1<br/>00:00:00,000 –> 00:00:01,407 2<br/>00:00:01,407 –> 00:00:03,740<br/>And I’m going to talk to you<br/>about pressure, resistance, 3<br/>00:00:03,740 –> 00:00:05,085<br/>and flow. 4<br/>00:00:05,085 –> 00:00:07,530<br/>We’re going to try to make<br/>sure you feel real comfortable 5<br/>00:00:07,530 –> 00:00:11,540<br/>with all three of these<br/>things by the time we’re done.
6<br/>00:00:11,540 –> 00:00:17,830<br/>So we start with the heart, and<br/>off of the heart is the aorta. 7<br/>00:00:17,830 –> 00:00:21,380<br/>This is the largest<br/>artery in the body. 8<br/>00:00:21,380 –> 00:00:23,207<br/>And this is one<br/>branch of the aorta.
9<br/>00:00:23,207 –> 00:00:24,790<br/>I didn’t draw a lot<br/>of the other ones. 10<br/>00:00:24,790 –> 00:00:26,830<br/>This is the brachial artery. 11<br/>00:00:26,830 –> 00:00:29,930<br/>And the blood is<br/>flowing from the aorta 12<br/>00:00:29,930 –> 00:00:31,534<br/>into the brachial artery. 13<br/>00:00:31,534 –> 00:00:33,950<br/>And let’s say that the blood<br/>is trying to make its way out 14<br/>00:00:33,950 –> 00:00:37,810<br/>to a fingertip, for example. 15<br/>00:00:37,810 –> 00:00:40,400<br/>So on its way out there, it<br/>makes its way to an arterial. 16<br/>00:00:40,400 –> 00:00:43,430 17<br/>00:00:43,430 –> 00:00:46,440<br/>And the blood continues<br/>flowing, and it 18<br/>00:00:46,440 –> 00:00:49,510<br/>goes into the capillary<br/>bed, and the vessels 19<br/>00:00:49,510 –> 00:00:52,600<br/>are too small to draw, so I<br/>just kind of do that thing.
20<br/>00:00:52,600 –> 00:00:56,200<br/>And it then goes<br/>into the other half 21<br/>00:00:56,200 –> 00:00:59,690<br/>of the capillary bed, where<br/>now the blood is deoxygenated. 22<br/>00:00:59,690 –> 00:01:01,850<br/>So I’m going to<br/>draw that as blue. 23<br/>00:01:01,850 –> 00:01:06,580<br/>That’s the part where now<br/>the blood is without oxygen. 24<br/>00:01:06,580 –> 00:01:10,130<br/>And then it continues<br/>to go and get collected 25<br/>00:01:10,130 –> 00:01:15,040<br/>into a venule, which sounds a<br/>little bit like the arterial 26<br/>00:01:15,040 –> 00:01:16,800<br/>on the other side, right? 27<br/>00:01:16,800 –> 00:01:19,480<br/>And we’ve got a vein over here. 28<br/>00:01:19,480 –> 00:01:22,300<br/>And then finally, the<br/>blood gets collected 29<br/>00:01:22,300 –> 00:01:26,480<br/>in a large vein<br/>called the vena cava.
30<br/>00:01:26,480 –> 00:01:28,690<br/>And there are actually<br/>two vena cavas, 31<br/>00:01:28,690 –> 00:01:30,900<br/>so this’ll be the<br/>superior vena cava. 32<br/>00:01:30,900 –> 00:01:33,950<br/>There’s also an<br/>inferior vena cava. 33<br/>00:01:33,950 –> 00:01:39,440<br/>And the blood flow through this<br/>half is, as you would guess, 34<br/>00:01:39,440 –> 00:01:41,240<br/>continues to go around. 35<br/>00:01:41,240 –> 00:01:44,610<br/>And if I was to try to figure<br/>out the pressures, the blood 36<br/>00:01:44,610 –> 00:01:48,377<br/>pressures, at different<br/>points along the system, 37<br/>00:01:48,377 –> 00:01:49,960<br/>I’m going to choose<br/>some points that I 38<br/>00:01:49,960 –> 00:01:51,930<br/>think would be<br/>interesting ones to check. 39<br/>00:01:51,930 –> 00:01:53,920<br/>So it would be good<br/>probably to check 40<br/>00:01:53,920 –> 00:01:56,130<br/>what the pressure is<br/>right at the beginning.
