)3.7 (0.38)SF12-MCS54.6 (6.85)55.6 (6.40)55.3 (4.39)54.7 (8.07)55.0 (7.34)55.3 (6.24)55.5 (7.49)55.9 (6.91)55.8 (4.90)53.8 (7.36)54.6 (6.86)54.8 (5.76)SF12-PCS48.2 (7.15)48.1 (7.57)50.5 (6.13) 48.7 (7.86)48.8 (8.47)49.8 (7.04)47.9 (8.20)47.4 (8.79)49.8 (6.68)49.1 (6.67)49.6 (7.00)50.6 (6.49)MCI = Mild Cognitive Impairment, WP = Walking Program, PAP = Placebo Activity Program, FA/B12/B6= Folic Acid, Vitamin B12, Vitamin B6 supplementation, D-QoL = Dementia Quality of Life, SF12-MCS = Short Form 12 Mental Component Summary, SF12-PCS = Short Form 12 Physical Component Summarya Higher rating indicates better QoL* P < 0.05 (difference between FA/B12/B6 and placebo)
Attendance to the WP and the PAP
Overall median attendance to the exercise programs (10th−90th percentile) was 63 (0–89) percent and did not differ between the WP and the PAP. Especially in the first weeks, a considerable number of subjects discontinued participation, mostly because they did not want to participate in the exercise programs after all. Most frequent reasons for discontinuation of the program after the first weeks were health-related problems. No adverse events of the WP or PAP itself were reported. Adherent subjects attending at least 75% of the sessions (n = 51) were more often living together (82% vs. 65%, P = 0.03) and less physically active than non-adherers (n = 101), (median [10th–90th percentile] was 36 [13–82] vs. 44 [10–169] min/day, P = 0.02). At baseline, adherers also had lower ratings of D-QoL-belonging (3.6 [0.41] vs. 3.8 [0.49], P = 0.02) and higher SF12-MCS values (56.5 [5.6] vs. 53.7 [8.1], P = 0.02). Other baseline and QoL characteristics did not differ significantly.
Compliance with the (FA/B12/B6)supplementation
Four participants did not return the blister packs. On the basis of pill counts in returned blister packs, median compliance (10th–90th percentile) with the FA/B12/B6-supplementation was 100 (97–100) percent and compliance with placebo-supplementation was 100 (35–100) percent. Even though median compliance in both groups was 100%, compliance in the placebo-group was significantly lower (P < 0.05). Eight subjects, one in the FA/B12/B6-group and seven in the placebo-group, did not take (vitamin)supplementation. Seven of them decided immediately after randomization not to participate in the interventions. The other wanted to participate in the exercise intervention only. Two participants discontinued taking vitamin pills during the trial after reporting sleep problems and increased forgetfulness; one participant discontinued taking the placebo pills after reporting not feeling well.
Modified intention to treat analyses
Results of the walking program and FA/B6/B12 supplementation are presented in Table 4. With respect to overall QoL, no positive significant main effect of the WP or FA/B6/B12 supplementation was found. A significantly detrimental effect of FA/B6/B12 supplementation was observed on D-QoL-belonging, (beta (95%CI) = −0.18 (−0.29; −0.07), P < 0.01). A positive interaction between the WP and attendance to the WP was observed on D-QoL-belonging and D-QoL-positive affect. With each percent increase in attendance, D-QoL-belonging increased with 0.003 points (P = 0.04) and D-QoL-positive affect with 0.002 points (P = 0.06) in the WP compared to the PAP. With respect to health-related QoL, an interaction between the WP and gender was observed on the SF12-MCS (P = 0.06) and therefore analysis for the SF12-MCS was stratified for gender. No main effects of the WP or FA/B12/B6-pills were observed. However, in men in the WP, SF12-MCS increased with 0.03 points with each percent increase in attendance (P = 0.08).
Table 4Results of longitudinal multi level analyses on the effect of the WP and FA/B6/B12 supplementation on change in QoL (adjusted model) WP versus PAP Beta (95%CI)P-valueFA/B12/B6 versus placebo Beta (95%CI)P-valueD-QoL sumscore0.04 (−0.03;0.10)0.25−0.06 (−0.12;0.004) 0.07D-QoL aesthetics0.06 (−0.07;0.20)0.37−0.07 (−0.20;0.07)0.33D-QoL belonging0.00 (−0.11;0.11)0.96−0.18 (−0.29; −0.07)0.00D-QoL negative affect−0.02 (−0.12;0.08)0.650.04 (−0.05;0.14)0.37D-QoL positive affect0.04 (−0.04;0.13)0.34−0.04 (−0.12;0.04)0.33D-QoL self esteem0.08 (−0.02;0.18)0.110.00 (−0.10;0.11)0.94SF12-PCS0.66 (−1.23;2.54)0.49−0.73 (−2.65;1.19)0.45SF12-MCS*Men−0.82 (−2.24;0.60)0.250.25 (−1.31;1.81)0.76Women1.66 (−1.50;4.81)0.301.32 (−1.93;4.56)0.42WP = Walking Program, PAP = Placebo Activity Program, FA/B12/B6= Folic Acid, Vitamin B12, Vitamin B6 supplementation, D-QoL = Dementia Quality of Life, SF12-MCS = Short Form 12 Mental Component Summary, SF12-PCS = Short Form 12 Physical Component Summary* Interaction WP and gender
Per protocol analyses
Subgroup analyses were performed in subjects attending 75% or more of the WP or PAP sessions (n = 51, 33 men and 18 women). No between group differences were observed for FA/B12/B6-pills versus placebo-pills. A significant positive effect of the WP compared to the PAP was observed on D-QoL-positive affect, beta (95%CI) = 0.23 (0.06; 0.39), P < 0.01 and a borderline significant positive effect on D-QoL-self esteem, beta (95%CI) = 0.17 (0.001; 0.34), P = 0.05.
Discussion
No positive main effect of walking or daily FA/B6/B12 supplementation was observed on QoL in community-dwelling adults with MCI. However, ratings of overall QoL (i.e., feelings of belonging, positive affect) and the mental component of health-related QoL improved slightly with increasing attendance to the walking program. In a subgroup that attended at least 75% of the sessions, a beneficial effect of the walking program was observed on positive affect and self esteem.
To our knowledge, this is the first intervention study on QoL in community-dwelling adults with MCI. While memory complaints are reported to be negatively associated with QoL in healthy older adults with subjective memory complaints [2], QoL ratings in our study population were already quite high at baseline. Baseline ratings on the DQOL sumscore and subscales fell ample above the midpoint of the scale, except for negative affect. Baseline scores on the SF-12MCS fell around a half standard deviation above the average in the general population and SF-12PCS fell about the average ratings. QoL-ratings have been reported to decrease as the severity of cognitive decline increases [28]. The possibility exists that MCI as operationalized in the present study may not have been serious enough to negatively influence overall and health-related QoL. In spite of the high baseline values, the QoL scales still allowed for further improvements, i.e., there was no ceiling effect. However, it has been discussed before that QoL may represent a stable concept, which is difficult to change or that existing measures may not be responsive to subtle changes [29].
The relationship between physical activity and QoL has been studied extensively. However, it is difficult to draw a clear conclusion, since various definitions and operationalizations of QoL circulate. Moreover, comparisons between studies are being complicated by the wide variety of study populations and features of exercise intentions such as intensity, exercise mode, frequency and session and total duration [30]. However, Rejeski et al. [31] concluded in a review including 28 studies, of which 11 RCT’s, that physical activity positively influenced aspects of health-related QoL. In a recent meta-analysis of Netz et al. [7] including 36 studies, a small positive effect of exercise was observed on wellbeing in healthy older adults. In that meta-analysis four components of wellbeing were considered, including aspects that were also measured in the FACT-study, such as positive and negative affect, perception of physical fitness and physical symptoms.