41<br/>00:01:56,130 –> 00:01:58,170<br/>And then maybe at all<br/>the branch points. 42<br/>00:01:58,170 –> 00:02:01,600<br/>So what the pressure is as<br/>the blood goes from the aorta 43<br/>00:02:01,600 –> 00:02:03,270<br/>to the brachial artery. 44<br/>00:02:03,270 –> 00:02:06,940<br/>Maybe as it ends the brachial<br/>artery and enters the arterial. 45<br/>00:02:06,940 –> 00:02:09,729<br/>Maybe the beginning and<br/>the end of the capillaries. 46<br/>00:02:09,729 –> 00:02:15,950<br/>Also from the venue to a vein,<br/>and also, wrapping it up, 47<br/>00:02:15,950 –> 00:02:18,520<br/>what the pressure is at the end. 48<br/>00:02:18,520 –> 00:02:21,190<br/>Now, these numbers,<br/>or these pressures, 49<br/>00:02:21,190 –> 00:02:22,850<br/>can be represented<br/>as numbers, right? 50<br/>00:02:22,850 –> 00:02:25,680<br/>Like what is the<br/>millimeters of mercury 51<br/>00:02:25,680 –> 00:02:28,080<br/>that the blood is<br/>exerting on the wall 52<br/>00:02:28,080 –> 00:02:31,009<br/>at that particular<br/>point in the system? 53<br/>00:02:31,009 –> 00:02:32,550<br/>And earlier, we<br/>talked about systolic 54<br/>00:02:32,550 –> 00:02:35,352<br/>versus diastolic<br/>pressure, and there we 55<br/>00:02:35,352 –> 00:02:37,060<br/>wanted to use two<br/>numbers, because that’s 56<br/>00:02:37,060 –> 00:02:40,830<br/>kind of the range, the upper<br/>and the lower range of pressure.
57<br/>00:02:40,830 –> 00:02:43,260<br/>But now I’m going to<br/>do it with one number. 58<br/>00:02:43,260 –> 00:02:45,470<br/>And the reason I’m using<br/>one number instead of two, 59<br/>00:02:45,470 –> 00:02:49,260<br/>is that this is the<br/>average pressure over time. 60<br/>00:02:49,260 –> 00:02:53,202<br/>So the average pressure over<br/>time, for me– keep in mind 61<br/>00:02:53,202 –> 00:02:54,660<br/>my blood pressure<br/>is pretty normal.
62<br/>00:02:54,660 –> 00:02:57,920<br/>It’s somewhere around<br/>120 over 80 in my arm. 63<br/>00:02:57,920 –> 00:03:01,730<br/>So the average pressure in<br/>the aorta kind of coming out 64<br/>00:03:01,730 –> 00:03:06,810<br/>would be somewhere around 95,<br/>and in the artery in the arm, 65<br/>00:03:06,810 –> 00:03:08,144<br/>probably somewhere around 90. 66<br/>00:03:08,144 –> 00:03:10,560<br/>Again, that’s what you would<br/>expect– somewhere between 80 67<br/>00:03:10,560 –> 00:03:11,950<br/>and 120. 68<br/>00:03:11,950 –> 00:03:14,610<br/>So 90 is the<br/>average, because it’s 69<br/>00:03:14,610 –> 00:03:17,880<br/>going to be not exactly<br/>100, because remember, it’s 70<br/>00:03:17,880 –> 00:03:22,420<br/>spending more time in diastole<br/>and relaxation than in systole.
71<br/>00:03:22,420 –> 00:03:25,200<br/>So it’s going to be closer<br/>to 80 for that reason. 72<br/>00:03:25,200 –> 00:03:27,900<br/>And then if you check the<br/>pressure over here by this x, 73<br/>00:03:27,900 –> 00:03:30,450<br/>it’d probably be something<br/>like, let’s say 80. 74<br/>00:03:30,450 –> 00:03:32,750<br/>And then as you<br/>cross the arterial, 75<br/>00:03:32,750 –> 00:03:34,700<br/>the pressure falls dramatically. 76<br/>00:03:34,700 –> 00:03:36,630<br/>So it’s somewhere closer to 30. 77<br/>00:03:36,630 –> 00:03:38,510<br/>And then here it’s about 20.
78<br/>00:03:38,510 –> 00:03:39,720<br/>Here it’s about 15. 79<br/>00:03:39,720 –> 00:03:42,280<br/>Let’s say 10 over here. 80<br/>00:03:42,280 –> 00:03:46,120<br/>And then at the very end, it’s<br/>going to be close to a 5 or so. 81<br/>00:03:46,120 –> 00:03:46,750<br/>So here. 82<br/>00:03:46,750 –> 00:03:47,958<br/>Let me just write that again.
83<br/>00:03:47,958 –> 00:03:49,140<br/>10 and 5. 84<br/>00:03:49,140 –> 00:03:51,954<br/>And the units here are<br/>millimeters of mercury. 85<br/>00:03:51,954 –> 00:03:53,120<br/>So I should just write that. 86<br/>00:03:53,120 –> 00:03:57,180<br/>Pressure in<br/>millimeters of mercury. 87<br/>00:03:57,180 –> 00:03:58,930<br/>That’s the units that<br/>we’re talking about. 88<br/>00:03:58,930 –> 00:04:02,830<br/>So the pressure falls<br/>dramatically, right? 89<br/>00:04:02,830 –> 00:04:05,310<br/>So from 95 all the way<br/>to five, and the heart 90<br/>00:04:05,310 –> 00:04:09,150<br/>is a pump, so it’s going to<br/>instill a lot of pressure 91<br/>00:04:09,150 –> 00:04:11,770<br/>in that blood again and<br/>pump it around and around.
92<br/>00:04:11,770 –> 00:04:15,710<br/>And that’s what keeps the<br/>blood flowing in one direction. 93<br/>00:04:15,710 –> 00:04:18,040<br/>So now let me ask<br/>you a question. 94<br/>00:04:18,040 –> 00:04:19,940<br/>Let’s see if we can<br/>figure this out. 95<br/>00:04:19,940 –> 00:04:23,420<br/>Let’s see if we can figure<br/>out what the resistance is 96<br/>00:04:23,420 –> 00:04:26,790<br/>in all of the vessels<br/>in our body combined.
97<br/>00:04:26,790 –> 00:04:28,800<br/>So we talked about<br/>resistance before, 98<br/>00:04:28,800 –> 00:04:30,460<br/>but now I want to<br/>pose this question. 99<br/>00:04:30,460 –> 00:04:31,626<br/>See if we can figure it out. 100<br/>00:04:31,626 –> 00:04:34,930<br/>So what is total<br/>body resistance? 101<br/>00:04:34,930 –> 00:04:37,670<br/>And that’s really<br/>the key question 102<br/>00:04:37,670 –> 00:04:40,660<br/>I want to try to<br/>figure out with you. 103<br/>00:04:40,660 –> 00:04:44,000<br/>We know that there is some<br/>relationship between radius 104<br/>00:04:44,000 –> 00:04:45,959<br/>and resistance, and we<br/>talked about vessels 105<br/>00:04:45,959 –> 00:04:47,250<br/>and tubes and things like that. 106<br/>00:04:47,250 –> 00:04:51,250<br/>But let’s really figure this out<br/>and make this a little bit more 107<br/>00:04:51,250 –> 00:04:53,330<br/>intuitive for us.
108<br/>00:04:53,330 –> 00:04:56,016<br/>So to do that, let’s<br/>start with an equation. 109<br/>00:04:56,016 –> 00:04:57,390<br/>And this equation<br/>is really going 110<br/>00:04:57,390 –> 00:05:00,550<br/>to walk us through this puzzle. 111<br/>00:05:00,550 –> 00:05:05,960<br/>So we’ve got pressure, P,<br/>equals Q times R.
Really easy 112<br/>00:05:05,960 –> 00:05:08,580<br/>to remember, because<br/>the letters follow 113<br/>00:05:08,580 –> 00:05:10,060<br/>each other in the alphabet. 114<br/>00:05:10,060 –> 00:05:12,230<br/>And here actually, instead<br/>of P, let me put delta 115<br/>00:05:12,230 –> 00:05:14,860<br/>P, which is really<br/>change in pressure. 116<br/>00:05:14,860 –> 00:05:19,250<br/>So this is change in pressure. 117<br/>00:05:19,250 –> 00:05:22,110<br/>And a little doodle<br/>that I always 118<br/>00:05:22,110 –> 00:05:25,240<br/>keep in my mind to remember<br/>what the heck that means 119<br/>00:05:25,240 –> 00:05:30,040<br/>is if you have a little tube,<br/>the pressure at the beginning– 120<br/>00:05:30,040 –> 00:05:33,670<br/>let me say start;<br/>S is for start– 121<br/>00:05:33,670 –> 00:05:38,220<br/>and the pressure at the end can<br/>be subtracted from one another.