In the present study no main effects of the WP were observed in the modified intention to treat analyses. First, a possible explanation for the lack of effect may be that only participants with good QoL were able to attend enough sessions. In contrast to an earlier study, no baseline differences in number of chronic diseases, physical health-related QoL and endurance were observed between adherers (attending ≥75% of the sessions) and non-adherers (attending <75% of the sessions) [32]. However, adherers rated their mental health-related QoL at baseline significantly better than non-adherers. The difference was three points, which approximately equaled a difference of 5%. The possibility exists that subjects with lower mental health-related QoL were inclined to attend less sessions. Nevertheless, it is not likely that this biased our results, because non-adherers and drop-outs from the exercise programs were included in the modified intention to treat analyses. In future studies in subjects with cognitive decline, session attendance may be improved by informing subjects extensively about the study aims and the consequences of participation. Moreover, if possible with respect to logistic and financial issues, we advice to schedule time and staff for the close personal follow-up of temporary drop-outs.
Second, it has been reported that the association between physical activity and QoL is lower among older adults who function at or above the norm [31]. By applying inclusion criteria for the present trial (e.g., community dwelling, no ADL disabilities, being able to perform moderate intensity physical activity), we presumably selected physically healthy and active subjects. This is supported by the high baseline activity levels. Two-thirds of the participants reported to be physically active at moderate intensity for 30 min or more per day. Subjects meeting this guideline are reported to have better health-related QoL than physically inactive adults [8]. Additionally, Netz et al. found that larger effects of exercise on wellbeing were observed in sedentary adults [7]. However, in the present study, no interaction between the walking program and baseline physical activity level was observed (results not presented), indicating that inactive participants did not benefit more from the WP than active participants. Therefore, it is not likely that baseline physical activity level was a main cause of the lack of main effects.
Finally, inconclusive evidence is available about the intensity and exercise mode of physical activity required to benefit QoL. Netz et al. [7] concluded that aerobic training of moderate intensity was most beneficial for wellbeing. In a cross-sectional study, it was also observed that moderate intensity physical activity was positively related to health-related QoL [8]. In contrast, in a review by Spirduso and Cronin [33] no evidence of a relationship between exercise intensity and the rate of improvement in QoL was found. If the former would be true, the possibility exists that the contrast between both programs in the present study would not have been large enough to induce differences in QoL. If the latter would be true, participants would have benefited from participation in both exercise programs regardless of intensity. Both programs may either have added to better self-efficacy, or may prevented a decline in self-efficacy. The walking program by training cardiovascular endurance; the placebo activity program by training e.g., balance and ADL. Self-efficacy refers to somebody’s belief that one has the capabilities to successfully manage situational demands and is mentioned to be a mediating mechanism for the effect of physical activity on QoL [7, 30, 34, 35]. Thus, the presence of the low intensity placebo activity program in our study may have contributed towards the lack of between group differences.
Nevertheless, several outcomes improved with increasing attendance to the walking program. In the per protocol analyses a beneficial effect was observed on positive affect. Self esteem also tended to improve. However, observed differences were small and approximated 5% differences from baseline QoL ratings. As a rule of thumb, a minimal change of 5% has been mentioned to signify clinical relevance. To obtain a change of 5% by increasing attendance, the required increase in attendance would be 62% for D-QoL-belonging and 94% for D-QoL-positive affect and the SF12-MCS. Therefore, it can be questioned whether the observed effects are clinically relevant.
No effect of the FA/B12/B6 supplementation was observed except for a negative effect on feelings of belonging. However, no theoretical rationale exists for this effect. Our findings are in line with previous RCT’s on the effect of vitamin B supplementation on aspects of QoL. Deijen et al. [11] observed no effect of supplementation with 20 mg vitamin B6 for 3 months on mood in healthy men (n = 76). Also no effect of supplementation with 750 μg folate, 15 μg vitamin B12 or 75 mg vitamin B6 daily for 35 days was observed on mood in women aged 65 or over (n = 75) [11]. Finally, no effect on health-related QoL was observed of a weekly injection with 1 mg vitamin B12 for 4 weeks in adults with vitamin B12 deficiency (n = 140) [13]. These findings may find its origin in the used operationalizations and measures of QoL that include very few items that directly relate to nutrition. Amarantos et al. [36] underline the need to develop QoL measures including items that relate nutrition to QoL.
To conclude, the walking program and vitamin B supplementation were not effective in improving QoL in community-dwelling older adults with MCI within 1 year. However, increasing attendance to moderate intensity physical activity may benefit certain aspects of QoL.

quality of life
aged
exercise
randomized controlled trial
dietary supplements


Contribution of P2Y1 receptors to ADP signalling in mouse spinal cord cultures

Mixed neuronal and glial cell spinal cord cultures from neonates express ADP sensitive P2Y1,12&13 receptors. ADP (10 μM) evoked increases in intracellular calcium that were essentially abolished by the P2Y1 receptor antagonist MRS2179 (10 μM), responses were also absent in preparations from P2Y1 receptor deficient mice however UTP (100 μM) evoked calcium rises were unaffected. ADP also evoked a robust increase in extracellular signal-regulated protein kinase (ERK) phosphorylation that was of similar magnitude in the cultures from wild type and P2Y1 receptor deficient mice. These results suggest that ADP acts through P2Y1 receptors to mediate an increase in intracellular calcium but not to stimulate ERK phosphorylation in the spinal cord.
Nucleotides released from neurons, glia and damaged cells play a signalling role in the nervous system. P2Y receptors are a family of G-protein coupled nucleotide receptors, and several of the eight subtypes (P2Y1,2,4,6,11,12,13,14) are expressed in the nervous system [11]. P2Y1 receptors have been shown to be involved in calcium signalling in a range of neurons and glial cells (e.g. [3,4,9,12]). In addition signalling through recombinant P2Y1 receptors stimulates mitogen-activated (MAP) kinases [10] and in native cells P2Y1 receptors have been implicated to play a role in extracellular signal related kinases (ERK) activation and stretch induced injury in astrocytes [8]. In this study the aim was to determine whether ADP evoked calcium and MAP kinase responses in cultured spinal cord neurons and glial cells and use knockout mice to determine the contribution of P2Y1 receptors to ADP evoked signalling.
Wild type or P2Y1 receptor deficient C57 neonatal mice [7] (3–7 days) of either sex were decapitated and the spinal column was removed and washed twice in a calcium/magnesium-free Hanks balanced salt solution (HBSS) containing HEPES (0.3 M), sodium pyruvate and penicillin/streptomycin (50 μg/ml each). The spinal cord was then cut into small pieces and placed in ice cold HBSS. The tissue pieces were then placed in a HBSS-trypsin solution (2.5%) and incubated at 37 °C for 30 min. The tissue was then transferred to a HBSS-trypsin inhibitor solution (1 mg/ml) for 5 min before being replaced with 1 ml Neurobasal media containing glutamine and B27 supplement. Mechanical trituration was used to dissociate the spinal cord cells. The resulting cell suspension was seeded onto poly-d-lysine-coated 16 mm coverslips and maintained at 37 °C in a humidified incubator with a 95% O2/5% CO2 atmosphere. After 2 h an additional 2 ml of Neurobasal media was added and cells left to grow for 2–5 days.
Spinal cord cultures were ester loaded with a calcium sensitive dye, Fluo-3 acetoxymethyl ester (Fluo-3-AM, final concentration 1 μM) for 30 min at 37 °C in a humidified incubator. The coverslips were then washed in extracellular solution (in mM; 150 NaCl, 10 HEPES, 10 Glucose, 2.5 KCl, 2.5 CaCl2, 1 MgCl2, pH 7.3) to remove any extracellular dye and maintained at room temperature. Coverslips were mounted in a perfusion chamber on the stage of a Fluoview FV300 confocal microscope and were continuously perfused with extracellular solution. The argon laser excitation of the dye was at 488 nm and the emissions were captured at wavelengths greater than 510 nm by Olympus Fluoview v4.2 software at a frequency of 0.5 Hz for a continuous time period of 280 s. Agonist application was via a U-tube [2]. ADP stocks were treated with hexokinase to remove any ATP contamination. Agonist applications were at intervals of ∼10 min. Antagonists were perfused for 8 min before test solution application so as to allow complete equilibration. Cells displaying ‘puff’ artefacts to just extracellular solution were discounted from analysis [1]. Baseline measurements of fluorescence were calculated as a mean of the 10 s of recording prior to agonist application. Peak changes in fluorescence for neuronal and glial cells were expressed as a ratio of the baseline (increases in fluorescence are expressed as a self-ratio, baseline value is 1).
Spinal cord cells were cultured for 2–5 days as described previously and agonists were applied to individual wells and incubated for 10 min. The cells were subsequently lysed in a solution (in mM; 10 β-glycerophosphate, 1 EDTA, 1 EGTA, 50 Tris–HCl, 1 benzamidine, 1 sodium orthovanadate, 0.2 PMSF, 50 sodium fluoride, 1 mg/ml pepstatin A, 1 mg/ml leupeptin, 0.1% β-mercaptoethanol, 1% Triton X-100). The samples were then mixed with sodium dodecyl sulphate sample buffer (containining β-mercaptoethanol) at a ratio of 1:1 and denatured for 5 min at 95 °C prior to loading on a 10% sodium dodecyl sulphate polyacrylamide gel. The protein was then transferred onto a nitrocellulose membrane and subsequently blocked with blocking medium (5% non-fat milk powder and Tris-Tween 20, buffered salts-TTBS) overnight at 4 °C. Nitrocellulose membranes were then incubated in 5% blocking medium containing either anti-phospho-ERK antibody (Cell Signaling Technology, MA, USA) at a dilution of 1:1000 or anti-non-phosphorylated ERK antibody (Cell Signaling Technology, MA, USA) at a dilution 1:1000. Immunoreactive bands were visualised by incubation of nitrocellulose membranes with anti rabbit peroxidase conjugate at 1:1500 for 2 h at room temperature and then detected with chemiluminiscence (ECL Plus, Amersham, UK) and recorded onto hyperfilm (Amersham, UK). Western blots were analysed using Image J, NIH, USA—http://rsb.info.nih.gov. Phospho ERK intensity was corrected for loading using non-phosphorylated ERK blotting and expressed as fold over basal.
Total RNA was isolated from either intact spinal cord or spinal cord using the RNeasy Mini Kit (QIAGEN, Valencia, CA). The RNA was treated with DNase I (Sigma) to remove any DNA contamination. Half of the purified RNA was reverse-transcribed to cDNA using SuperScript II-reverse transcriptase (Invitrogen, Carlsbad, CA), and the remainder of the RNA was used as a negative control to ensure that there was no genomic contamination. The primers have been described previously [1]. PCR reactions were carried out with 2 μl of cDNA and a final concentration of 500 nM of each primer. Amplification took place in a Techne Genius PCR machine (Techne, Cambridge, UK) using the following protocol: denaturation at 94 °C for 5 min; repeated cycles of denaturation at 94 °C, followed by annealing at 57 °C and extension at 72 °C, each for 30 s; final extension at 72 °C for 10 min. Thirty-five cycles were used. The amplification products were examined by electrophoresis on a 1% agarose gel and visualized using ethidium bromide under UV light.
Statistical tests were preformed using an unpaired t-test with a p-value of <0.05 considered as significant. Data are expressed as mean ± standard error of the mean.
Spinal cord cells cultured from neonates for 3–7 days contained both neuronal and glial cells that could be distinguished by their morphology and staining with glial fibrillary acidic protein; approx 43% of cells were glia and 57% neuronal (n = 576 cells from 4 coverslips). We have previously used calcium imaging to look at P2Y receptor signalling in mouse superior cervical ganglia [1] and similar protocols were used in this study. ADP (10 μM) evoked robust increases in intracellular calcium for both neurons (64% cells responding with peak self-ratio amplitude of 2.20 ± 0.14, n = 120 cells from 12 coverslips) and glial cells (57% of cells responded with a peak self-ratio amplitude of 2.17 ± 0.2, n = 120 cells from 12 coverslips). Responses were not sustained and generally decayed during the time-course of application (self-ratio at end of 30 s application 1.34 ± 0.08 and 1.27 ± 0.04 for neurons and glia, respectively, n = 20 for each).
The selective P2Y1 receptor antagonist MRS2179 reduced ADP evoked calcium rises in a concentration-dependent manner and these effects were reversed on antagonist washout (Fig. 1). ADP evoked calcium rises were essentially abolished in spinal cord cultures from P2Y1 receptor deficient mice with small residual responses in 11% of neurons (self-ratio 1.14 ± 0.05, n = 100 cells from 10 coverslips) and 17% of glial cells (self-ratio 1.21 ± 0.05, n = 115 cells from 11 coverslips)(Fig. 2). Responses to the P2Y2/4 receptor agonist UTP (100 μM) in cultures from P2Y1 receptor deficient mice were the same as for WT for neurons (45 and 48% responding with amplitudes of 1.96 ± 0.09 and 1.79 ± 0.08, n = 60, 114 from 6 and 12 coverslips, respectively for WT and P2Y1 receptor deficient mice) and glial cells (58 and 62% responding with amplitudes of 1.88 ± 0.13 and 1.67 ± 0.04, n = 60, 119 from 6 to 12 coverslips, respectively for WT and P2Y1 receptor deficient mice) indicating that Gαq coupled receptor calcium signalling was not affected in the P2Y1 receptor deficient mouse (Fig. 2). Taken together these results define a role of the P2Y1 receptor in calcium signalling in spinal cord neurons and glial cells. These studies support the role of P2Y1 receptors in calcium signalling in the nervous system [3,9,12] and corroborate previous studies using sympathetic ganglion cultures from the P2Y1 receptor deficient mouse [1].
P2Y1 receptor stimulation has also been reported to mediate ERK phosphorylation in recombinant [10] and native systems [8] and this may contribute to changes in the spinal cord following injury. In spinal cord cultures ADP evoked a time-dependent phosphorylation of p44/42 ERK that was detected at 5 min, peaked at 10 min, and declined back to basal levels by 30 min (Fig. 3A). When just media was added to the cultures there was no change in ERK phosphorylation (Fig. 3B) indicating that ERK stimulation does not result from a mechanical artefact. Adenosine (10 μM) also had no effect demonstrating that adenosine receptors are not involved. We therefore compared ADP evoked ERK phosphorylation in spinal cord cultures from WT and P2Y1 receptor deficient mice. Surprisingly ADP (10 μM) evoked similar levels of ERK phosphorylation (∼3-fold increase over basal) in WT and P2Y1 receptor deficient cultures (Fig. 3) demonstrating that a receptor other than the P2Y1 receptor mediates this ADP response.
Of the currently eight identified P2Y receptor genes ADP is an agonist at Gαq coupled P2Y1, and Gαi coupled P2Y12 and P2Y13 receptors [11]. ADP is also an agonist at the human P2Y11 receptor; however a corresponding mouse homologue of the P2Y11 receptor has not been detected suggesting that mice do not express P2Y11-like receptors [11]. Transcripts for P2Y1,12&13receptors were detected in 3–7 days old spinal cord cultures (data not shown). Amplification of RNA for ADP sensitive P2Y12&13 receptors raised the possibility that these may contribute to the ERK phosphorylation. AR-C66931MX [6] is an antagonist of P2Y12 and P2Y13 receptors with a reported pA2 of 8.7 at P2Y12 receptors and 0.01 μM reduced ADP responses by ∼80% at recombinant P2Y13 receptors (see review [11]). AR-C66931MX (10 μM a supra-maximal concentration at P2Y12 receptors) had no effect on ADP evoked ERK phosphorylation indicating that P2Y12 receptors did not mediate the ERK phosphorylation. AR-C66931MX may have complex actions at P2Y13 receptors, possibly dependent on cell type, and has been described as an activator of P2Y13 receptor dependent high density lipoprotein endocytosis in hepatocytes [5] questioning the use of this compound as a selective antagonist at the P2Y13 receptor. Thus it remains to be determined whether the P2Y13 receptor, or a novel ADP sensitive receptor, mediates the ADP evoked ERK phosphorylation in the spinal cord.