122<br/>00:05:38,220 –> 00:05:43,700<br/>And that gives you PS<br/>minus PE equals delta 123<br/>00:05:43,700 –> 00:05:47,510<br/>P. The change in pressure<br/>is really the change 124<br/>00:05:47,510 –> 00:05:50,440<br/>from one part of tube<br/>the end of the tube. 125<br/>00:05:50,440 –> 00:05:52,790<br/>And that’s the first<br/>part of the equation. 126<br/>00:05:52,790 –> 00:05:55,660<br/>So next we’ve got<br/>Q. So what is Q? 127<br/>00:05:55,660 –> 00:06:00,970<br/>This is flow, and more<br/>specifically it’s blood flow.
128<br/>00:06:00,970 –> 00:06:06,600<br/>And this can be thought of<br/>in terms of a volume of blood 129<br/>00:06:06,600 –> 00:06:07,940<br/>over time. 130<br/>00:06:07,940 –> 00:06:09,500<br/>So let’s say minutes. 131<br/>00:06:09,500 –> 00:06:12,720<br/>So how much volume–<br/>how many liters of blood 132<br/>00:06:12,720 –> 00:06:14,935<br/>are flowing in a minute? 133<br/>00:06:14,935 –> 00:06:15,560<br/>Or two minutes? 134<br/>00:06:15,560 –> 00:06:18,020<br/>Or whatever number of<br/>minutes you decide? 135<br/>00:06:18,020 –> 00:06:21,055<br/>And that’s kind of a hard<br/>thing to figure out actually.
136<br/>00:06:21,055 –> 00:06:27,050<br/>But what we can figure<br/>out is that Q, the flow, 137<br/>00:06:27,050 –> 00:06:32,650<br/>will equal the stroke<br/>volume, and I’ll 138<br/>00:06:32,650 –> 00:06:34,850<br/>tell you what this is<br/>just after I write it. 139<br/>00:06:34,850 –> 00:06:38,010<br/>The stroke volume<br/>times the heart rate. 140<br/>00:06:38,010 –> 00:06:42,430<br/>So what that means<br/>is that basically, 141<br/>00:06:42,430 –> 00:06:46,410<br/>if you can know how much<br/>blood is in each heartbeat– 142<br/>00:06:46,410 –> 00:06:52,130<br/>so if you know the<br/>volume per heartbeat– 143<br/>00:06:52,130 –> 00:06:56,650<br/>and if you know how many<br/>beats there are per minute, 144<br/>00:06:56,650 –> 00:07:00,080<br/>then you can actually figure out<br/>the volume per minute, right? 145<br/>00:07:00,080 –> 00:07:02,830<br/>Because the beats would<br/>just cancel each other out.
146<br/>00:07:02,830 –> 00:07:05,840<br/>And it just turns<br/>out, it happens to be, 147<br/>00:07:05,840 –> 00:07:09,110<br/>that I’m about 70 kilos. 148<br/>00:07:09,110 –> 00:07:11,620<br/>That’s me. 149<br/>00:07:11,620 –> 00:07:14,000<br/>I’m 70 kilos. 150<br/>00:07:14,000 –> 00:07:17,670<br/>And for a 70 kilogram<br/>person, the stroke volume 151<br/>00:07:17,670 –> 00:07:20,870<br/>is about 70 milliliters.