p2y1
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Dependence of Intramyocardial Pressure and Coronary Flow on Ventricular Loading and Contractility: A Model Study

The phasic coronary arterial inflow during the normal cardiac cycle has been explained with simple (waterfall, intramyocardial pump) models, emphasizing the role of ventricular pressure. To explain changes in isovolumic and low afterload beats, these models were extended with the effect of three-dimensional wall stress, nonlinear characteristics of the coronary bed, and extravascular fluid exchange. With the associated increase in the number of model parameters, a detailed parameter sensitivity analysis has become difficult. Therefore we investigated the primary relations between ventricular pressure and volume, wall stress, intramyocardial pressure and coronary blood flow, with a mathematical model with a limited number of parameters. The model replicates several experimental observations: the phasic character of coronary inflow is virtually independent of maximum ventricular pressure, the amplitude of the coronary flow signal varies about proportionally with cardiac contractility, and intramyocardial pressure in the ventricular wall may exceed ventricular pressure. A parameter sensitivity analysis shows that the normalized amplitude of coronary inflow is mainly determined by contractility, reflected in ventricular pressure and, at low ventricular volumes, radial wall stress. Normalized flow amplitude is less sensitive to myocardial coronary compliance and resistance, and to the relation between active fiber stress, time, and sarcomere shortening velocity.
Introduction
Coronary arterial inflow varies in time during the cardiac cycle. Systolic inflow is smaller than diastolic inflow, demonstrating that the pulsatility of coronary flow is not caused by variation of the arterial venous pressure difference. Instead, the phasic pattern of coronary inflow has been attributed to changes in cross-sectional area of the myocardial vessels. For example, a transient decrease in cross-sectional area affects coronary flow in two ways. First, coronary inflow decreases and outflow increases because blood is squeezed out of the coronary bed. Second, both coronary inflow and outflow decrease because of the increase of coronary resistance.
Vessel cross-sectional area depends on the local coronary pressure, the vessel wall mechanical properties and the embedment of the vessel in the myocardial tissue. The relation between vessel cross-sectional area and transmural pressure is nonlinear,11 and changes due to autoregulation. The embedment in the myocardial tissue can be represented by myocardial wall stress, which consists of two contributions: the stress in the collagen matrix, through which the vessel is tied to the surrounding tissue, and the intramyocardial pressure in the interstitial fluid. In the end, the pattern of coronary flow is mainly determined by contraction of the myofibers in the cardiac wall, since myofiber contraction determines the level of both myocardial wall stress and coronary pressure.
Many experiments have been performed to elucidate the interplay between the factors governing coronary flow. It has been observed that the pulsatile component of the coronary inflow signal (1) is about proportionally related to left ventricle (LV) contractility, flow amplitude being about zero when contractility is about zero,16 (2) is virtually independent of systolic LV pressure in isovolumic beats, executed at various LV volumes, for pressures up to about 13 kPa,15,17 and (3) is about the same in isobaric beats at low LV pressure as in isovolumic beats at LV pressures up to about 13 kPa.15 It was observed also that minimum systolic flow (4) is virtually independent of LV pressure for pressures below 13 kPa, but (5) decreases with increasing LV pressure for pressures above about 13 kPa.20 In addition, it has been found that (6) systolic intramyocardial pressure may exceed left ventricular pressure in subendocardial layers in low afterload beats,18 and (7) that an increase of coronary perfusion pressure leads to an increase of intramyocardial pressure.18
Mathematical models have been proposed as a tool to interpret the experimental data. In early models, the interaction between the coronary vessel and the myocardium was modeled through the intramyocardial pressure only. In the waterfall model9 and the intramyocardial pump model,1,2,6,22 this pressure was assumed to be determined completely by left ventricular pressure, with intramyocardial pressure decreasing linearly from left ventricular pressure at the endocardial surface to zero at the epicardial surface. These models can explain the pulsatility of coronary inflow under normal physiological conditions, and the experimental observations (1) and (5), listed above.
In later models, the interaction between vessel and tissue was still modeled through intramyocardial pressure only, but intramyocardial pressure was assumed to depend both on left ventricular pressure and on transverse tissue stress, i.e. stress perpendicular to the muscle fiber direction. In a finite element model of the beating heart, incorporating transverse tissue stress, observation (6) was replicated.12 Transverse stress is also included in models by Beyar et al., together with nonlinear characteristics of the properties of the coronary bed, and exchange of fluid between the coronary vessels and the myocardial interstitium.5,29,30 In these models experimental observations (1) through (6) are replicated.
Vis et al.26,27 extended the model for interaction between the vessel and the cardiac wall, by assuming that the coronary vessel is subject to an extravascular pressure that depends both on intramyocardial pressure and local tissue stress. So the effective compliance of the coronary vessel depends both on the compliance of the vessel wall and the stiffness of the myocardium, thus implementing an idea introduced before as the time-varying elastance concept.15,17 In a finite element model of one vessel in the myocardial wall Vis et al. investigated the influence of contractility, pressure, and circumferential wall stretch on vessel area, for static diastole and systole. With the model, observations (6) and (7) were reproduced.
With the increasing complexity of the models, more experimental observations have been replicated. Simultaneously, the number of model parameters has increased, making it difficult to perform a detailed parameter sensitivity analysis and identify the critical model parameters. Therefore, our aim was to study the primary relations between left ventricular pressure and volume, wall stress in fiber and transverse direction, intramyocardial pressure and the coronary blood flow, with a mathematical model with a limited number of parameters, and to assess the sensitivity of the model results to the model parameter settings.
Material and methods
The complete model consists of four parts, describing ventricular wall mechanics, myocardial constitutive properties, intramyocardial pressure, and the coronary and systemic circulation.Figure 1.Passive material behavior. Top: passive stress as a function of stretch ratio λ for uniaxial stretch along fiber direction (σm,f) and radial direction (σm,r). Bottom: passive left ventricular pressure–volume relation according to model (solid line) and experimental data;19 experimental data given for average minimum and maximum volume (dashed line), and minimum and maximum volume ± 1 SD (dash-dot lines).
Ventricular Wall Mechanics
The model of ventricular wall mechanics describes how left ventricular pressure and volume are related to local tissue properties, i.e. fiber stress and strain, and radial wall stress and strain. The model is based on a previously published model,3 which is extended to describe the influence of radial wall stress. While the original model is derived for arbitrary ventricular geometries with rotational symmetry, here we will derive the equations for the special case of a thick walled sphere. We consider the sphere to consist of a set of nested thin spherical shells. In each shell, stresses satisfy the condition of force equilibrium in radial direction:
where σr, σc, and σl denote the radial, circumferential and longitudinal component of the tissue stress tensor, respectively, and r indicates the radial position in the wall. We neglected shear stress components in view of the low shear stiffness of the tissue. The myocardial tissue was assumed to be incompressible, and to consist of myofibers, embedded in a collagen matrix. The Cauchy stress tensor
in tissue is written as:
where pim denotes the intramyocardial pressure,
, the stress in the collagen matrix, and σa the stress generated in the myofibers along the myofiber direction
We assume that the fibers are located in spherical shells at an angle α with the circumferential direction, and adopt the assumption by Arts,3 that the stress in the collagen matrix in the plane of a shell is completely determined by the passive stress σm,f in the fibers. Then it holds:
where σm,r represents the radial wall stress, generated in the collagen matrix, and the total fiber stress σf is introduced as the sum of passive and active fiber stress. Substitution in (1) yields:
This equation describes how, in each shell, fiber stress σf and radial wall stress in the collagen matrix σm,r contribute to the variation of total radial wall stress σr in radial direction. Together, all shells increase radial wall stress from zero stress at the outer surface (r = ro) to minus left ventricular pressure at the inner surface (r = ri):
The relation between wall stress and left ventricular pressure is found by integrating Eq. (4) from the endocardial to the epicardial surface. To evaluate the integral, we first adopt the assumption by Arts3 that σf is constant across the wall. Secondly, we assume that a representative position
can be found, such that:
Evaluation of the integral and substitution of the boundary conditions (5) yields:
where ri and ro are rewritten in terms of the cavity volume Vlv and wall volume Vw, and
is introduced as a short notation of
Apart from the term
this relation is identical to that derived in Arts et al.3 To complete the model relating wall mechanics to cavity mechanics, Eq. (7) is complemented by a relation between ventricular volume and tissue strain. We choose the passive ventricle at zero transmural pressure as a reference state. In this state, we assume a sarcomere length ls0 and a cavity volume Vlv0. It has been shown,3 that the fiber stretch ratio λf can be approximated by:
This ratio corresponds to the circumferential stretch ratio at the outer surface of a shell that contains the left ventricular cavity volume and one third of the wall volume. At the same location, the radial stretch ratio λr equals:
where we assumed incompressibility of the myocardial tissue. Equations (7)–(9) describe how global ventricular properties Vlv and plv are related to local tissue properties λf, λr, σf and
Myocardial Constitutive Properties
The model of ventricular mechanics is completed with constitutive laws for fiber stress and radial stress. The active fiber stress σa was modeled to depend on contractility c, sarcomere length ls, time elapsed since activation ta and sarcomere shortening velocity vs as:
with contractility c (0 ≤ c ≤ 1), scaling constant σar, and:
Here, ls,a0 denotes the sarcomere length below which active stress becomes zero and ls,ar represents the sarcomere length to which the reference stress σar is referred to. Times ta and tmax denote the time elapsed since activation, and the duration of the twitch, respectively. Velocity v0 represents the unloaded sarcomere shortening velocity, while cv governs the shape of the stress–velocity relation. Parameter values in the active stress law (Table 1) are chosen in agreement with experimental data.8,13Table 1.Reference settings for parameters in the model of the left ventricle.ParameterValueUnitParameterValueUnitVw20010−6 m3σar55103 PaVlv,06010−6 m3c1–ls,01.910−6 mls,a01.510−6 mσf00.9103 Pals,ar2.010−6 mσc00.2103 Patmax40010−3 scf12–v01010−6 m s−1cr9–cv0–
The passive stress along the fiber direction is modeled as:
where it was assumed that no stress can be transmitted in compression. Passive transverse stress is modeled similarly. Since the radial direction at ventricular level coincides with the transverse direction at the tissue level, we write the transverse stress model in terms of radial stress and stretch ratio:
Settings of parameter values σf0, cf, σr0 and cr are based on experimental data on the pressure volume relation of the passive left ventricle.19 In the latter study, the pressure volume relation was described by a logarithmic relation, involving chamber stiffness at positive and negative pressures, and maximum and minimum attainable volume. The bottom panel of Fig. 1 shows the experimental data, and our model prediction for parameter settings in Table 1. Uniaxial stress–strain responses are shown in the top panel of Fig. 1.Figure 2.Schematic representation of the left ventricle (LV) in the systemic circulation and coronary circulation; Rart, Rper and Rven represent the systemic arterial, peripheral and venous resistance, respectively; MV and AV represent the mitral and aortic valve, respectively; Cart and Cven the systemic arterial and venous compliance; Lven and Lart the inertia of the blood in the venous and arterial system; Rart,c, Rmyo,1, Rmyo,2 and Rven,c represent the coronary arterial, the two intramyocardial and venous resistances; Cart,c, Cmyo,c and Cven,c the coronary arterial, intramyocardial and venous compliance; part,c, pmyo,c and pven,c the pressure in the coronary arteries, myocardium and veins, respectively; pao and pla the aortic and left atrial pressure, respectively; qao, qm represent the AV flow and MV flow; qart,c and qven,c the coronary arterial inflow and venous outflow;
represents the intramyocardial pressure at the representative radial position
When simulating isovolumic and isobaric contractions, the pressure drop across the coronary circulation is switched from pao− pla to a constant perfusion pressure pper.Figure 3.Hemodynamics in the beating heart. Left: simulation of the physiological state with aortic pressure driving the coronary circulation. Right: simulation of isolated heart experiment with a constant perfusion pressure and maximum vasodilation. From top to bottom: ventricular pressure plv, intramyocardial pressure
(bold) and radial wall stress
aortic valve (AV) flow qao (bold) and mitral valve (MV) flow qm; left ventricular cavity volume Vlv; coronary perfusion pressure pper, myocardial coronary pressure pmyo,c (bold) and left atrial pressure pla; coronary inflow
(bold) and outflow
per 100 g wall volume; volume of myocardial coronary bed Vmyo,c.Figure 4.Hemodynamics at maximal vasodilatation and constant perfusion pressure, expressed in time courses of ventricular pressure plv, ventricular volume Vlv, radial wall stress
intramyocardial pressure
and coronary arterial inflow
Left: isovolumic beats for ventricular volumes ranging from 120 to 20 ml. Middle: isovolumic beats at 60 ml for contractility parameter c ranging from 1.0 to 0.1. Left: isobaric beats for systolic pressures ranging from 16 to 2 kPa.
Intramyocardial Pressure
To derive the expression for the intramyocardial pressure, again we consider the ventricular wall to be composed of a number of nested shells. The pressure in between two shells is assumed to be a fraction β of the left ventricular pressure. In analogy to Eq. (5), this pressure is in equilibrium with radial tissue stress σr:
In the model, we assume a linear variation of β with the transmural position in the wall, with β = 1 at the endocardial surface, and β = 0 at the epicardial surface. Again stress at the shell containing the LV cavity volume and one third of LV wall volume is considered representative. For this location at a radius
in the wall we find:
where we introduced the notation
and the radial positions ri, ro and
are defined as:
Equation (17) describes intramyocardial pressure as a function of LV pressure and volume: the volume dependency enters the equation through the radial stress σm,r [Eq. (15)], which depends the radial stretch ratio λr [Eq. (9)], which in turn depends on LV volume [Eq. (8)].
Systemic and Coronary Circulation
The model of left ventricular wall mechanics is incorporated in lumped parameter models for the coronary and systemic circulation (Fig. 2). The aortic (AV) and mitral valve (MV) are modeled as an ideal diode. Vessels are modeled with constant resistances R, inertances L and capacitances C. The pressure drop Δp across each of these components is given by
with V the volume in the capacitance and q the flow through a resistance or an inertance. The pressure–volume relation of the capacitance represents a linearization around the physiologic working point, V0 representing the volume at zero pressure. Values of parameters in the circulation model were based on literature (Table 2).Table 2.Reference settings for parameters in the circulation model; coronary resistance values in parentheses represent maximum vasodilation.Systemic circulationCoronary circulationParameterValueUnitParameterValueUnitRart5106 Pa s m−3Rart,c700 (200)106 Pa s m−3Rper120106 Pa s m−3Rmyo,1900 (100)106 Pa s m−3Rven5106 Pa s m−3Rmyo,2900 (100)106 Pa s m−3Cart2010−9 m3 Pa−1Rven,c200106 Pa s m−3Cven80010−9 m3 Pa−1Cart,c0.0310−9 m3 Pa−1Vart,050010−6 m3Cmyo,c1.410−9 m3 Pa−1Vven,0300010−6 m3Cven,c0.710−9 m3 Pa−1Lart60103 Pa s m−3Vart,c0610−6 m3Lven60103 Pa s m−3Vmyo,c0710−6 m3Vblood500010−6 m3Vven,c01010−6 m3
The connection between the model of LV mechanics and the coronary circulation model is made through the intramyocardial pressure, that acts on the myocardial capacitance Cmyo,c. The values of the coronary capacitances were based on measurements by Spaan et al.:23 0.0022, 0.091 and 0.045 ml mm Hg−1 100 g−1 LV in large coronary arteries, myocardial coronary bed, and coronary veins, respectively. Zero pressure volumes were chosen such that under normal physiological conditions, time-averaged coronary volume was about 15 ml 100 g−1 of LV tissue, distributed over arterial, myocardial and venous vessels in a ratio of 1:2:2.23
In the coronary circulation, resistance values during normoxia and hyperemia were derived from Chilian et al.7 In that study, total coronary resistance under normal and vasodilated conditions was measured to be 66 and 14 mm Hg min g ml−1, respectively. Distribution of resistance over the arterial, myocardial and venous compartment was measured to be 25, 68 and 7% under normal conditions, and 42, 27 and 31% under maximal vasodilation.