152<br/>00:07:20,870 –> 00:07:26,500<br/>So for a 70 kilo person, you<br/>can expect about 70 milliliters 153<br/>00:07:26,500 –> 00:07:29,390<br/>per beat. 154<br/>00:07:29,390 –> 00:07:32,180<br/>And as I write this,<br/>let’s say my heart 155<br/>00:07:32,180 –> 00:07:34,860<br/>rate is about 70<br/>beats per minute. 156<br/>00:07:34,860 –> 00:07:40,110<br/>I feel pretty calm, and<br/>so it’s not too fast. 157<br/>00:07:40,110 –> 00:07:42,410<br/>So the beats cancel<br/>as we said, and I’m 158<br/>00:07:42,410 –> 00:07:46,290<br/>left with 70 milliliters<br/>times 70 per minute. 159<br/>00:07:46,290 –> 00:07:54,420<br/>So that’s about 4,900<br/>milliliters per minute. 160<br/>00:07:54,420 –> 00:07:58,900<br/>Or if I was to simplify,<br/>that’s a 5, let’s say about. 161<br/>00:07:58,900 –> 00:08:02,730<br/>So the flow is about<br/>5 liters per minute.
162<br/>00:08:02,730 –> 00:08:06,130<br/>So I figured out the blood<br/>flow, and that was simply 163<br/>00:08:06,130 –> 00:08:07,960<br/>because I happen<br/>to know my weight, 164<br/>00:08:07,960 –> 00:08:10,820<br/>and my weight tells<br/>me the stroke volume. 165<br/>00:08:10,820 –> 00:08:13,530<br/>And I know that there’s<br/>a change in pressure. 166<br/>00:08:13,530 –> 00:08:15,450<br/>We’ve got to figure<br/>that out soon. 167<br/>00:08:15,450 –> 00:08:20,200<br/>And lastly, this last thing<br/>over here is resistance. 168<br/>00:08:20,200 –> 00:08:22,060<br/>And know I’ve said it before. 169<br/>00:08:22,060 –> 00:08:24,150<br/>I just want to point<br/>out to you again, 170<br/>00:08:24,150 –> 00:08:27,320<br/>the resistance is going to<br/>be proportional to 1 over R 171<br/>00:08:27,320 –> 00:08:28,490<br/>to the fourth.
172<br/>00:08:28,490 –> 00:08:33,309<br/>And so just remember that<br/>this is an important issue. 173<br/>00:08:33,309 –> 00:08:35,049<br/>R is radius. 174<br/>00:08:35,049 –> 00:08:37,340<br/>And that’s the<br/>radius of the vessel. 175<br/>00:08:37,340 –> 00:08:39,730<br/>So let’s figure<br/>out this equation.
176<br/>00:08:39,730 –> 00:08:42,289<br/>Let’s figure out the<br/>variables in this equation 177<br/>00:08:42,289 –> 00:08:45,450<br/>and how it’s going to help<br/>us solve the question I asked 178<br/>00:08:45,450 –> 00:08:48,840<br/>you– what is the<br/>total body resistance? 179<br/>00:08:48,840 –> 00:08:49,340<br/>OK. 180<br/>00:08:49,340 –> 00:08:51,500<br/>So if I have to figure out<br/>total body resistance– 181<br/>00:08:51,500 –> 00:08:57,530<br/>let me clear out the board–<br/>I’ve got, let’s say, the heart.
182<br/>00:08:57,530 –> 00:08:59,440<br/>I like to do the heart in red. 183<br/>00:08:59,440 –> 00:09:02,640<br/>And it’s pumping<br/>blood at my aorta. 184<br/>00:09:02,640 –> 00:09:05,750<br/>So blood is going<br/>out of the aorta. 185<br/>00:09:05,750 –> 00:09:09,150<br/>And then it’s going<br/>and branching here. 186<br/>00:09:09,150 –> 00:09:13,200 187<br/>00:09:13,200 –> 00:09:14,984<br/>And then it’s going<br/>to branch some more.
188<br/>00:09:14,984 –> 00:09:16,650<br/>And then it’s going<br/>to branch some more. 189<br/>00:09:16,650 –> 00:09:18,935<br/>And you can see<br/>where this is going. 190<br/>00:09:18,935 –> 00:09:20,310<br/>It’s going to keep branching. 191<br/>00:09:20,310 –> 00:09:25,070<br/>And eventually every branch kind<br/>of collects on the venous side. 192<br/>00:09:25,070 –> 00:09:28,640<br/>All the blood is kind of<br/>filtering back in slowly 193<br/>00:09:28,640 –> 00:09:30,930<br/>into venules and veins.