Systemic parameters are chosen to yield representative function curves for a 70 kg adult, at a heart rate of 75 bpm. LV wall volume was set to 200 ml, and cavity volume at zero pressure was set to 30% of this volume. The arterial load was modeled by a three-element windkessel model, consisting of a characteristic aortic impedance Rart, an arterial compliance Cart, and a peripheral resistance Rper. The peripheral resistance was chosen to yield realistic time-averaged values of aortic pressure and aortic flow. Next, arterial capacitance was chosen to yield realistic values of minimum and maximum aortic pressure. Total blood volume was set to 5000 ml. The blood volume at which mean systemic pressure is zero was assumed to be equal 70% of total blood volume, about 85% of which is contained in the venous system. Venous capacitance was chosen such that the additional 30% of blood volume leads a mean systemic pressure of about 2 kPa.
Simulations Performed
With the model, a number of simulations were performed. First we considered the normal physiological situation, with normal vessel tone and coronary flow driven by the difference between aortic and left atrial pressure. Next we investigated the changes induced in the isolated heart setup used by Krams et al.,16,17 by the combination of maximum vasodilation, constant perfusion pressure and zero coronary outflow pressure. Then, under these conditions we simulated isovolumic and isobaric beats, for various settings of LV volume, pressure and contractility. Following Krams et al.16,17 and Pagliaro et al.,20 results were analyzed in terms of minimal systolic coronary flow
and the normalized coronary flow amplitude (NFA):
Finally, we investigated sensitivity of NFA to changes in myocardial radial stiffness, active material properties, coronary myocardial resistance, and coronary capacitance.Figure 5.Analysis of coronary inflow data from simulations in Fig. 4, expressed in normalized arterial coronary flow amplitude (NFA), defined in Eq. (22), and minimal coronary arterial inflow
Left: NFA (top) and
(bottom) in isovolumic beats as a function of maximum left ventricular pressure for contractility parameter c varying from 0.1 to 1.0; in top panel experimental data15 are given by the dashed line (reference), dash-dotted line (high contractility) and dotted line (low contractility). Middle: NFA and
in isovolumic beats as a function of contractility parameter c for LV volumes of 40, 60, and 100 ml. Right: NFA and
in isobaric beats as a function of maximum ventricular pressure for contractility parameter c ranging from 0.6 to 1.0.
Results
The Normal Beating Heart
To illustrate the behavior of the model, first the normal physiological situation was simulated, with normal vessel tone and coronary flow driven by the difference between aortic and left atrial pressure. Ventricular and intramyocardial pressure rise to 16.1 and 9.1 kPa, respectively (Fig. 3, left panel). Intramyocardial pressure is almost completely determined by ventricular pressure, since radial wall stress is virtually zero. Maximum aortic and mitral flow are 646 and 307 ml/s, respectively. Stroke volume is 75.6 ml at an ejection fraction of 64%. Perfusion pressure equals aortic pressure and varies between 11.4 and 16.3 kPa. Myocardial coronary pressure varies between 3.0 and 12.3 kPa. Left atrial pressure remains about constant at 1.45 kPa. Mean coronary arterial inflow and venous outflow are 2.2 ml s−1 100 g−1 LV wall volume. Coronary arterial inflow displays a two peaked pattern, the peaks occurring in early filling and in ejection. Diastolic inflow is larger than systolic inflow. Coronary arterial outflow shows only one peak per cycle, occurring during ejection. Myocardial coronary volume varies between 10.7 and 12.5 ml.
Constant Perfusion Pressure and Maximal Vasodilation
This simulation represents the experimental situation in the isolated heart with a constant perfusion pressure of 10 kPa and maximal vasodilation. Myocardial coronary pressure varies between 1.5 and 10.0 kPa (Fig. 3, right panel). Arterial inflow varies between −0.1 and 14.2 ml s−1 100 g−1 LV wall volume, with a mean of 8.3 ml s−1 100 g−1 LV wall volume. In the arterial inflow curve, the positive flow peak in early systole has disappeared. Myocardial coronary volume varies between 5.8 and 12.4 ml.
The Isovolumic Beating Heart
The isovolumic experiments by Krams et al.15–17 were simulated at a constant perfusion pressure of 10 kPa and maximal vasodilation. Maximum LV pressure decreases with decreasing LV volume (Fig. 4, left panel). As LV volume decreases below 60 ml, the volume at which pressure in the passive LV is zero, diastolic LV pressure becomes negative. At these volumes, radial wall stress becomes positive, while being constant during a beat. With decreasing volume, maximum intramyocardial pressure and coronary arterial inflow decrease, whereas minimum coronary arterial inflow increases.
The normalized coronary flow amplitude (NFA) [Eq. (22)] decreases with decreasing LV pressure (Fig. 5, top left panel), but pulsatility persists at zero ventricular pressure. NFA decreases with decreasing contractility as well. Minimum coronary arterial inflow increases with decreasing LV pressure (Fig. 5, bottom left panel). At low pressures, the slope of the pressure–flow relation decreases.
For a constant LV volume of 60 ml, developed LV pressure decreases with decreasing contractility (Fig. 4, middle panel). At this volume of 60 ml, radial wall stress is zero. Maximum intramyocardial pressure decreases with maximum LV pressure. Maximum coronary arterial inflow decreases slightly, whereas minimum coronary arterial inflow increases strongly. With decreasing contractility, normalized coronary flow amplitude (NFA) decreases about linearly, while minimal arterial inflow increases linearly (Fig. 5, middle panel). For other volumes, a similar behavior is found.
The Isobaric Beating Heart
Simulations of hemodynamics in the isobaric beating heart were performed at a filling pressure of 1 kPa, a constant perfusion pressure of 10 kPa, maximal vasodilation and contractility parameter c = 1. With decreasing LV pressure during ejection, minimal LV volume decreases and radial wall stress increases (Fig. 4, right panel). Reduction of maximum LV pressure from 16 to 12 kPa is accompanied by a reduction of maximum intramyocardial pressure to 7.6 kPa. Maximum arterial inflow decreases, whereas minimum arterial inflow increases. Further reduction of LV pressure below 12 kPa hardly affects maximum intramyocardial pressure, due to the increasing contribution of radial wall stress. Maximum and minimum arterial inflow remain about constant. These changes are reflected in the right panel of Fig. 5. With decreasing left ventricular pressure, initially NFA decreases and minimum arterial inflow increases. Below a threshold pressure of about 10 kPa, these quantities become about constant. A similar behavior is found for lower contractilities.
Sensitivity Analysis
Results of the sensitivity analysis are shown in Fig. 6. Sensitivity to settings of parameters in the model for radial wall stress was investigated, since in our model radial wall stress is an important determinant of intramyocardial pressure. If the radial stress parameter cr0 [Eq. (15)] is decreased or increased by a factor 2, the pulsatile character of the coronary inflow at lower pressures persists, both for isovolumic and isobaric beats (Fig. 6, top panel). In isovolumic beats, maximum LV pressure increases with decreasing cr0. At the lowest LV volume simulated, 15 ml, maximum left ventricular pressure does not drop below 14 kPa, when cr0 is set to zero. In isobaric beats, at high pressures NFA is not affected by changes in cr0. Below an ejection pressure of 10 kPa, NFA increases with increasing radial stiffness. When cr0 is set to zero NFA decreases proportionally with left ventricular pressure, until pulsatility is lost at zero left ventricular pressure.
Sensitivity to settings of parameters in active stress model was investigated, since myofiber contraction is the origin of both left ventricular pressure and radial wall stress [Eq. (7)], and thus of intramyocardial pressure and of coronary flow impediment. In both isovolumic and isobaric beats, NFA increases slightly if the twitch duration tmax [Eq. (12)] is reduced from 400 to 300 ms (Fig. 6, 2nd panel from top). Changing the linear relation between fiber stress and sarcomere shortening velocity into a hyperbolic one (by setting cv = 1 in Eq. (13) does not affect NFA in isovolumic beats, where shortening velocity is zero. NFA in isobaric beats is hardly affected. Increasing the sarcomere length ls,a0, below which active stress is zero [Eq. (11)], from 1.5 to 1.6 μm yields a reduction in NFA in isovolumic and isobaric beats with a ventricular pressure below about 10 kPa (Fig. 6).Figure 6.Sensitivity of relation between maximum left ventricular pressure and normalized flow amplitude (NFA) to settings of model parameters, for isovolumic beats (left) and isobaric beats (right). Results for reference parameter settings are indicated with ‘ref’. Top: radial stiffness parameter cr0 set to twice (‘high’) or half (‘low’) the reference value, or set to zero (‘zero’). Next: variation of active stress model: twitch duration reduced from 400 to 300 ms (‘tim’), stress–velocity relation changed from linear into hyperbolic (‘vel’), and stress-free sarcomere length increased from 1.5 to 1.6 μm (‘len’). Next: all coronary resistances Rart,c, Rmyo,1, Rmyo,2 and Rven,c set to twice (‘high’) or half (‘low’) their reference values. Bottom: coronary myocardial capacitance Cmyo,c set to twice (‘high’) or half (‘low’) the reference value.
Sensitivity to coronary resistance was studied to mimic change in resistance due to variation in perfusion pressure. A two-fold simultaneous increase or decrease of all resistances in the coronary circulation model (Rart,c, Rmyo,1, Rmyo,2 and Rven,c) does affect NFA more in isovolumic beats than in isobaric beats (Fig. 6, 3rd panel from top). Still, changes in NFA are limited, and pulsatility at low pressures is maintained.
Finally, sensitivity to myocardial compliance Cmyo,c was studied, since pulsatility of coronary inflow is closely related to changes in coronary volume. When myocardial compliance Cmyo,c is set to twice or half its reference value, NFA-values change quantitatively, but the phasic nature of coronary flow at low left ventricular pressure remains, both in isovolumic and isobaric beats (Fig. 6, bottom panel). Again, the effect is larger in isovolumic beats than in isobaric beats.
Discussion
Model Setup
The aim of this study was to design a model with a limited number of parameters for investigation of the primary relations between left ventricular pressure and volume, wall stress in fiber and transverse direction, intramyocardial pressure and the coronary blood flow. Central to the model are Eq. (7), which shows how fiber stress, that ultimately drives the cardiac cycle, is converted into both LV pressure and radial wall stress, and Eq. (17), that describes how LV pressure and radial wall stress contribute to intramyocardial pressure. Finally, it is the variation of intramyocardial pressure that causes a variation in arterial coronary inflow through a change in coronary volume, represented by intramyocardial compliance. Since the use of a simple model is not without danger, we will address the impact of the main model simplifications.
In the model of ventricular wall mechanics spatial homogeneity of fiber stress and strain was assumed. The plausibility of this assumption has been illustrated in finite element models of ventricular mechanics.21,24 The assumption that in plane stress is dominated by fiber stress [Eq. (3)] is realistic during systole, when myofibers are active and the main flow impediment occurs. Obviously, radial wall stress is spatially inhomogeneous, since the ventricle is thick walled. Yet we introduced a representative stress
computed at a representative radial position enclosing one third of the wall volume, in evaluating the integral of σm,r over the wall thickness [Eq. (6)]. In principle, since the transmural variation of radial strain is known once LV cavity volume is known, using the constitutive Eq. (15), the integral in Eq. (6) can be determined exactly. Due to the strong increase of radial wall strain from the outside to the inside surface and the nonlinearity of the constitutive law, its value would be dominated by the inner layers. However, in those layers the assumption of a solid wall with a smooth endocardial surface is in error: the endocardial surface shows many invaginations, relieving any radial stress that would build up in the subendocardial tissue. The choice to use representative positions, strains and stresses is compatible with the aim of the study, to investigate determinants of the coronary flow signal. Obviously the model cannot describe spatial differences in coronary perfusion,4 which are clinically relevant in relation to vulnerability to ischemia.10 In view of the use of a representative intramyocardial pressure, and the use of average values for the coronary compliances and resistances, the flow in the model should be regarded as a mean flow over the myocardial wall.
In the constitutive model for the cardiac tissue, the description of the active stress component is chosen as simple as possible, while maintaining the basic dependence of active stress on time, sarcomere length, and sarcomere shortening velocity. Within the limitations of the model, parameter settings are chosen to mimic experimental data.8,13 The model could be extended to incorporate the sigmoidal relation between stress and sarcomere length, or the increase of twitch duration with increasing sarcomere length. However, we prefer the current version with a limited number of parameters, in view of the sensitivity analysis. The model for passive tissue stress is simplified, since we do not model a complete three-dimensional state of stress. Yet, the behavior shown in Fig. 1 agrees well with experimental data.28
We approximate extravascular pressure by intramyocardial pressure, thus neglecting the contribution of local tissue stress.26 In fact this assumption is made in many other models, including the waterfall model,9 the intramyocardial pump model,1,2,6,22 and the models by Huyghe et al.12 and Beyar et al.5,22,30 In addition, in our model intramyocardial pressure is determined completely by the model of LV wall mechanics. Thus, we can not replicate the observation that intramyocardial pressure depends on perfusion pressure.18 We feel this simplification is allowed in our simulations of isovolumic and isobaric beats, in which we assumed a constant perfusion pressure.
In the coronary circulation model resistances are constant. This is an approximation to the real situation, in which vessel diameter and therefore vessel resistance depend on vessel transmural pressure. The nature of the approximation is two-fold. First, we neglect the chronic change in resistance due to a chronic change in perfusion pressure. This is not critical for the value of NFA, as is apparent from our sensitivity analysis where we applied a two-fold change of coronary resistance (Fig. 6). Second, we neglect cyclic changes in resistance during the cardiac cycle, which seems incompatible with the ability in the model to temporarily store blood in the coronary capacitance. Yet, the phasic nature of coronary flow is reproduced in the model. We explain this by noting that a change in vessel diameter during the cardiac cycle is associated with change in coronary volume, that affects coronary inflow irrespective of the location in the coronary tree where the volume change takes place. However, the associated change in resistance is important in the smallest vessels only, due to the nonlinear relation between vessel diameter and resistance. Obviously, the effect of changes in coronary resistance during the cycle may show up in aspects of the coronary flow signal, that are not captured by the normalized flow amplitude NFA.
The simplifications in the model may be seen as limitations, if one has the goal to explain all experimental observations available. In this study, we consider it a strength of the model, in view of our aim to investigate primary interactions and dependence on parameter settings.
Results
In contrast to the situation in all other organs, coronary inflow of the heart muscle occurs mainly in diastole and is significantly impeded in systole. Experimentally, the amplitude of the coronary inflow signal was found to be only weakly coupled to systolic LV pressure in isovolumic beats at various LV volumes.15 This behavior is illustrated by the three fits to experimental data sets, shown in top left panel of Fig. 5. As in the experiment, in our model pulsatility of coronary inflow is maintained at low left ventricular pressure, although dependence of NFA on pressure is slightly higher than in the experiment.