194<br/>00:09:30,930 –> 00:09:33,360<br/>And finally into a vena cava. 195<br/>00:09:33,360 –> 00:09:37,506<br/>And I should really draw<br/>this going like that. 196<br/>00:09:37,506 –> 00:09:40,260<br/>The blood is going to go<br/>back into the vena cava. 197<br/>00:09:40,260 –> 00:09:41,750<br/>So that’s my system. 198<br/>00:09:41,750 –> 00:09:48,920<br/>And I got to figure out what the<br/>total body resistance is here. 199<br/>00:09:48,920 –> 00:09:52,160<br/>So if I have a system<br/>drawn out for myself, 200<br/>00:09:52,160 –> 00:09:56,460<br/>and I happen to know<br/>that here I said 95. 201<br/>00:09:56,460 –> 00:09:59,230<br/>And here I said<br/>the pressure was 5. 202<br/>00:09:59,230 –> 00:10:06,080<br/>Then delta P equals 95<br/>minus 5, which is 90.
203<br/>00:10:06,080 –> 00:10:11,570<br/>And I know that there are 5<br/>liters of blood flowing through 204<br/>00:10:11,570 –> 00:10:13,440<br/>per minute. 205<br/>00:10:13,440 –> 00:10:17,070<br/>And that was my<br/>Q. So I could say 206<br/>00:10:17,070 –> 00:10:23,920<br/>90 equals 5 liters per minute. 207<br/>00:10:23,920 –> 00:10:26,570<br/>Actually let me take<br/>a step back from that. 208<br/>00:10:26,570 –> 00:10:28,580<br/>Instead of 90, let<br/>me write the units. 209<br/>00:10:28,580 –> 00:10:34,230<br/>90 millimeters of mercury<br/>equals 5 liters per minute. 210<br/>00:10:34,230 –> 00:10:37,230<br/>That was my flow. 211<br/>00:10:37,230 –> 00:10:44,620<br/>That’s my Q. And I’ve<br/>got delta P here. 212<br/>00:10:44,620 –> 00:10:46,450<br/>And my resistance<br/>is the unknown. 213<br/>00:10:46,450 –> 00:10:48,700<br/>So I’ll just leave that as R.
214<br/>00:10:48,700 –> 00:10:51,290<br/>So let’s just solve<br/>for R. So I’ll 215<br/>00:10:51,290 –> 00:10:54,140<br/>move my flow to the other side. 216<br/>00:10:54,140 –> 00:11:01,850<br/>So R equals– I’ll put it here–<br/>90 divided by 5, which is 18. 217<br/>00:11:01,850 –> 00:11:03,500<br/>And the units are<br/>a little funky, 218<br/>00:11:03,500 –> 00:11:05,690<br/>but I’ll just write<br/>them out anyway.
219<br/>00:11:05,690 –> 00:11:13,200<br/>Millimeters of mercury times<br/>minutes divided by meters. 220<br/>00:11:13,200 –> 00:11:16,420<br/>So this is the answer<br/>to my question– 221<br/>00:11:16,420 –> 00:11:18,100<br/>what is the total<br/>body resistance? 222<br/>00:11:18,100 –> 00:11:19,680<br/>Well, we know what<br/>the pressures are 223<br/>00:11:19,680 –> 00:11:22,240<br/>at the beginning and<br/>end of our system. 224<br/>00:11:22,240 –> 00:11:26,710<br/>And we know that the flow has to<br/>be around 5 liters per minute, 225<br/>00:11:26,710 –> 00:11:30,520<br/>because that’s based on my<br/>weight and my heart rate. 226<br/>00:11:30,520 –> 00:11:33,430<br/>Therefore, the resistance<br/>must be 18 millimeters 227<br/>00:11:33,430 –> 00:11:36,590<br/>of mercury times<br/>minutes over liters.
228<br/>00:11:36,590 –> 00:11:38,750<br/>Whatever that set of<br/>units means to you. 229<br/>00:11:38,750 –> 00:11:40,459<br/>It’s kind of an abstract thing. 230<br/>00:11:40,459 –> 00:11:42,250<br/>But basically, I want<br/>to demonstrate to you 231<br/>00:11:42,250 –> 00:11:44,570<br/>that this powerful<br/>equation helps 232<br/>00:11:44,570 –> 00:11:47,280<br/>us solve for what<br/>would otherwise 233<br/>00:11:47,280 –> 00:11:50,470<br/>become a tricky<br/>problem to figure out.