The mechanism by which pulsatility of coronary inflow is maintained in isovolumic beats is explained as follows (Fig. 4, left panel). Total LV pressure is the sum of diastolic pressure in the passive ventricle, and the extra pressure, generated by muscle contraction. Diastolic pressure decreases with decreasing volume and becomes negative as volume decreases below the resting volume of 60 ml. We note that in the experiments by Krams et al. negative diastolic pressure was induced as well, by applying suction to the balloon, inserted in the LV cavity.16 Since LV volume is constant during a beat, radial wall stress and its contribution to LV pressure are constant as well. The extra pressure, related to muscle contraction, reduces with decreasing volume, but at the lowest volume of 20 ml it still is about 15 kPa, and maximum total LV pressure is still about 11 kPa. The fact that the variation in LV pressure, which determines pulsatility of coronary flow, decreases more slowly with decreasing volume than maximum LV pressure, is reflected in the value of NFA shown in Fig. 5.
The relation between maximum LV pressure and minimum coronary inflow, shown in the bottom left panel of Fig. 5, qualitatively corresponds with experimental data by Kouwenhoven et al.14 and Pagliaro et al.20 In the latter study, minimum coronary inflow was found to decrease with increasing maximum LV pressure for pressures above 13 kPa, but was virtually independent of systolic LV pressure below 13 kPa. It was suggested that at low pressures ‘the shielding effect of the contracting ventricle prevents ventricular pressure from being transmitted in the myocardial wall’.20 In our model, this shielding effect is identified as radial wall stress.
Experimentally, NFA in isobaric beats at low LV pressure was found to be about equal to NFA in isovolumic beats.15 This finding is replicated in our model (Fig. 5, right panel). In contrast to the isovolumic case, the relation between maximum pressure and NFA is non monotonous, with distinct behavior at high and low pressures. At high pressures, LV volume remains mostly above the passive resting volume of 60 ml, and intramyocardial pressure is dominated by LV pressure. At low pressures, the LV ejects to far below the passive resting volume of 60 ml, and the decreasing contribution of LV pressure to intramyocardial pressure is compensated by the increasing contribution of radial wall stress.
It is to be noted that in the isobaric beats both contributions to intramyocardial pressure, radial wall stress and left ventricular pressure, vary in time, while in the isovolumic beats radial wall stress is constant and cyclic flow impediment is due to the varying contribution of left ventricular pressure only (Fig. 4). This explains the two peaks in the intramyocardial pressure-signal in Fig. 4: the first one is related to the rise in left ventricular pressure, while the second one arises from the rise in radial wall stress, related to the decrease in left ventricular volume.
Another experimental observation is that NFA is about proportionally related to LV contractility, expressed by maximum elastance, NFA being about zero when contractility was about zero.17 This observation is replicated by our model, in which NFA changes about proportionally with the contractility parameter c, irrespective of the volume setting (Fig. 5). For low contractilities, minimum coronary inflow approaches the theoretical value of 8.3 ml s−1 100 g−1 of tissue, obtained from the coronary perfusion pressure of 10 kPa, the total coronary resistance of 6 × 108 Pa s m−3, and a wall volume of 200 g.
Finally, it has been observed that intramyocardial pressure may exceed left ventricular pressure in low afterload beats.18 This is also the case in our model (Fig. 4, right panel), and explained again from the contribution of radial wall stress at the low ventricular volumes associated with the low LV ejection pressures.
Sensitivity Analysis
Sensitivity of NFA to the radial stiffness parameter cr0 in isovolumic beats is low (Fig. 6, top left). This can be best understood from Eq. (17), which shows that only the constant level of radial wall stress is affected by changing cr0, while the variation of left ventricular pressure, and thus of intramyocardial pressure and arterial inflow, is unaffected. The increase in left ventricular pressure with decreasing stiffness is explained from Eq. (7), which shows that fiber stress is converted into both LV pressure and radial wall stress. With decreasing radial stiffness, an increasing part of fiber stress is converted into LV pressure. In the extreme case of zero radial stiffness, minimum left ventricular pressure is about 14 kPa, which is higher than the pressure measured in the experiment (Fig. 6).15
Variation of NFA with radial stiffness is more prominent in isobaric beats at low LV pressure (Fig. 6, top right). An increase of radial stiffness causes a more rapid increase of radial wall stress with decreasing volume below the equilibrium volume. Thus the pressure at which the contribution of radial wall stress to intramyocardial pressure takes over from the contribution of ventricular pressure is increased (17), and pulsatility of coronary inflow is maintained. At zero radial stiffness, intramyocardial pressure is determined fully by left ventricular pressure, explaining loss of pulsatility of coronary flow with decreasing ejection pressure, in disagreement with experimental findings.15
Sensitivity of NFA to settings of the active stress model (Fig. 6) is low, as far as the velocity and time dependence is concerned. NFA was more affected by increasing the stress-free sarcomere length from 1.5 to 1.6 μm. In fact this variation has the same effect as decreasing contractility at low sarcomere lengths. Thus, in this case the decrease of NFA is explained from the decrease in variation of left ventricular pressure, which is reflected in a decreased variation of intramyocardial pressure.
The increase of NFA with increasing myocardial compliance (Fig. 6), both in isovolumic and isobaric beats, is explained from the fact that, at the same variation of intramyocardial pressure, the volume change of the myocardial bed increases. Hence the pulsatility of arterial inflow is increased as well. A decrease of myocardial compliance has the opposite effect.
The first order effect of a variation of coronary resistance is a change in both the average and pulsatile component of coronary flow, as was illustrated already in Fig. 3. In this approximation, the relative changes in average and pulsatile flow component are equal, causing NFA to remain unaffected. However, since coronary compliance is kept constant, the relative contribution of flow related to volume change of the coronary bed becomes less when decreasing coronary resistance, causing the decrease of NFA, observed in Fig. 6. Increasing coronary resistance has the opposite effect.
Relation with Other Models
In comparison to the waterfall model9 and the intramyocardial pump model,1,2,6,22 our model is more advanced in its description of intramyocardial pressure, adding the effect of radial wall stress. Radial wall stress becomes important only below the zero-pressure volume of the passive ventricle. Thus, the early models still are applicable in normal physiological conditions, in which ventricular volume is higher than this zero-pressure volume during the major part of the cardiac cycle.
In comparison to the models by Beyar et al.5,29,30 our model is simpler, emphasizing primary interactions, at the cost of information on transmural variation of coronary flow and long-term exchange of fluid between the coronary vessels and the interstitium. However, the reduced complexity yields increased insight into primary determinants of coronary flow impediment.
Main limitation of our model with respect to the model presented by Vis et al.,26,27 lies in neglecting the direct contribution of tissue stress to the extravascular pressure and effective compliance of the coronary vessel. The approach of Vis et al. requires a detailed analysis of the equilibrium between the pressure in a cavity in the LV wall, and the stress in the surrounding tissue. However, such an analysis would compromise the simplicity, that we aim for in this study.
Conclusion
In conclusion, a mathematical model of the interaction between coronary flow and cardiac mechanics is presented, with a limited number of model parameters. The model replicates the experimental observations, that the phasic character of coronary inflow is virtually independent of maximum left ventricular pressure, that the amplitude of the coronary flow signal depends linearly on cardiac contractility, and that intramyocardial pressure in the left ventricular wall may exceed left ventricular pressure. The normalized amplitude of coronary inflow is mainly determined by contractility, reflected in dependence of active fiber stress on sarcomere length, and maintained at low ventricular volumes by radial wall stress. The sensitivity of the NFA to myocardial coronary compliance and resistance, and to the relation between active fiber stress, time, and sarcomere shortening velocity is low.

intramyocardial pump
radial wall stress
ventricular mechanics
lumped parameter model
empty beating heart